The Eratosthenes Pizza explanation is very helpful for understanding the geometry of the "slice" of Earth near Alexandria and Syene, Egypt. I will be sure to try the experiment to see if I could measure the circumference of the Earth.
Thank you ! I wrote a worksheet based on your video that I plan to use with my students next week. I will definitely be giving credit using this video link. Please let me know if that is enough.
I developed a class lab for students to actually repeat eratosthenes measurements. Every year I would have students measure the earth. If you would like more info about this, send me a message at "tmartclimber" at Gmail
How was he able to know exactly where the sun would be in one city while he was in another ? Can this be replicated today ? I have been searching for recent videos that calculate the earth circumference using the method today
It was recorded, it was known that every year on or about the 21st of June the sun would shine directly down the well... Another example of why documenting observations and record keeping furthers our collective knowledge.
At local apparent noon the shadow cast by the Sun is at its shortest. In Syene the Sun casts no shadow at LAN, in Alexandria you would measure the shadow every few minutes before and after LAN. The shortest shadow is the one you would use to calculate the angle.
This is a very brilliant experiment and Very well Explained, I thank you. However , the way I see it, it would only work if Syene is on the same Longitude as Alexandria. How would Eratosthenes know if they are on the exact same Longitude and the distance of 925 km is indeed the distance between the 2 latitudes
@@aemrt5745 Well if the 2 places are not on the same longitude the 925 km distance being indicated would be greater than the distance between the 2 latitudes thus his calculations would end up being inaccurate
@@aemrt5745 yes that's what I am talking about. I think he was lucky that they were close to each other latitude wise, compared to longitude. Otherwise, his calculations would've been way off
If you understand trigonometry, measure the length of the shadow, measure the length of the object causing a shadow. Divide those two then that will be the tangent of the angle. If you do not understand trigonometry, draw a smaller scale triangle and measure the angle with a protractor.
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 understand your question... but no need to have communication to measure the sun angle at the same time. It was well documented that the sun shown to the bottom of the well in Syene at solar noon on the solstice. Therefore, the sun angle measurement in Alexandria needed to be completed at solar noon on the solstice. This works as long as the measuring location and the location of a direct sun are on a shared meridian (same longitude)
There is no need for a watches, only some observation. When he first puts the stick on the ground before noon, there will be a shadow. As it gets closer to noon, the shadow will keep getting shorter and shorter until it's exactly noon, then the shadow will start getting longer and longer. The exact moment the shadow starts getting longer is considered noon. I think thats how it works. Note: The video mentions that it should be on the solstice and the measurements should be on the same longitude.
#1. They effectively are parallel due to the sun's great distance. While technically, they do diverge, the divergence at Earth is basically imperceptible, especially with primitive measuring tools. #2 this amount elevation is insignificant over these distances.
@@TMartScience How do I know the Sun is not closer & smaller than what is taught to me? I want to know how I can verify the religious claims being spewed to me as though they were scientific.
@@thomasg4324 at the time of Eratosthenes, this would have been difficult. If you want to know more about how we learned the distance and therefore the size of the sun, the very early measurements were using geometry and the very rare occurrence of when the planet Venus transits the sun. As of the 1960s, we can bounce a radar beam off of the Venus so through precise measurements of venus and knowing that Venus passes between earth and sun, we can measure the great distance to the Sun.
@@TMartScience I want to verify the claim, because I am a scientist. I want to know how I can validate the claim, by checking if the experiment/calculation is repeatable. *Venus is just begging the question: How do I know the Sun & Venus are not closer and smaller?*
@@thomasg4324 for a discussion on the early Greek observation/ calculations of these distances, you may find this mathematical explanation helpful czcams.com/video/2R81tau1heY/video.htmlsi=deK0qgIW28Ik48X-
If you want to test both models you can. If you try to fit the angles into a Flat Earth Model, using two observations, you could conclude a small close Earth. Do you know what happens when results would fit TWO models? you keep investigating. Do you realise how little it would take to amend this method in order to test the shape of the Earth? Just add a few more measurement points. Once you add three or more observations, and plug the different angles into your Flat Earth Model, you will get _multiple_ locations and altitudes for the sun. The more observations you add, the more quickly the Flat Earth model falls apart. That problem doesn't arise on a spheroid. Adding more points of observations consistently shows that there is a change in angle of 1 degree for every 69 miles north or south.
