There is a problem with the video.. you said in the end he used egyptian stadia he actually used the standard unit of measure of the time which was greek stadia. He had a 15% error not a few percentages like you said. This margin of error is still incredible because he assumed the earth was a perfect sphere (isaac newton was the first to suggest that earth is an oblate spheroid almost 2000 years later!!), the distance between the two cities was wrong by 81 km, the two cities where no at the same longitud by 3 degrees of difference and syene was actually 41 km away from parallel of the tropic of cancer (where sunlight reflects vertically). Taking all of this into account 15% erros is still amazing.
Unlike Eratosthenes, we live in modern day! Where we can take a hot air balloon to the stratosphere, and find that unaltered footage, captured without a fish eye/wide angle lens shows us undeniable truth; the horizon is flat in every direction for hundreds of miles. Spherical trigonometry predicts some 6000 feet of curvature at 100 miles, yet, in the stratosphere, where you can see for several hundred, this curvature is nonexistent...despite being told that the horizon at sea level "curves out of sight for the average viewer 6 ft in height at 3 miles distance". The 8 inches per mile squared formula is accurate within several inches up to 300 or so miles for the calculation of curvature. The truth is that this high altitude footage reveals what early aviators said throughout the 1800's, when most people still had inquisitive minds, thanks to the lack of digital propaganda being pushed down their throats daily; the horizon does not curve away and out of sight from the observer, as the convex hull of a sphere would. In fact, it rises to meet the eye level of the observer regardless of altitude, forming a rather concave shape relative to the observer. This is the exact OPPOSITE observation of a globe earth. Of course, this gets ignored as "refraction", which, in turn, is an erroneously applied theory that is manipulated to suit the arguments of both the deceiver and the hopelessly deceived, when the argument is convenient. Simply put, you are told that you're not seeing what you are seeing, because we *know* the Earth is a globe, never-mind what you see with your own two eyes. Wakey wakey Grason
@@I_dreamed_my_name_was_Brandon You're a flat-Earther, and I'm curious. If we live on the top of a flat disk, what's on the underside? If one would go up to the edge of the disk and jump off, what would happen? Can one go from one side of the disk to the other side? Are you also a conspiracy theorist?
The horizon is 'apparent'. The distance not only depends on observer height but also obstacles and weather conditions. That's why some days you can see much further than other days. @@marcg1686
I always wondered how people knew about the Earth and space before we could see the Earth FROM space, and apparently ASTROLOGY was one of the early ideas that lead to our knowledge of geography as well as astronomy!!! People who could "read" the stars were able to figure out things about the positioning of the Earth at various times of the year, because people were more in touch with seasons and natural time in agrarian and tribal societies. This video showed me the importance of geometry in that puzzle, it makes total sense too, because they observed patterns in nature, and Eratosthenes just applied that pattern on a global scale, which is extremely abstract thinking, but at the same time is a usage of tools and theories prominent in his time period. Pretty amazing stuff!
Furthermore, that 23.5 degrees north is the Tropic of Cancer whereas the 23.5 degrees south is the Tropic of Capricorn. The Sun can be directly overhead between 23.5 north and south on the longest day of the year - the Summer Solstice. All due to the 23.5 declination (tilt) of Earth on its axis. Combine that with the rotation rate of Earth, the time to orbit the Sun and the Earth's elliptical orbit around the Sun and we can build a an accurate sundial including the 'equation of time'. Similarly, given shadow length at solar noon on a given day of the year, you want work out your latitude. All verifiable.
Regarding 4:34, the one day during the year that the sun is directly overhead at noon along the Tropic of Cancer is on the Summer Solstice which typically has been on June 21 or June 20.
@Berialavrenti Well, Augustine does come to mind as an early church father who originally came from an arab region, but I don't think I would agree that "most" of the early church fathers were arabs. As for Eurpoe stealing science, I think you overstate your case. Newton was a European Christian. Einstein was a European Jew. They just thought up some good physics - didn't steal it from anyone. Gauss was German. Pascal was French. Archimedes was Greek, as was Euclid and Pythagoras...
There’s one thing I‘m having a problem with! 🤔 How could he know the exact time of midday (high noon) in Assuan, when being in Alexandria, measuring the angle of the poles shadow? Any response appreciated! 🙏🏼
He was able to know because the towns are pretty close to the same longitude. That is, they are nearly directly north and south of each other. So high noon in one location would occur at the same time as high noon in the other. My understanding is that Eratosthenes was aware of this when he made the measurement.
The human brain is able to figure out things like this using the tools of the time. GPS, surveyor tools etc. make this so much easier, but Eratosthenes used deductive reasoning and his knowledge of geometry.
My only question is what kind of clock did he have available to him so that he would know it was noon in both places at the same moment. I would be tempted to think that time was locally calibrated by, say, a sundial, so that noon is always when the sun is directly overhead, more or less.
He didn't necessarily need a clock. He just needed to know that the sun was at the highest point in the sky. This would happen at the same time in both cities only if they are at the same longitude. They are not exactly, but are pretty close.
John Pavlou: Eratosthenes knowsthat the two Citys are not on the same latitude. This means a calculation error he cant solve. The distance is little bit longer. From this the circumference of the earth becomes too big. A small inaccuracy for this time. He should have to take the noon time to the second place! This problem was solved later. ;)
I had the same trouble understanding this. That the two cities are separated by latitude, but on close to the same longitude was key. When you think of replicating this experiment, there are so many things that could go wrong. I'm still trying to decide how much luck was involved. Friggin remarkable though. Measurements from two cities separated by longitudes, and the sun dial readings would be taken at different real times, but high noon on the sun dial. And the stick shadow would have been Nil. Luckily magnetic North was roughly "up" for the Earth in relation to the sun. Okay done babbling. Thx.
In the calculation doesn't matter whether we circle the light source or it circles us I suppose. THe Greeks had a pretty good idea the earth was round. Took a while for the idea to spread but they nknew
no, the majority of greeks thought the world was flat, just like every other ancient society. The only ones who though it could be a globe were hermits and mystics
Actually, Aswan is 24.1 degrees therefore not exactly on the Tropic of Cancer. Also, Alexandria and Aswan are not exactly on the same meridian about 3 degrees off. Still very remarkable for the time.
My guy I was having an argument with my boyfriend about how Eratosthenes knew that the angle of the shadow the stick created at Alexandria determined that the two cities must be 7.2 degrees away from each other because he said that the relationship of the interior angles didn't matter to the equation, well then how would Eratosthenes have known that sticking the pole at the ground and measuring its shadow would produce the angle between the two cities if he had no knowledge of the relationship of angles created by a transversal through two parallel lines? Your explanation at around 6:12 proved me right. Thank you!
I think that noon is when the sun is on the highest point. That probably means that the shadow of a stick that is vertical to the ground is the smallest that it could ever be any other hour of the same day.
@@madrandomize5115 If the two different locations measured it in the way that you suggest, neither stick would have a shadow. It seems that you need the locations to talk via phone or walky-talky to synchronize measurements. Of course, no such technology existed.
@@oscarg7460 I quote from Wikipedia. "Solar noon (informally high noon and formally local apparent solar noon)[3] is the moment when the Sun contacts the observer's meridian, reaching its highest position above the horizon on that day ("Sun transit time") and leaving the shortest shadow." So on that particular day Eratosthenes could have measured the smallest shadow of the day (since you can easily mark it on the ground) . The only real problem on the matter is the length between 2 cities and for them to be able to synchronize on the date.
@@oscarg7460 "If the two different locations measured it in the way that you suggest, neither stick would have a shadow. " The sun is never directly overhead Alexandria, so how would the stick/pillar in Alexandria _not_ have a shadow?
That was super, thanks! I'm curious now, how did people measure large distances, like the 5,000 stadia between Alexandria and Syene, in the first place? Did they do it manually, by counting paces or some such method? :D :D
I think they had surveyors, if you know a sticks hight, and walk farawar from the 1 person to place b, and use a bit of string to measure how high the stick is now, you could triangulate that out
I will restate my confusion. The 2 measurements have to be synchronized, right? They need to take place simultaneously. But how did they know they were measuring simultaneously? I appreciate for one spot the answer is that the sun was directly overhead. But how did they know to measure the other spot simultaneously? It's not like they had stop watches.
Ah, I understand your question. The assumption is that the sun would be directly overhead at the same time in both cities. This would only be the case if the cities were at the same longitude, or in other words, if they were aligned directly north and south of each other. They aren't *exactly* aligned north-south, but are actually pretty close, close enough for the method to give a good result. This arrangement arose from the fact that Nile happens to flow south to north.
@@derekowens Again, I don't understand how this works. Say that your are in spot B, the place where the sun is NOT directly overhead at noon. When do you say, "NOW" to measure the length of the stick's shadow? I know it's noon, but how does the person know it's the exact same noon as spot A?
@@oscarg7460 Because in both places, noon will be the moment the sun is at the highest point in the sky. They could determine that fairly accurately without clocks, by using a sundial or similar mechanism. That would be the same moment in both cities, as long as the cities were aligned north-south, which they basically are.
@@derekowens AAHH! Noon is the point when the sun is the highest point in the sky and they were equipped to figure that out. You don't know how long this has bugged me. Years? Thank you, much. You are generous with your knowledge.
Funny thing: over the past few years, I've mentioned Eratosthenes on many occasions. I was ridiculed, heckled, mocked, blocked, and trolled every time. 🙄 It's unbelievable how arrogant and ignorant society (especially via "social media") people have become. They don't even know who Carl Sagan is. It's fuggin' embarrassing. 🤮
@Berialavrenti Just cause he was against the privileges the greeks had dosent make him a non-greek. Just means he saw humans as equals, meaning just cause your greek dosent make you better then the other guy.
He did not measure the circumference of the earth. He calculated it. Seeing that the Sun and the Moon are spherical, it's not unreasonable to assume that the earth is likewise spherical.
What about the assumption that sunlight rays are parallel? How could he verify it? Did he have a reliable estimate of the distance of the Sun from Earth? As far they knew at that time, the Sun could be a very small ball very close to the Earth.
Cornell institute said he got less than 1% accuracy. And they use different numbers. Some one is wrong badly here. Even Wikipedia have 3th set of numbers. Yet again Neil deGrass Tyson told 4th story Michalle Thaller have, hers story 5th edition... How's that even possible? Crap i forgot Carl Sagan.. As 6th...
One reason is because nobody knows for sure how long a stadia was. Considering the technology at the time, he came very close. The stories all use the same methodology and locations.
What are you suggesting? That the earth is not round? No, all these calculations prove that it is. All that the different results prove is that the calculations all differ by small amounts. Often these are down to people using different measurements of their day. The answer is the same - the earth is round and certainly not flat.
The calculation can be performed without the clever geometry. You simply move the stick which is producing the shadow at Alexandria until no shadow is produced. Measure the angle between the stick that cast a shadow and the same stick that was moved to produce no shadow. You get 7 degrees. You don't have to measure the lengths of shadows using this technique, and you don't need the clever geometry either. I suspect this is how he actually did it but we will probably never know.
It is a _little_ more complex than that. ;) You'd still need a reference point of which you *know* the sun to be 90° overhead at that time. If you don't have that - it won't work. Example: let's say he was in Alexandria - and measured the angle to be 7° to true vertical ... then what? ;) You now can't do this calculation, because you are now missing the distance to the point where the sun is 90° overhead. All the information you have is: where you are right now, the angle to true vertical is 7° At another place it will be different - of course. To choose an extreme example: do this in Madrid - or Paris ... Now the angle to true vertical is much larger. Then what? ;) You need the distance to the place where the sun is indeed at true vertical. Cheers!
The only problem is before the stick reached zero degrees over 800km must be moved. No way anyone can move that distance on foot instantly. If more than a few seconds pass the Sun will noticeably shift. 800km there be no sun in the sky.
A wierzący w kulistą Ziemie opierają się na założeniach Eratostenesa o równoległości promieni słonecznych jednocześnie na innych rysunkach krzyżują te promienie od Słońca by nakłamać o przyczynie małego cienia Księżyca w czasie zaćmienia Słońca, bo ten cień ma średnicę tylko ok. 100 km, a cień obiektu zawsze jest większy od swojego oryginału, czyli Księżyc ma rzeczywistą średnicę tylko 50 km. czcams.com/video/QOREOUU4r7o/video.html
How did he know the radius of the earth? Just because the lines converge at a said point doesnt mean that is the center of the earth? This whole thing is assuming he already knew the radius!
This is assuming that the surface is equal across, having zero graduation of land mass aka elevation that we say doesnt need to be taken into account for. Also assuming that the sun is truly as far as it is...
I was trying to say it in a more hypothetical way, but the sticks would be pointing oppoiste to gravity, and the centre of gravity is the centre of the earth
MultiGazman No radius not required. Just the fraction of a circle, and the distance between cities. Rough approximation? yes. But not off by a magnitude. And the distance was measured by walking and counting steps.
I beleive the Earth to be big and round but I don't get how Eratosthenes knew that the sun was big and far. If the Earth was flat and sun was small and close yet be directly above the well it would cast no shadow in the well yet make the shadow on the stick.
Look even further back, people like Aristarchus had done other measurements involving the moon, that indicated the sun to be far away (their estimate for the distance was not very accurate but still indicated it to be very far) As for getting the same results assume a Flat Earth, sure you could use just two points of measurements, assume a flat Earth and a close and small sun,... *but* once you use more than two points, it falls apart completely. That's why in science if your initial results can fit more than one assumption, you have to keep testing and checking until one of them fails.
What people don't seem to know is classical greeks proved the earth to be round 500 bc, but it took judeo christian 1000 years more to figure this out.
@@Graymenn Of course most Greeks wouldn't believe or understand it. Same as today most people would be at a loss to explain how the 100-year-old radio works. The round earth knowledge(then) is in the same vein as today's CERN hydro Collider, or the ISS(international space station). You would be lucky to find 100 people in the world that can explain it in full.
From what I understand, he was able to do this because the two towns are pretty close to being lined up north to south. Because they are at the same longitude, the moment of noon, the moment the sun is its highest point in the sky, occurs at the same time in both cities.
@@derekowens see this is where I get stuck. Because that is still kind of a vague measurement. It seems to me that someone would want to do something that is replicable and verifiable and to me that means that you can accurately determine what quote “noon“ is for you in your location. And that would be the moment when a vertical and straight shaft which you could create, which cast no shadow. So I still don’t know how he knew it was noon time at Syrene while he was in Alexandria.
@@JohnnyArtPavlou You will only get the "no shadow" condition when the sun is directly overhead, and you need to be close to the equator for that to happen. It simply won't happen in the northern latitudes. But you can still determine the moment of noon, at least approximately. That will be the moment that the sun is at its highest point in the sky, and at that moment the shadow will be at its shortest. The shadow at this moment doesn't change much from day to day, so you could mark the shadow at its shortest point one day, and then watch the shadow the next day as that moment approaches. It will be noon at that moment. And if the cities are aligned north to south, it will be noon in both places.
@@derekowens Yes, you’re right. I had to go over as many times in my mind. Because the vertical stick in Alexandria is acting as an imperfect gnomon. Because it doesn’t compensate for the elevation or position on the globe. And is the fact that it’s not compensating that gives the shadow that gives the number of degrees.
He didn't have to. It was already known that on the summer solstice (June 21st or 22nd), sunlight could reach the bottom of a deep well in Syene, so the Sun had to be directly overhead on that day. Eratosthenes just had to measure how much the Sun's position deviated from directly overhead (zenith) in Alexandria on the summer solstice. It didn't matter if that measurement happened many _years_ after the observation in Syene as long as both were done on the summer solstice.
The knew for hundreds of years the earth was round. If they didn't know the earth was round then obviously this experiment would fail. Ptolemic models work just as good though.
One small problem: An assumption is made the earth is spherical. A second assumption is made the sun's rays parallel. This is not what we obviously see every day. Use the same observation and calculate the distance of the sun from earth. This is so simple, and makes more sense. But no, we insist that the earth is a globe. Silliness.
Y'know you _can_ use the same observation, and if you assume a flat Earth, you can assume the sun to be small and just a few thousand miles up. Now, where you run into a whole heap of trouble is when you use more than two points... cos you can fool yourself into thinking you have a solid figure for the location of the sun, if you just use two points and plot where the lines of observation intersect. If you add a third point, it still agrees with a spheroid Earth, but you end up with 3 different heights and locations for the supposed small close sun. But you didn't bother to work that out did you? you just heard someone say you can make this work on a Flat Earth, and didn't bother being in any way rigourous before swallowing it as a good argument. It ain't. You go on insisting the earth ain't a globe. Tell you what... why don't you tell us where we should re-draw the lines of latitude? Cos on a flat Earth they would not be the same distance apart for every degree... If you're measuring the elevation of the sun at an equinox, on a flat Earth the distance between 0 and 1 degree North will be smaller than the distance between 1 and 2 and 89 - 90 would be much, much bigger, and then to make it worse, the problem would go the other direction when measuring the angle to the pole star at night. 90-89 would be small, and 45-44 would be a larger distance. How would you redraw the lines of latitude there buddy? And how did those ancient sailors ever manage to determine how far north they were by using the elevation of the pole star, if the Earth wasn't a globe? On a flat Earth, there would not be a consistent 69 mile (60 nautical mile) interval for each 1 degree of latitude... But y'know people who've never had to find their way home without a smart phone aren't so likely to think about that, but they sure seem eager to act like they know more than people who _did_ have to work things out for themselves.
This literally does not prove the Earth is round. This can also prove the sun is smaller, closer, and revolves around us It works both ways if you just think about the 2 different models and not try to put one in the other box. Think...
Correct, this is not a proof that the earth is round. The Greeks and others already knew the earth was round by other means, such as seeing its curved shadow on the moon during a lunar eclipse. Based on already knowing the earth is round, this was an attempt to measure its size, and it was done remarkably well.
This experiment was not designed to prove that the Earth is round. If you reject the shape of the earth and feed the angles into a flat earth model, then you will get an arbitrary height for a small, close sun. However, if you add three or more observation points, you end up with multiple locations for the sun. The spheroid calculations give consistent results of 1 degree for 69 miles north or south. So, you couldn't have considered testing this with more than two points of observation, Marcos? _Think_ ...
+mousehead2000 Yes. Throughout history, nearly everyone has known that the earth was curved. The idea that people thought the earth was flat in the time of Columbus, or any other time for that matter, is more myth than history.