@@jimbobeire 'The more observations you add, the more quickly the Flat Earth model falls apart.' I don't think this moron has any interest conducting experiments or making observations.
@@mazdadon1985 We have physically measured the distance along a meridian (line of longitude). From direct observations, we know the sun is directly overhead at solar noon at the equator. If we go 5000 kilometers north from the equator, the sun appears at 45 degrees depression (angle down from vertical); again, from direct observation. This also happens to be 45 degrees latitude. Cool, we know the base, and two angles of a triangle so we can find the other angle and sides. The altitude of the sun should be 5000 kilometers. . However, if we go north 2500 kilometers from the equator and do the same observations (sun at 22.5 depression), the sun is now at 6035 kilometers in altitude. . But at 7500 kilometers north of the equator, the sun is at 67.5 degrees depression, meaning the sun should be 3100 kilometers altitude. . Three separate observations, each contradicting the other. How is that possible?
An impressive explanation! keep such things up.
Thank you for a very good explanation. Inspiring, I will try to do this measurement:)
What a genius
I learned a lot from this video but there are different explanation of different videos out there on how he computes the circumference of the Earth.
The Eratosthenes Pizza explanation is very helpful for understanding the geometry of the "slice" of Earth near Alexandria and Syene, Egypt. I will be sure to try the experiment to see if I could measure the circumference of the Earth.
I have some basic instructions for doing this with students...if you are interested, I am happy to share it...
good job
At first, I took issue with you using the equator as your reference point… but then I realized you said Autumnal equinox!
great
Thank you ! I wrote a worksheet based on your video that I plan to use with my students next week. I will definitely be giving credit using this video link. Please let me know if that is enough.
I developed a class lab for students to actually repeat eratosthenes measurements. Every year I would have students measure the earth. If you would like more info about this, send me a message at "tmartclimber" at Gmail
Interesting
How was he able to know exactly where the sun would be in one city while he was in another ? Can this be replicated today ? I have been searching for recent videos that calculate the earth circumference using the method today
It was recorded, it was known that every year on or about the 21st of June the sun would shine directly down the well... Another example of why documenting observations and record keeping furthers our collective knowledge.
At local apparent noon the shadow cast by the Sun is at its shortest. In Syene the Sun casts no shadow at LAN, in Alexandria you would measure the shadow every few minutes before and after LAN. The shortest shadow is the one you would use to calculate the angle.
🤝🏻
This is a very brilliant experiment and Very well Explained, I thank you. However , the way I see it, it would only work if Syene is on the same Longitude as Alexandria. How would Eratosthenes know if they are on the exact same Longitude and the distance of 925 km is indeed the distance between the 2 latitudes
@@aemrt5745 Well if the 2 places are not on the same longitude the 925 km distance being indicated would be greater than the distance between the 2 latitudes thus his calculations would end up being inaccurate
@@aemrt5745 yes that's what I am talking about. I think he was lucky that they were close to each other latitude wise, compared to longitude. Otherwise, his calculations would've been way off
@@aemrt5745 And Thanks for all the Math! 👍
@@aemrt5745 lol I apologise for the late response, busy at work.
I didn't understand how he found 7 degrees from the pole to the sun ray?
If you understand trigonometry, measure the length of the shadow, measure the length of the object causing a shadow. Divide those two then that will be the tangent of the angle. If you do not understand trigonometry, draw a smaller scale triangle and measure the angle with a protractor.
I found another video in the recommended that explained it in a better way, thanks anyway for the quick reply@@TMartScience
3:32 did he use an instrument to measure the angle? He even got a decimal.
He likely used basic trigonometry. By measuring the height of an object and the length of the shadow, the angle can be easily calculated.
According to legend, he used an open well in Syene, and an obelisk's shadow in Alexandria, on two separate summer solstices.