+mousehead2000 People knew the earth was curved, but they dont have the courage to prove it was curved, until....Eratosthenes. What if Eratosthenes did not travel to Syene, then is it possible for others to discover the planet was curved based on different spot on the planet. is it possible for someone else who living in Asia for example to be able to find a pond in which light reaches the bottom and eventually find out the earth was curved?
mousehead2000 How do you tell if the red apple is red? it might be green. If you look at a beautiful photo that have green grass, blue sky, blue sea. and then when you look to a same photo but this one has no color. however somehow you still seeing green grass and blue sea/sky. Why is that? Your brain filling in the gap. Do you see what your brain tell your to see or you see because what it is? so how do we prove something that is real?
No, the experiment proves option 1 due to the huge size of the earth discovered. Parallel rays are also proven, thus disproving a close-by sun. You also don't do this experiment in one place. You triangulate from other points for which the ONLY conclusion is that the Earth is a sphere. BTW, are you aware that Eratosthenes wasn't trying to prove a spherical Earth? He already knew that. He did this experiment to determine its size. The number of flat earthers who simply don't grasp what Eratosthenes was about reflects their limited ability to understand maths and science generally.
Your absolutely right, option two would make the Rays unparallel and give a similar effect. Nice Observation! However, a few hundred years before Aristotle had already shown the earth ot be round, leaving Option 1as the only possible explanation.
@COVID 1984 Sorry you can't truly prove positive in science except in mathematics. You need to use statistical analysis like chi-square, fisher, Bernoulli distribution, and hundreds of others depending on the data you are trying to model. However, Aristotle *showed* by three observations that the earth *must* be round. (1) Observing other celestial bodies, in particular the moon/Sun. (2) The Moon must be spherical by observing the shape of the terminator (the line between the part of the Moon in light and the part of the Moon in the dark) (3) the shadow cast by the earth on the moon during a lunar eclipse. QED ( "quod erat demonstrandum")
Some scientists are lucky that their results are correct. How can you prove the radius of the whole planet by measuring only 1/50th of the circumference. What if the rest of the circumference didn't have the same curvature? What if the planet was an asteroid like planet? He was lucky that Earth is very close to a sphere.
Yes, that's correct. If the earth were not roughly spherical, that would throw off the calculation. The ancient Greeks knew, though, that the earth was round, because they could see the shadow of the earth on the moon during an eclipse.
@@rlupara This is from Grade9Science.com: 1. Travelers discovered that they saw different constellations as they traveled north or south. 2. They noticed that ships sailing into view on the horizon had their masts gradually appear as they approached, and that the horizon became further away when viewed from higher elevations on hilltops or mountains. 3. They noticed the curved shadow of Earth on the Moon during lunar eclipses. There, three pieces of evidence, observed by the ancient Greeks, that let them to conclude that the earth is round. Keep working on it and you can reach the Grade8Sciecne level of thinking. Grade 8 is a good goal. You can do it. Reach grade 8, then keep going, and one day you will be able to contribute some useful thought to the world.
Derek Owens, Don't waste time on the cretin who calls himself/herself the dynamic athlete. I'm sure he/she is neither dynamic nor an athlete. He/she is a flat-head, and any words longer than two syllables, or sentences longer than four words elicit the same childish, head-in-the-sand response from that sort. I thought your video was well-produced and enjoyable. Don't waste time with flat-heads.
Modern terminology to aid in the clarity of the discussion. If the video had said "scrolls" that would have meant something different to many viewers. "Books" is a clearer concept and is more easily understandable.
Greeks earlier than Eratosthenes had been suggesting that the earth was round for quite a long time but had not come up with a method to make the observation. Eratosthenes great breakthrough was that he was the person who made that breakthrough. He held assumptions about a round Earth but this experiment was the proof needed. He knew from geometry that we divide a circle into 360 degrees. This is an arbitrary man-made construct. Once he knew the angle of the shadow at Alexandria was 7.2 degrees (1/50th of 360), he then only needed to know how far the stick in Alexandra was from Syrene. Other accounts suggest he paid a man to walk between the two cities and count the paces. In today's distance the result was about 800km. Multiply 800 x 50 and you get the distance around the Earths surface in km. The result tells the observer that the Earth is round, but not that it is a sphere. However if you do the same calculation from other points and they give the same answer you know that the circumference is the same in all directions which means the earth is a sphere.
@@zurviver_3747 Eratosthenes used degrees. The Greeks invented geometry. Our use of 360 degrees within a circle is one of their great mathematical constructs.
that because we are already familiar with it, and have debunked it. The experiment assumes a spherical earth and an extremely distant and large sun. The exact same results are explained easily with a flat earth and a smaller, closer sun
@@Graymenn I agree with you about getting the same results with a close sun and flat earth. Does the same results mean you agree that the circumference, that would be at the equator, is about 25,000 miles? Using that figure, what’s the mileage you come up with for the circumference at the edge, the ice wall? I come up with a circumference of 48,000 miles. Diameter of 16,000 miles.
@@jamesjeson6207 if it is flat there is no potential limit to the size of it.... if by the ice wall you mean the icy coast of antarctica, a good way to get a rough estimate of what it would be on a flat earth would be to measure the distance from the north pole to the coast of antarctica and use that as the radius of a circle and you get something like 69k miles in circumference. Thats is of course and estimate.
I have been studying this problem for a few days now and my main problem is different. He had to perform the measurements of the shadows at the exact same time, that is, when it was noon in Syene. Oh, but little problem. They didn’t have watches nor cell phones back then. Not even a telegraph. Say Syenagoras was in Syene and at some point said “now, now there is no shadow! Hurry and take the measurement over there!” What, did he shout so loud that it could be heard 800 kms away? Still his voice would have taken 37 minutes to get to Eratosthenes. So, joking aside, how did he pull this off?
I think I can answer this. The success of this method depends on the two cities being at the same longitude, which they are, at least approximately. Since they are basically lined up North-South, noon will occur at the same moment in each city. All he had to do was wait until the sun was at the highest point in the sky in one city, and he knew that was also the case in the other.
@@derekowens I don't think Jeriko does either. I find it sad that there are humans, the most intelligent species on the globe, some of whom are so... so stupid. What must life be like living inside such a limited mind?
No. Not a single thing presumed. This is all about asking questions, and making observations and calculations. Mathematics. Geometry. Applied knowledge and wisdom. Learning.
suares Eratosthenes used his brain power - nothing more. Just like Newton, Maxwell, Einstein, etcMaybe you could do the same, and advance our knowledge.
yes that's true but when applied to the earth and done as an experiment on earth the triangulation point is straight down towards the core of the earth so the circular plate idea can't be applied as around the horizon. the earth is a oblate spheroid deal with it
You just repeat the same experiment at a number of points anywhere you like and they all give a curve, therefore proving the Earth is a sphere. If the Earth were curved as a flat plate shape the experiment would fail at any place other than on the edge of the plate... and of course it would be very obvious to any observer that they were standing on the edge of a flat plate. Please use your brain and THINK before you go off writing utter rubbish.
@@theresaquinn8525 The only place a parallel light ray would cast different length shadows would be on a curved surface. If it were flat as a plate the shadows would always be of the same length in any point on the flat surface. If you look at a plat there is a center but no center core. Take a paper plate and put several toothpick perpendiculars to the plate. See no center core they point at different places.
Yes, I can explain. This experiment started by assuming the earth was round, and the measurements allowed Eratosthenes to calculate the circumference, which was his goal. If the earth were flat, the concept of a circumference would not apply.
I'll try to explain again. Eratosthenes was not trying to prove anything about the shape of the earth. The fact that the earth is round was one of his starting assumptions. The goal here was not to prove that it was round or flat, but to calculate the circumference, assuming that it was round. Whether the math works the same way or not isn't the point. The point is that he calculated the circumference, and he did it correctly, within a reasonable margin of error.
+Derek Owens Make sure you explain why this isn't the same as on that flat earth like I asked... And not go off on another long winded tangent... AAAGAIN...
If the Earth were flat, and the sun's rays are parallel (which they essentially are - this is easily testable with something as simple as a piece of pipe and a sunny day) then at the same time on the same day in two different cities the shadows of the measuring pole would be the same length. The only explanation for them being different lengths at the same time on the same day is that the surface of the earth is curved.
It proves that geometry is correct, but it does not prove the true shape of the earth. why he assumed the subject to be round or a circle since we don't have the true perspective of the earth.
because ppl can follow the course of the sun and know were it is at specific times and do measurements like this based off geometry and the suns movements this would NOT work the same on a flat earth because either A..the sun wouldnt act the same or B the geometry wouldnt..
He didn't assume the earth was round. He already knew that. Eratosthenes was doing this experiment to discover the SIZE of the spherical Earth, not its shape. And... of course... if geometry is correct that DOES prove the earth is round, as well as its size. That's how geometry works. Its a mathematical tool that aids you in reaching accurate conclusions about the size and shape of things once you measure and observe.
Was the experiment aimed at “proving anything”, in the first place? And to answer your question, he didn’t know how far the Sun was, but he was aware it had to be very distant, because of its constant angular size and because the angle very close to 90 degrees of the Sun-Earth-Moon triangle at Moon quarters; in fact he could even have known the distance, but we are not sure. Anyway, he knew it was VERY distant and therefore, he could take the rays as parallel.
@@truthbetold818 Because at the quarter Moon phase, the Sun, the Earth and the Moon form a rectangle triangle with the 90 degrees angle at the Moon. Then, measuring the angles from the Earth to the Moon and the Sun, we can conclude by means of trigonometry that the Sun is much farther away. Aristarchus already knew that method.
That's assuming a flat plane and a close sun. You can fool yourself into believing that so long as you only take those two measurements. If you take three or more, you just end up with multiple heights and locations for the sun, because the starting assumption is _wrong_ .
What are you saying? That we can't do this calculation today and make the same observations? Or that the earth was a sphere in 300 BC but is now flat? Can you hear yourself? Can you hear how stupid you sound? You're talking rubbish.
5:03 - You said that the rays of sunlight "won't" be vertical. WRONG!!!!!!!!!! The rays of sunlight WILL be vertical, that is why the shadow at Alexandria was cast in the first place. Because light travels in straight lines. It's the SHADOW cast that gets formed because of the vertical rays of light and because of the curvature of the earth, the shadow at Alexandria is cast. RAY OF LIGHT DOES NOT BEND IT IS ALWAYS VERTICAL AND PARALLEL AT NOON!!! Dude, you are a bad teacher. ROFL!. ;-)
If the suns rays are vertical, how does an object that is vertical to the earths surface cast a shadow? The sun's rays are not "vertical", the sun's rays are parallel. This is why you get longer shadows cast by the same sized objects towards the poles. This is why you get different length shadows in the same place at different times of the year. Why is this not known to you? BTW, the fact they are parallel also proves the sun is a very long way away and is not close.
Derek it's going to have to be a thumbs down because 1. It would have been impossible for Eratosthenes to measure at different locations at the same time considering the distance between the two points, unless he had a friend measure for him, he just had to call his mate with his iPhone. 2. Do you think they used an atomic clock to synchronize these measurements? 3. No one except NASA has been able to find any curvature anywhere on earth.
he knew when to measure the angle: when the sun was at the highest point in the sky, because they are roughly at the same longitude. you can actually visualize it with a small globe
"1. It would have been impossible for Eratosthenes to measure at different locations at the same time considering the distance between the two points, unless he had a friend measure for him, he just had to call his mate with his iPhone." Where is it claimed he made the measurements at the same time? He didn't. And he didn't need to. He only had to make them on the same day of the year - midsummer's day. I don't think he used an iPhone either as there wasn't a mast near Syrene. He did have a friend though. According to one version of the account, this person walked between Alexandria and Syrene to let Eratosthenes know how many paces it was. "2. Do you think they used an atomic clock to synchronize these measurements?" Since atomic clocks had not been invented in 300 BC then, no, I don't think he had an atomic clock. Then again he didn't need one. He didn't need a timepiece at all for the mathematics to work. Tell us why any clock is needed to conduct this experiment. "3. No one except NASA has been able to find any curvature anywhere on earth." That's total bollocks. I have seen curvature on earth. I have a curved path in my back garden. Or was that perhaps not what you meant? Could you write your posts in correct language so we all have a clue what you mean by them? If you perhaps meant that no-one before NASA has observed the Earth's curvature then that statement is wrong. Yuri Gagarin did. The ancient Greeks observed it - ships sailing away over the horizon for example and the shape of the earth's shadow cast on the moon during a lunar eclipse. Many explorers since the 1400s have circumnavigated the globe - a task impossible on a flat earth. I am sorry you give the proof of the Earth's size a thumbs down. I guess great mathematicians will just have to work harder to please the likes of you. But that's not an issue, the rest of us are happy with the proof and of course airline pilots rely on these facts hundreds of times a day around the globe. So, yeah. Fine. Whatever.
This person took a film proving the curvature of the earth during a 9 minute low altitude helicopter flight. Next inane question? czcams.com/video/xTkz6Lov7oI/video.html
apodictic - You haven't even seen the video. Eratosthenes needed to make the measurement only at 1 place, not both. He carried out his measurement at the time of year when he knew that one of the places would not have a shadow.Bridge and tunnel builders need to account for the curvature of the Earth, so nothing to do with NASA.Don't you think airline pilots would find it a bit strange to fly from London to Australia if the Earth was flat ?I'd think their navigation systems wouldn't exactly work correctlySR71 pilots could see the curvature of the Earth because they flew so high. Again - nothing to do with NASA.If you believe in a flat Earth then you're just being idiotic.
@@joejoealmeida3219 Thank you for giving us the benefit of your wisdom. Which part of the video proving you are wrong are you struggling with? Maybe someone here can help.
Eratosthenes did. He got this answer. If you do the same experiment today you will get exactly the same results. We know this which is why we DON'T need to "do our own research and experiments". Science moves on. Once something is proven by theory humans do not need to keep repeating the proofs, we move on and learn knew things. What is this weird obsession with you people that unless you do the calculations and experiments with your own hands, eyes and mind then all facts are worthless? I don't get it. Enlighten me.
It's really sad that you refuse to believe it? What did you find when you performed this experiment? Or did you just look out yer window and decide that it looks flat to you?
But Eratosthenese measured the circumference. If the earth were not round, it wouldn't have a circumference. But Eratosthense measured the circumference. The earth is round.
the name Eratosthenes and error .... Coincidence? I don't think so... The whole experiment have a lack of horizontal Earth as measurement was made on the earth so we and he don't know those two measurements was made down or uphill as it makes sense to shadow building.Also he couldn't know an altitude difference between two cities as it makes sense for shadow building. Ideally the measurements should be made on the water it is on the sea level.... The Earth is FLAT! The whole story is a big BS. Egyptian stadia length is also the point of discussions....
wow, I salute for such a very easily understanding illustration,
You are junior Eratosthenes ! Thank you so much for your intellect and teaching.
You nailed it.Thank you
There is a problem with the video.. you said in the end he used egyptian stadia he actually used the standard unit of measure of the time which was greek stadia. He had a 15% error not a few percentages like you said. This margin of error is still incredible because he assumed the earth was a perfect sphere (isaac newton was the first to suggest that earth is an oblate spheroid almost 2000 years later!!), the distance between the two cities was wrong by 81 km, the two cities where no at the same longitud by 3 degrees of difference and syene was actually 41 km away from parallel of the tropic of cancer (where sunlight reflects vertically). Taking all of this into account 15% erros is still amazing.
You're simply pointing out an error of scale, his equation is right and if you use the correct scale you get the correct number.
@@buxadonoff ...and furthermore, Egypt was 'Greek' during that period so an 'Egyptian stadia' was almost certainly just a 'Greek stadia'.
Love your explanation.
Very good. More people should watch this. It's amazing to think what Eratosthenes could do in about 250BC when most still thought the Earth was flat.
Unlike Eratosthenes, we live in modern day! Where we can take a hot air balloon to the stratosphere, and find that unaltered footage, captured without a fish eye/wide angle lens shows us undeniable truth; the horizon is flat in every direction for hundreds of miles. Spherical trigonometry predicts some 6000 feet of curvature at 100 miles, yet, in the stratosphere, where you can see for several hundred, this curvature is nonexistent...despite being told that the horizon at sea level "curves out of sight for the average viewer 6 ft in height at 3 miles distance". The 8 inches per mile squared formula is accurate within several inches up to 300 or so miles for the calculation of curvature.
The truth is that this high altitude footage reveals what early aviators said throughout the 1800's, when most people still had inquisitive minds, thanks to the lack of digital propaganda being pushed down their throats daily; the horizon does not curve away and out of sight from the observer, as the convex hull of a sphere would. In fact, it rises to meet the eye level of the observer regardless of altitude, forming a rather concave shape relative to the observer. This is the exact OPPOSITE observation of a globe earth. Of course, this gets ignored as "refraction", which, in turn, is an erroneously applied theory that is manipulated to suit the arguments of both the deceiver and the hopelessly deceived, when the argument is convenient. Simply put, you are told that you're not seeing what you are seeing, because we *know* the Earth is a globe, never-mind what you see with your own two eyes.
Wakey wakey Grason
@@I_dreamed_my_name_was_Brandon You're a flat-Earther, and I'm curious. If we live on the top of a flat disk, what's on the underside? If one would go up to the edge of the disk and jump off, what would happen? Can one go from one side of the disk to the other side?
Are you also a conspiracy theorist?
@@I_dreamed_my_name_was_Brandon How do you calculate the distance to the flat earth horizon based on the height of the observer?
The horizon is 'apparent'. The distance not only depends on observer height but also obstacles and weather conditions. That's why some days you can see much further than other days. @@marcg1686
Perfect explanation... Thanks for share.
Eratosthenes is a genius! Great job!
Thank you so much I understood every step ! :,) very well explained
This a great explanation video.Thanks
Thank you so much..Great explanation sir. Legend
I always wondered how people knew about the Earth and space before we could see the Earth FROM space, and apparently ASTROLOGY was one of the early ideas that lead to our knowledge of geography as well as astronomy!!! People who could "read" the stars were able to figure out things about the positioning of the Earth at various times of the year, because people were more in touch with seasons and natural time in agrarian and tribal societies. This video showed me the importance of geometry in that puzzle, it makes total sense too, because they observed patterns in nature, and Eratosthenes just applied that pattern on a global scale, which is extremely abstract thinking, but at the same time is a usage of tools and theories prominent in his time period. Pretty amazing stuff!
Thalassa Fischer but then astrology pushed to the edge from the astronomy. The same happened to alchemy, it pushed to the edge by chemistry.