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 understand your question... but no need to have communication to measure the sun angle at the same time. It was well documented that the sun shown to the bottom of the well in Syene at solar noon on the solstice. Therefore, the sun angle measurement in Alexandria needed to be completed at solar noon on the solstice. This works as long as the measuring location and the location of a direct sun are on a shared meridian (same longitude)
There is no need for a watches, only some observation.
When he first puts the stick on the ground before noon, there will be a shadow. As it gets closer to noon, the shadow will keep getting shorter and shorter until it's exactly noon, then the shadow will start getting longer and longer. The exact moment the shadow starts getting longer is considered noon.
I think thats how it works.
Note: The video mentions that it should be on the solstice and the measurements should be on the same longitude.
Is my comment right? Does it make sense?
@@Name-is2bp yes... correct
@@TMartScience okay thanks
The nane is exact delivering from word error 😂👆
Coincidence? I don’t think so
*Um....two things:*
1) Why is it assumed the sunrays are parallel?
2) Syene is over 600ft above sea level.
#1. They effectively are parallel due to the sun's great distance. While technically, they do diverge, the divergence at Earth is basically imperceptible, especially with primitive measuring tools.
#2 this amount elevation is insignificant over these distances.
@@TMartScience
How do I know the Sun is not closer & smaller than what is taught to me? I want to know how I can verify the religious claims being spewed to me as though they were scientific.
@@thomasg4324 at the time of Eratosthenes, this would have been difficult. If you want to know more about how we learned the distance and therefore the size of the sun, the very early measurements were using geometry and the very rare occurrence of when the planet Venus transits the sun. As of the 1960s, we can bounce a radar beam off of the Venus so through precise measurements of venus and knowing that Venus passes between earth and sun, we can measure the great distance to the Sun.
@@TMartScience
I want to verify the claim, because I am a scientist. I want to know how I can validate the claim, by checking if the experiment/calculation is repeatable. *Venus is just begging the question: How do I know the Sun & Venus are not closer and smaller?*
@@thomasg4324 for a discussion on the early Greek observation/ calculations of these distances, you may find this mathematical explanation helpful czcams.com/video/2R81tau1heY/video.htmlsi=deK0qgIW28Ik48X-
1st step,... Presuppose a globe. Begging the question fallacy.
Not such a radical idea considering, the spherical earth, had been proposed three centuries earlier!
If you want to test both models you can.
If you try to fit the angles into a Flat Earth Model, using two observations, you could conclude a small close Earth.
Do you know what happens when results would fit TWO models? you keep investigating.
Do you realise how little it would take to amend this method in order to test the shape of the Earth? Just add a few more measurement points.
Once you add three or more observations, and plug the different angles into your Flat Earth Model, you will get _multiple_ locations and altitudes for the sun.
The more observations you add, the more quickly the Flat Earth model falls apart.
That problem doesn't arise on a spheroid. Adding more points of observations consistently shows that there is a change in angle of 1 degree for every 69 miles north or south.
@@jimbobeire what model? Are you trying to strawman a flat earth model or just committing a harmless reification fallacy?
@@jimbobeire 'The more observations you add, the more quickly the Flat Earth model falls apart.'
I don't think this moron has any interest conducting experiments or making observations.
@@mazdadon1985
We have physically measured the distance along a meridian (line of longitude).
From direct observations, we know the sun is directly overhead at solar noon at the equator.
If we go 5000 kilometers north from the equator, the sun appears at 45 degrees depression (angle down from vertical); again, from direct observation. This also happens to be 45 degrees latitude.
Cool, we know the base, and two angles of a triangle so we can find the other angle and sides. The altitude of the sun should be 5000 kilometers.
.
However, if we go north 2500 kilometers from the equator and do the same observations (sun at 22.5 depression), the sun is now at 6035 kilometers in altitude.
.
But at 7500 kilometers north of the equator, the sun is at 67.5 degrees depression, meaning the sun should be 3100 kilometers altitude.
.
Three separate observations, each contradicting the other.
How is that possible?