Furthermore, that 23.5 degrees north is the Tropic of Cancer whereas the 23.5 degrees south is the Tropic of Capricorn. The Sun can be directly overhead between 23.5 north and south on the longest day of the year - the Summer Solstice. All due to the 23.5 declination (tilt) of Earth on its axis. Combine that with the rotation rate of Earth, the time to orbit the Sun and the Earth's elliptical orbit around the Sun and we can build a an accurate sundial including the 'equation of time'. Similarly, given shadow length at solar noon on a given day of the year, you want work out your latitude. All verifiable.
Hello, I'm french I studied this at school and thank you for your understandable explanations!
Good video teacher. Thanks for your sharing
awesome explanation :D
amazing
Regarding 4:34, the one day during the year that the sun is directly overhead at noon along the Tropic of Cancer is on the Summer Solstice which typically has been on June 21 or June 20.
Graet explnation, thank You ..
erastothenes measured the distances to all koines in illyricum. He was a scholar of ilyro-helenic origin living in egypt
Best explanation saw compared to others and language used is too good
@Berialavrenti Well, Augustine does come to mind as an early church father who originally came from an arab region, but I don't think I would agree that "most" of the early church fathers were arabs. As for Eurpoe stealing science, I think you overstate your case. Newton was a European Christian. Einstein was a European Jew. They just thought up some good physics - didn't steal it from anyone. Gauss was German. Pascal was French. Archimedes was Greek, as was Euclid and Pythagoras...
Can we please change Aswan back to Syene because it fits and sounds much more better than its today's name
thanks for teaching so well
awesome **
There’s one thing I‘m having a problem with! 🤔 How could he know the exact time of midday (high noon) in Assuan, when being in Alexandria, measuring the angle of the poles shadow?
Any response appreciated! 🙏🏼
He was able to know because the towns are pretty close to the same longitude. That is, they are nearly directly north and south of each other. So high noon in one location would occur at the same time as high noon in the other. My understanding is that Eratosthenes was aware of this when he made the measurement.
Just wait until the angle of the pole is at its shortest. So you keep measuring around noon.
The human brain is able to figure out things like this using the tools of the time. GPS, surveyor tools etc. make this so much easier, but Eratosthenes used deductive reasoning and his knowledge of geometry.
Thanks for this really great explanation! It's really good and even I, as a german, understood it very well!
This guy really was a genius!
okay. how did they got those figures?
My only question is what kind of clock did he have available to him so that he would know it was noon in both places at the same moment. I would be tempted to think that time was locally calibrated by, say, a sundial, so that noon is always when the sun is directly overhead, more or less.
He didn't necessarily need a clock. He just needed to know that the sun was at the highest point in the sky. This would happen at the same time in both cities only if they are at the same longitude. They are not exactly, but are pretty close.
+Derek Owens Ah, longitude!
+John Pavlou try going outside bra..
John Pavlou: Eratosthenes knowsthat the two Citys are not on the same latitude. This means a calculation error he cant solve. The distance is little bit longer. From this the circumference of the earth becomes too big. A small inaccuracy for this time. He should have to take the noon time to the second place! This problem was solved later. ;)
I had the same trouble understanding this. That the two cities are separated by latitude, but on close to the same longitude was key. When you think of replicating this experiment, there are so many things that could go wrong. I'm still trying to decide how much luck was involved. Friggin remarkable though. Measurements from two cities separated by longitudes, and the sun dial readings would be taken at different real times, but high noon on the sun dial. And the stick shadow would have been Nil. Luckily magnetic North was roughly "up" for the Earth in relation to the sun. Okay done babbling. Thx.
1 stadia =.1 mile or .16 km
360/7.2 = 50 * 5000 stadia = 250000 stadia
250,000 *.1 mile = 25,000 miles or 250,000 * .16 km = 40,000 km
noob
Happy Summer Solstice, Northern Hemisphere, Earth 2017 !!
I came here almost three years too late.
In the calculation doesn't matter whether we circle the light source or it circles us I suppose. THe Greeks had a pretty good idea the earth was round. Took a while for the idea to spread but they nknew
no, the majority of greeks thought the world was flat, just like every other ancient society. The only ones who though it could be a globe were hermits and mystics
Nicely explained!
Actually, Aswan is 24.1 degrees therefore not exactly on the Tropic of Cancer. Also, Alexandria and Aswan are not exactly on the same meridian about 3 degrees off. Still very remarkable for the time.
Hence 2 causes for the lack of absolute precision in the calculatios but, as you said, still a remarkable achievement in the Ancient world.
My guy I was having an argument with my boyfriend about how Eratosthenes knew that the angle of the shadow the stick created at Alexandria determined that the two cities must be 7.2 degrees away from each other because he said that the relationship of the interior angles didn't matter to the equation, well then how would Eratosthenes have known that sticking the pole at the ground and measuring its shadow would produce the angle between the two cities if he had no knowledge of the relationship of angles created by a transversal through two parallel lines? Your explanation at around 6:12 proved me right. Thank you!
Is it ok if i use a screenshot from 6:04 for a school project about Eratosthenes. Of course you’ll be credited.
Yes, certainly, and I hope your project goes very well.
thank you
really good video btw
He had to measure the shadow's angle in Alexandria at precisely noon on the summer solstice. How did he know when noon was?
Fair enough.a
I think that noon is when the sun is on the highest point. That probably means that the shadow of a stick that is vertical to the ground is the smallest that it could ever be any other hour of the same day.
@@madrandomize5115 If the two different locations measured it in the way that you suggest, neither stick would have a shadow. It seems that you need the locations to talk via phone or walky-talky to synchronize measurements. Of course, no such technology existed.
@@oscarg7460 I quote from Wikipedia.
"Solar noon (informally high noon and formally local apparent solar noon)[3] is the moment when the Sun contacts the observer's meridian, reaching its highest position above the horizon on that day ("Sun transit time") and leaving the shortest shadow."
So on that particular day Eratosthenes could have measured the smallest shadow of the day (since you can easily mark it on the ground) . The only real problem on the matter is the length between 2 cities and for them to be able to synchronize on the date.
@@oscarg7460 "If the two different locations measured it in the way that you suggest, neither stick would have a shadow. " The sun is never directly overhead Alexandria, so how would the stick/pillar in Alexandria _not_ have a shadow?
That was super, thanks! I'm curious now, how did people measure large distances, like the 5,000 stadia between Alexandria and Syene, in the first place? Did they do it manually, by counting paces or some such method? :D :D
I think they had surveyors, if you know a sticks hight, and walk farawar from the 1 person to place b, and use a bit of string to measure how high the stick is now, you could triangulate that out
History indicates he had someone pace off the distance from Alexandria to Siene.
@@davemmar Now you mention it I think I remember talk of pacing. You'd be in trouble if you forgot where you were up to :D
Why are all the rays parallels 3:38 ?
because the source of light (the Sun) is insanely far away (about 150 million kilometers).
I will restate my confusion. The 2 measurements have to be synchronized, right? They need to take place simultaneously. But how did they know they were measuring simultaneously? I appreciate for one spot the answer is that the sun was directly overhead. But how did they know to measure the other spot simultaneously? It's not like they had stop watches.
Ah, I understand your question. The assumption is that the sun would be directly overhead at the same time in both cities. This would only be the case if the cities were at the same longitude, or in other words, if they were aligned directly north and south of each other. They aren't *exactly* aligned north-south, but are actually pretty close, close enough for the method to give a good result. This arrangement arose from the fact that Nile happens to flow south to north.
@@derekowens Again, I don't understand how this works. Say that your are in spot B, the place where the sun is NOT directly overhead at noon. When do you say, "NOW" to measure the length of the stick's shadow? I know it's noon, but how does the person know it's the exact same noon as spot A?
@@oscarg7460 Because in both places, noon will be the moment the sun is at the highest point in the sky. They could determine that fairly accurately without clocks, by using a sundial or similar mechanism. That would be the same moment in both cities, as long as the cities were aligned north-south, which they basically are.
@@derekowens AAHH! Noon is the point when the sun is the highest point in the sky and they were equipped to figure that out. You don't know how long this has bugged me. Years? Thank you, much. You are generous with your knowledge.
how a cool, analytical mind can beat anything.
...and how a hot, stupid mind can understand nothing (see comments below from flat earthers).
Funny thing: over the past few years, I've mentioned Eratosthenes on many occasions. I was ridiculed, heckled, mocked, blocked, and trolled every time. 🙄 It's unbelievable how arrogant and ignorant society (especially via "social media") people have become. They don't even know who Carl Sagan is. It's fuggin' embarrassing. 🤮
I'd be interested to know the context. Why were you ridiculed for mentioning Eratosthenes? Can you provide some details?
@Berialavrenti Just cause he was against the privileges the greeks had dosent make him a non-greek. Just means he saw humans as equals, meaning just cause your greek dosent make you better then the other guy.
...and he measured the circumference of the earth, here is a picture of the earth...And Eratoshenes knew geometry, here is a book on geometry.
He did not measure the circumference of the earth. He calculated it. Seeing that the Sun and the Moon are spherical, it's not unreasonable to assume that the earth is likewise spherical.
@@marcg1686 Here is a picture of s sphere...
What about the assumption that sunlight rays are parallel? How could he verify it? Did he have a reliable estimate of the distance of the Sun from Earth? As far they knew at that time, the Sun could be a very small ball very close to the Earth.
Even back in the day it was known that the Sun was very distant. Sun rays being parallel was a reasonable assumption.
"This is exaggerated obviously"... I laughed out loud.
What did you think so funny?
@@grasonicus Oh don't mind them their flat earthers.
Cornell institute said he got less than 1% accuracy. And they use different numbers. Some one is wrong badly here.
Even Wikipedia have 3th set of numbers.
Yet again Neil deGrass Tyson told 4th story
Michalle Thaller have, hers story 5th edition...
How's that even possible?
Crap i forgot Carl Sagan.. As 6th...
One reason is because nobody knows for sure how long a stadia was. Considering the technology at the time, he came very close. The stories all use the same methodology and locations.
What are you suggesting? That the earth is not round? No, all these calculations prove that it is. All that the different results prove is that the calculations all differ by small amounts. Often these are down to people using different measurements of their day. The answer is the same - the earth is round and certainly not flat.
The calculation can be performed without the clever geometry. You simply move the stick which is producing the shadow at Alexandria until no shadow is produced. Measure the angle between the stick that cast a shadow and the same stick that was moved to produce no shadow. You get 7 degrees. You don't have to measure the lengths of shadows using this technique, and you don't need the clever geometry either. I suspect this is how he actually did it but we will probably never know.
It is a _little_ more complex than that. ;)
You'd still need a reference point of which you *know* the sun to be 90° overhead at that time.
If you don't have that - it won't work.
Example:
let's say he was in Alexandria - and measured the angle to be 7° to true vertical
... then what? ;)
You now can't do this calculation, because you are now missing the distance to the point where the sun is 90° overhead.
All the information you have is:
where you are right now, the angle to true vertical is 7°
At another place it will be different - of course.
To choose an extreme example:
do this in Madrid - or Paris ...
Now the angle to true vertical is much larger.
Then what? ;)
You need the distance to the place where the sun is indeed at true vertical.
Cheers!
We know exactly how he did it.
czcams.com/video/G8cbIWMv0rI/video.html
The only problem is before the stick reached zero degrees over 800km must be moved. No way anyone can move that distance on foot instantly. If more than a few seconds pass the Sun will noticeably shift. 800km there be no sun in the sky.
A wierzący w kulistą Ziemie opierają się na założeniach Eratostenesa o równoległości promieni słonecznych jednocześnie na innych rysunkach krzyżują te promienie od Słońca by nakłamać o przyczynie małego cienia Księżyca w czasie zaćmienia Słońca, bo ten cień ma średnicę tylko ok. 100 km, a cień obiektu zawsze jest większy od swojego oryginału, czyli Księżyc ma rzeczywistą średnicę tylko 50 km. czcams.com/video/QOREOUU4r7o/video.html
How did he know the radius of the earth? Just because the lines converge at a said point doesnt mean that is the center of the earth? This whole thing is assuming he already knew the radius!
He didn't. He calculated the circumference of the Earth. Once can calculate the radius from that.
The sticks are parallel to a tangent of the surface of the earth, meaning that they point to the centre
This is assuming that the surface is equal across, having zero graduation of land mass aka elevation that we say doesnt need to be taken into account for. Also assuming that the sun is truly as far as it is...
I was trying to say it in a more hypothetical way, but the sticks would be pointing oppoiste to gravity, and the centre of gravity is the centre of the earth
MultiGazman
No
radius not required. Just the fraction of a circle, and the distance between cities. Rough approximation? yes. But not off by a magnitude. And the distance was measured by walking and counting steps.
I beleive the Earth to be big and round but I don't get how Eratosthenes knew that the sun was big and far. If the Earth was flat and sun was small and close yet be directly above the well it would cast no shadow in the well yet make the shadow on the stick.
Look even further back, people like Aristarchus had done other measurements involving the moon, that indicated the sun to be far away (their estimate for the distance was not very accurate but still indicated it to be very far) As for getting the same results assume a Flat Earth, sure you could use just two points of measurements, assume a flat Earth and a close and small sun,... *but* once you use more than two points, it falls apart completely. That's why in science if your initial results can fit more than one assumption, you have to keep testing and checking until one of them fails.
What people don't seem to know is classical greeks proved the earth to be round 500 bc, but it took judeo christian 1000 years more to figure this out.
@@gentlestormtoo wrong, most greeks did not believe the earth was round, it was a thought experiment among hermits and mystics
@@Graymenn Yes most didn't of course! Most were not critical thinkers! Same as today, ask someone how the radio works?
@@Graymenn Of course most Greeks wouldn't believe or understand it. Same as today most people would be at a loss to explain how the 100-year-old radio works. The round earth knowledge(then) is in the same vein as today's CERN hydro Collider, or the ISS(international space station). You would be lucky to find 100 people in the world that can explain it in full.
So Stadia is equivalent to an American Football field?
Yes, that's roughly correct. From what I understand, the exact length is still a matter of discussion and debate.
Erste Bestimmung der Größe der Erde durch Eratosthenes juergenfritz.com/2019/07/01/erste-bestimmung-der-groesse-der-erde/
Si tan solo entendiera igles
How did he synchronize the readings of the shadows 800km away from each other without clocks and telecommunication?!
From what I understand, he was able to do this because the two towns are pretty close to being lined up north to south. Because they are at the same longitude, the moment of noon, the moment the sun is its highest point in the sky, occurs at the same time in both cities.
@@derekowens see this is where I get stuck. Because that is still kind of a vague measurement. It seems to me that someone would want to do something that is replicable and verifiable and to me that means that you can accurately determine what quote “noon“ is for you in your location. And that would be the moment when a vertical and straight shaft which you could create, which cast no shadow. So I still don’t know how he knew it was noon time at Syrene while he was in Alexandria.
@@JohnnyArtPavlou You will only get the "no shadow" condition when the sun is directly overhead, and you need to be close to the equator for that to happen. It simply won't happen in the northern latitudes. But you can still determine the moment of noon, at least approximately. That will be the moment that the sun is at its highest point in the sky, and at that moment the shadow will be at its shortest. The shadow at this moment doesn't change much from day to day, so you could mark the shadow at its shortest point one day, and then watch the shadow the next day as that moment approaches. It will be noon at that moment. And if the cities are aligned north to south, it will be noon in both places.
@@derekowens Yes, you’re right. I had to go over as many times in my mind. Because the vertical stick in Alexandria is acting as an imperfect gnomon. Because it doesn’t compensate for the elevation or position on the globe. And is the fact that it’s not compensating that gives the shadow that gives the number of degrees.
He didn't have to.
It was already known that on the summer solstice (June 21st or 22nd), sunlight could reach the bottom of a deep well in Syene, so the Sun had to be directly overhead on that day. Eratosthenes just had to measure how much the Sun's position deviated from directly overhead (zenith) in Alexandria on the summer solstice. It didn't matter if that measurement happened many _years_ after the observation in Syene as long as both were done on the summer solstice.
doesn't this calculation posit a heliocentric universe and a circular earth? i wasn't aware the ancients thought this.
iss Aristarchus proposed the heliocentric model, but Ptolemy's geocentric model won until got disproven
The knew for hundreds of years the earth was round. If they didn't know the earth was round then obviously this experiment would fail. Ptolemic models work just as good though.
One small problem:
An assumption is made the earth is spherical. A second assumption is made the sun's rays parallel. This is not what we obviously see every day.
Use the same observation and calculate the distance of the sun from earth.
This is so simple, and makes more sense.
But no, we insist that the earth is a globe. Silliness.
Y'know you _can_ use the same observation, and if you assume a flat Earth, you can assume the sun to be small and just a few thousand miles up.
Now, where you run into a whole heap of trouble is when you use more than two points... cos you can fool yourself into thinking you have a solid figure for the location of the sun, if you just use two points and plot where the lines of observation intersect.
If you add a third point, it still agrees with a spheroid Earth, but you end up with 3 different heights and locations for the supposed small close sun. But you didn't bother to work that out did you? you just heard someone say you can make this work on a Flat Earth, and didn't bother being in any way rigourous before swallowing it as a good argument. It ain't.
You go on insisting the earth ain't a globe. Tell you what... why don't you tell us where we should re-draw the lines of latitude? Cos on a flat Earth they would not be the same distance apart for every degree... If you're measuring the elevation of the sun at an equinox, on a flat Earth the distance between 0 and 1 degree North will be smaller than the distance between 1 and 2 and 89 - 90 would be much, much bigger, and then to make it worse, the problem would go the other direction when measuring the angle to the pole star at night. 90-89 would be small, and 45-44 would be a larger distance. How would you redraw the lines of latitude there buddy? And how did those ancient sailors ever manage to determine how far north they were by using the elevation of the pole star, if the Earth wasn't a globe? On a flat Earth, there would not be a consistent 69 mile (60 nautical mile) interval for each 1 degree of latitude... But y'know people who've never had to find their way home without a smart phone aren't so likely to think about that, but they sure seem eager to act like they know more than people who _did_ have to work things out for themselves.
This literally does not prove the Earth is round. This can also prove the sun is smaller, closer, and revolves around us
It works both ways if you just think about the 2 different models and not try to put one in the other box.
Think...
Correct, this is not a proof that the earth is round. The Greeks and others already knew the earth was round by other means, such as seeing its curved shadow on the moon during a lunar eclipse. Based on already knowing the earth is round, this was an attempt to measure its size, and it was done remarkably well.
Then why don’t you make that calculation
This experiment was not designed to prove that the Earth is round. If you reject the shape of the earth and feed the angles into a flat earth model, then you will get an arbitrary height for a small, close sun.
However, if you add three or more observation points, you end up with multiple locations for the sun.
The spheroid calculations give consistent results of 1 degree for 69 miles north or south.
So, you couldn't have considered testing this with more than two points of observation, Marcos?
_Think_ ...
Godamn grandpa 👴 Eratostanes
Are you suggesting that Eratosthenes knew that the earth was curved before he did his experiment?
+mousehead2000 Yes. Throughout history, nearly everyone has known that the earth was curved. The idea that people thought the earth was flat in the time of Columbus, or any other time for that matter, is more myth than history.
+mousehead2000 People knew the earth was curved, but they dont have the courage to prove it was curved, until....Eratosthenes. What if Eratosthenes did not travel to Syene, then is it possible for others to discover the planet was curved based on different spot on the planet. is it possible for someone else who living in Asia for example to be able to find a pond in which light reaches the bottom and eventually find out the earth was curved?
***** How does someone know something unless they've proved it? There are no indications to the naked eye that the earth is round.
mousehead2000 How do you tell if the red apple is red? it might be green. If you look at a beautiful photo that have green grass, blue sky, blue sea. and then when you look to a same photo but this one has no color. however somehow you still seeing green grass and blue sea/sky. Why is that? Your brain filling in the gap. Do you see what your brain tell your to see or you see because what it is? so how do we prove something that is real?
***** well exactly. if i relied on my senses i would say the earth was flat. there is nothing telling me otherwise. only science tells me it is round.
There can be TWO conclusions that we can get. 1. That the sun is far away and big with a spherical earth or 2. A small, local sun with a flat earth.
It's option 1.
No, the experiment proves option 1 due to the huge size of the earth discovered. Parallel rays are also proven, thus disproving a close-by sun. You also don't do this experiment in one place. You triangulate from other points for which the ONLY conclusion is that the Earth is a sphere.
BTW, are you aware that Eratosthenes wasn't trying to prove a spherical Earth? He already knew that. He did this experiment to determine its size.
The number of flat earthers who simply don't grasp what Eratosthenes was about reflects their limited ability to understand maths and science generally.
Your absolutely right, option two would make the Rays unparallel and give a similar effect. Nice Observation!
However, a few hundred years before Aristotle had already shown the earth ot be round, leaving Option 1as the only possible explanation.
@@gentlestormtoo how did aristotle prove the earth was round?
@COVID 1984 Sorry you can't truly prove positive in science except in mathematics. You need to use statistical analysis like chi-square, fisher, Bernoulli distribution, and hundreds of others depending on the data you are trying to model. However, Aristotle *showed* by three observations that the earth *must* be round.
(1) Observing other celestial bodies, in particular the moon/Sun. (2) The Moon must be spherical by observing the shape of the terminator (the line between the part of the Moon in light and the part of the Moon in the dark) (3) the shadow cast by the earth on the moon during a lunar eclipse. QED ( "quod erat demonstrandum")
st augustin was not an arab , he was a berber from modern algeria ...
Some scientists are lucky that their results are correct.
How can you prove the radius of the whole planet by measuring only 1/50th of the circumference. What if the rest of the circumference didn't have the same curvature?
What if the planet was an asteroid like planet?
He was lucky that Earth is very close to a sphere.
Yes, that's correct. If the earth were not roughly spherical, that would throw off the calculation. The ancient Greeks knew, though, that the earth was round, because they could see the shadow of the earth on the moon during an eclipse.
@@derekowens *The ancient Greeks knew....*
No they don't that's what YOU are saying now to explain this round Earth BS
@@rlupara This is from Grade9Science.com:
1. Travelers discovered that they saw different constellations as they traveled north or south.
2. They noticed that ships sailing into view on the horizon had their masts gradually appear as they approached, and that the horizon became further away when viewed from higher elevations on hilltops or mountains.
3. They noticed the curved shadow of Earth on the Moon during lunar eclipses.
There, three pieces of evidence, observed by the ancient Greeks, that let them to conclude that the earth is round.
Keep working on it and you can reach the Grade8Sciecne level of thinking. Grade 8 is a good goal. You can do it. Reach grade 8, then keep going, and one day you will be able to contribute some useful thought to the world.
Derek Owens,
Don't waste time on the cretin who calls himself/herself the dynamic athlete. I'm sure he/she is neither dynamic nor an athlete. He/she is a flat-head, and any words longer than two syllables, or sentences longer than four words elicit the same childish, head-in-the-sand response from that sort. I thought your video was well-produced and enjoyable. Don't waste time with flat-heads.
Scrolls not books.
Modern terminology to aid in the clarity of the discussion. If the video had said "scrolls" that would have meant something different to many viewers. "Books" is a clearer concept and is more easily understandable.
so he was aware that earth is round and inside a circle, angular total 360 ???
or what ever angle measure ments where used at the time.
I could use the stick and a piece of string,
Greeks earlier than Eratosthenes had been suggesting that the earth was round for quite a long time but had not come up with a method to make the observation. Eratosthenes great breakthrough was that he was the person who made that breakthrough. He held assumptions about a round Earth but this experiment was the proof needed. He knew from geometry that we divide a circle into 360 degrees. This is an arbitrary man-made construct. Once he knew the angle of the shadow at Alexandria was 7.2 degrees (1/50th of 360), he then only needed to know how far the stick in Alexandra was from Syrene. Other accounts suggest he paid a man to walk between the two cities and count the paces. In today's distance the result was about 800km. Multiply 800 x 50 and you get the distance around the Earths surface in km. The result tells the observer that the Earth is round, but not that it is a sphere. However if you do the same calculation from other points and they give the same answer you know that the circumference is the same in all directions which means the earth is a sphere.
@@zurviver_3747 Eratosthenes used degrees. The Greeks invented geometry. Our use of 360 degrees within a circle is one of their great mathematical constructs.
Flat earth supporters don't want you to watch this video. 🙄🙄🙄
that because we are already familiar with it, and have debunked it. The experiment assumes a spherical earth and an extremely distant and large sun. The exact same results are explained easily with a flat earth and a smaller, closer sun
@@Graymenn I agree with you about getting the same results with a close sun and flat earth. Does the same results mean you agree that the circumference, that would be at the equator, is about 25,000 miles? Using that figure, what’s the mileage you come up with for the circumference at the edge, the ice wall?
I come up with a circumference of 48,000 miles. Diameter of 16,000 miles.
@@jamesjeson6207 if it is flat there is no potential limit to the size of it.... if by the ice wall you mean the icy coast of antarctica, a good way to get a rough estimate of what it would be on a flat earth would be to measure the distance from the north pole to the coast of antarctica and use that as the radius of a circle and you get something like 69k miles in circumference. Thats is of course and estimate.
I have been studying this problem for a few days now and my main problem is different. He had to perform the measurements of the shadows at the exact same time, that is, when it was noon in Syene. Oh, but little problem. They didn’t have watches nor cell phones back then. Not even a telegraph. Say Syenagoras was in Syene and at some point said “now, now there is no shadow! Hurry and take the measurement over there!” What, did he shout so loud that it could be heard 800 kms away? Still his voice would have taken 37 minutes to get to Eratosthenes. So, joking aside, how did he pull this off?
I think I can answer this. The success of this method depends on the two cities being at the same longitude, which they are, at least approximately. Since they are basically lined up North-South, noon will occur at the same moment in each city. All he had to do was wait until the sun was at the highest point in the sky in one city, and he knew that was also the case in the other.
@@derekowens yes, of course. Thank you Derek, I almost couldn’t sleep last night! You are a blessing.
Earth is multiplane.
Well, thanks for clearing that up.
Seriously, though, I don't know what you mean by "multiplane".
@@derekowens I don't think Jeriko does either. I find it sad that there are humans, the most intelligent species on the globe, some of whom are so... so stupid. What must life be like living inside such a limited mind?
Just all presumptions
No. Not a single thing presumed. This is all about asking questions, and making observations and calculations. Mathematics. Geometry. Applied knowledge and wisdom. Learning.
suares Eratosthenes used his brain power - nothing more. Just like Newton, Maxwell, Einstein, etcMaybe you could do the same, and advance our knowledge.
Nope. Observations and calculations.
ERASTOSTHENES
CLEVER,
AS I SEE FROM HERE
You can apply this formula to a round plate or any circle for that matter. The problem is that this does not mean that the plate is not flat.
yes that's true but when applied to the earth and done as an experiment on earth the triangulation point is straight down towards the core of the earth so the circular plate idea can't be applied as around the horizon.
the earth is a oblate spheroid deal with it
You just repeat the same experiment at a number of points anywhere you like and they all give a curve, therefore proving the Earth is a sphere. If the Earth were curved as a flat plate shape the experiment would fail at any place other than on the edge of the plate... and of course it would be very obvious to any observer that they were standing on the edge of a flat plate.
Please use your brain and THINK before you go off writing utter rubbish.
@@theresaquinn8525 The only place a parallel light ray would cast different length shadows would be on a curved surface. If it were flat as a plate the shadows would always be of the same length in any point on the flat surface.
If you look at a plat there is a center but no center core. Take a paper plate and put several toothpick perpendiculars to the plate. See no center core they point at different places.
Explain how this experiment isn't the same on the flat earth?
Yes, I can explain. This experiment started by assuming the earth was round, and the measurements allowed Eratosthenes to calculate the circumference, which was his goal. If the earth were flat, the concept of a circumference would not apply.
+Derek Owens
Stuuupid...
It's already a proven fact this works on a flat disc and the math is the same...
I'll try to explain again. Eratosthenes was not trying to prove anything about the shape of the earth. The fact that the earth is round was one of his starting assumptions. The goal here was not to prove that it was round or flat, but to calculate the circumference, assuming that it was round. Whether the math works the same way or not isn't the point. The point is that he calculated the circumference, and he did it correctly, within a reasonable margin of error.
+Derek Owens
Make sure you explain why this isn't the same as on that flat earth like I asked...
And not go off on another long winded tangent...
AAAGAIN...
If the Earth were flat, and the sun's rays are parallel (which they essentially are - this is easily testable with something as simple as a piece of pipe and a sunny day) then at the same time on the same day in two different cities the shadows of the measuring pole would be the same length. The only explanation for them being different lengths at the same time on the same day is that the surface of the earth is curved.
ZOb HuMiDe frere
It wasn´t so obvius if they weren´t spend his life in the study and discovery of math, don´t be so Haughty Guys be greatful of them.
It proves that geometry is correct, but it does not prove the true shape of the earth. why he assumed the subject to be round or a circle since we don't have the true perspective of the earth.
because ppl can follow the course of the sun and know were it is at specific times and do measurements like this based off geometry and the suns movements this would NOT work the same on a flat earth because either A..the sun wouldnt act the same or B the geometry wouldnt..
He didn't assume the earth was round. He already knew that. Eratosthenes was doing this experiment to discover the SIZE of the spherical Earth, not its shape.
And... of course... if geometry is correct that DOES prove the earth is round, as well as its size. That's how geometry works. Its a mathematical tool that aids you in reaching accurate conclusions about the size and shape of things once you measure and observe.
The sun rays are parallel. If the earth is flat, then the shadows of the sticks in both cities would be in the same length.
What distance did Eratosthenes believe the sun was from the earth? Because im believing his experiment didn't prove anything.
Was the experiment aimed at “proving anything”, in the first place?
And to answer your question, he didn’t know how far the Sun was, but he was aware it had to be very distant, because of its constant angular size and because the angle very close to 90 degrees of the Sun-Earth-Moon triangle at Moon quarters; in fact he could even have known the distance, but we are not sure. Anyway, he knew it was VERY distant and therefore, he could take the rays as parallel.
It wasn't much of an experiment. Two measurements and a basic understanding of geometry was all he needed.
@@betaorionis2164 Both the sun and the moon appear in the sky to be the same size...how is he deducing the sun is farther away than the moon?
@@truthbetold818 Because at the quarter Moon phase, the Sun, the Earth and the Moon form a rectangle triangle with the 90 degrees angle at the Moon. Then, measuring the angles from the Earth to the Moon and the Sun, we can conclude by means of trigonometry that the Sun is much farther away. Aristarchus already knew that method.
@@betaorionis2164 But how did he or Aristarchus know the earth's distance from the moon? Like I said, they both appear the same size in the sky.
IF THAT'S. 7.2° THEN SUN IS 6350 KM far away
Show your math.
How on euclidean geometry did you come up with that?
That's assuming a flat plane and a close sun. You can fool yourself into believing that so long as you only take those two measurements. If you take three or more, you just end up with multiple heights and locations for the sun, because the starting assumption is _wrong_ .
if this was true what is the modern day way of calculating the curvature ?, ill tell you there isn't, the earth my friend is flat
The flat earth theory has avid supporters from all over the globe.
@@derekowens LOL!
What are you saying? That we can't do this calculation today and make the same observations? Or that the earth was a sphere in 300 BC but is now flat? Can you hear yourself? Can you hear how stupid you sound? You're talking rubbish.
5:03 - You said that the rays of sunlight "won't" be vertical. WRONG!!!!!!!!!!
The rays of sunlight WILL be vertical, that is why the shadow at Alexandria was cast in the first place. Because light travels in straight lines.
It's the SHADOW cast that gets formed because of the vertical rays of light and because of the curvature of the earth, the shadow at Alexandria is cast.
RAY OF LIGHT DOES NOT BEND IT IS ALWAYS VERTICAL AND PARALLEL AT NOON!!!
Dude, you are a bad teacher. ROFL!. ;-)
If the suns rays are vertical, how does an object that is vertical to the earths surface cast a shadow?
The sun's rays are not "vertical", the sun's rays are parallel. This is why you get longer shadows cast by the same sized objects towards the poles. This is why you get different length shadows in the same place at different times of the year. Why is this not known to you?
BTW, the fact they are parallel also proves the sun is a very long way away and is not close.
Yes sun rays are parallel because the sun is much much bigger than earth and is really far away from earth.
Derek it's going to have to be a thumbs down because 1. It would have been impossible for Eratosthenes to measure at different locations at the same time considering the distance between the two points, unless he had a friend measure for him, he just had to call his mate with his iPhone. 2. Do you think they used an atomic clock to synchronize these measurements? 3. No one except NASA has been able to find any curvature anywhere on earth.
He probably didn't have to measure Syene's angle, as it was known that no shadows would be cast. As for your last point, what do you mean?
he knew when to measure the angle: when the sun was at the highest point in the sky, because they are roughly at the same longitude. you can actually visualize it with a small globe
"1. It would have been impossible for Eratosthenes to measure at different locations at the same time considering the distance between the two points, unless he had a friend measure for him, he just had to call his mate with his iPhone."
Where is it claimed he made the measurements at the same time? He didn't. And he didn't need to. He only had to make them on the same day of the year - midsummer's day. I don't think he used an iPhone either as there wasn't a mast near Syrene. He did have a friend though. According to one version of the account, this person walked between Alexandria and Syrene to let Eratosthenes know how many paces it was.
"2. Do you think they used an atomic clock to synchronize these measurements?"
Since atomic clocks had not been invented in 300 BC then, no, I don't think he had an atomic clock. Then again he didn't need one. He didn't need a timepiece at all for the mathematics to work. Tell us why any clock is needed to conduct this experiment.
"3. No one except NASA has been able to find any curvature anywhere on earth."
That's total bollocks. I have seen curvature on earth. I have a curved path in my back garden. Or was that perhaps not what you meant? Could you write your posts in correct language so we all have a clue what you mean by them? If you perhaps meant that no-one before NASA has observed the Earth's curvature then that statement is wrong. Yuri Gagarin did. The ancient Greeks observed it - ships sailing away over the horizon for example and the shape of the earth's shadow cast on the moon during a lunar eclipse. Many explorers since the 1400s have circumnavigated the globe - a task impossible on a flat earth.
I am sorry you give the proof of the Earth's size a thumbs down. I guess great mathematicians will just have to work harder to please the likes of you. But that's not an issue, the rest of us are happy with the proof and of course airline pilots rely on these facts hundreds of times a day around the globe. So, yeah. Fine. Whatever.
This person took a film proving the curvature of the earth during a 9 minute low altitude helicopter flight. Next inane question?
czcams.com/video/xTkz6Lov7oI/video.html
apodictic - You haven't even seen the video. Eratosthenes needed to make the measurement only at 1 place, not both. He carried out his measurement at the time of year when he knew that one of the places would not have a shadow.Bridge and tunnel builders need to account for the curvature of the Earth, so nothing to do with NASA.Don't you think airline pilots would find it a bit strange to fly from London to Australia if the Earth was flat ?I'd think their navigation systems wouldn't exactly work correctlySR71 pilots could see the curvature of the Earth because they flew so high. Again - nothing to do with NASA.If you believe in a flat Earth then you're just being idiotic.
Fixed and immovable earth. The globe is insanity
Feckless 🤡.
the earth is flat
+a king Thanks for letting us know. We can all go to sleep peacefully now, knowing that this issue is finally settled.
and what`s next ? china is in south america? lol
earth is flat this is not accured
@@joejoealmeida3219 Thank you for giving us the benefit of your wisdom. Which part of the video proving you are wrong are you struggling with? Maybe someone here can help.
its really sad that you believe this crap, do your own research and experiments
you are pathetic
Eratosthenes did. He got this answer. If you do the same experiment today you will get exactly the same results. We know this which is why we DON'T need to "do our own research and experiments". Science moves on. Once something is proven by theory humans do not need to keep repeating the proofs, we move on and learn knew things.
What is this weird obsession with you people that unless you do the calculations and experiments with your own hands, eyes and mind then all facts are worthless? I don't get it. Enlighten me.
It's really sad that you refuse to believe it? What did you find when you performed this experiment? Or did you just look out yer window and decide that it looks flat to you?
@hootsmin9818
🤡
the earth is flat....
But Eratosthenese measured the circumference. If the earth were not round, it wouldn't have a circumference. But Eratosthense measured the circumference. The earth is round.
Lee Wilson is stupid. There. Now we're all happy.
lee Wilson Stop being stupid
Earth is not flat. Get used to it.
the name Eratosthenes and error .... Coincidence? I don't think so...
The whole experiment have a lack of horizontal Earth as measurement was made on the earth so we and he don't know those two measurements was made down or uphill as it makes sense to shadow building.Also he couldn't know an altitude difference between two cities as it makes sense for shadow building. Ideally the measurements should be made on the water it is on the sea level.... The Earth is FLAT! The whole story is a big BS. Egyptian stadia length is also the point of discussions....
@benjaminbennett7486