Why is a Circle 360 Degrees, Why Not a Simpler Number, like 100?
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- čas přidán 24. 07. 2022
- A circle is 360 degrees But have you ever thought why is a circle not a simpler number, like 10 degrees or 100 degrees? As it turns out 360 is actually a very good number. From a purely mathematical standpoint, a number like 10 or 100 would have been more inconvenient.
You see, the number 360 is divisible by every number from 1 to 10, aside from 7. In addition to that, 360 has 24 divisors. This is the highest number of divisors for any positive whole number up to its own value of 360. This is just one of the reasons why a circle is 360 degrees.
In this video, we have discussed some other reasons that make 360 an idea number for calculations.
#circle #geometry #mathematics
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Remember a maths lesson aged 11 where we were asked, why 360°. I offered that it was highly factorisable, and the teacher was, like, meh. The answer she was looking for was that 360 was close to the number of days in a year. Pleased to be vindicated some 46 years later!
My god that's a terrible lesson
Seems that maybe it wasn't as bad as it seems:
I always thought 360 got the nod not only because it was so highly composite (I guessed that part correctly), but also because it happens to be very close to the number of days in a year, so that we have 1 second or arc being 1/60th of a minute, 1 minute of arc being 1/60th of a degree, 1 degree of arc being 1/360th of an Earth revolution (i.e., a day) and 1 Earth revolution being (roughly) 1/360th of a Solar orbit (i.e., a year). I'm sure that would have been a useful metric for early navigators to predict star positions and plot vectors therefrom.
You so smart.....
yuh
I don't think the year length was unrelated to the circular degree measurement, but it doesn't explain why we still use the system- the decimal system of metric is only like 350 years old, so it's not like there was never a chance to overturn 360 as a measurement
Fun fact: Babylonians had sixty fingers.
Interestingly they had Five fingers on one hand and four fingers with three parts each on the other hence counting sixty digits on hands.
@@indianhistorybuff No, no. They had 15 fingers on each hand and 15 toes on each foot.
Hahaha, my brother was born with 14 fingers and 14 toes. Inherited from my mothers father
@@TinekeWilliams Aha, your grandfather must have been 14/15ths Babylonian!
Yeah real funny
Thank you for explaining this. I lived for 3 decades and not even once heard anyone say why 360 is better than any other number, not even in school. I was always met with: "Well, it just is, live with it." I finally have understanding behind why that number is good for circles.
360 is also very close to the number of days in a year, so it’s better than 60 or some other highly-composite number
They tried gradian with 400 gradians in a circle. Never hit. And we have radians. Little more useful.
The Indo-Arabic decimal-place notation system has become so ingrained in our civilization that few of us are aware that it's been around for only about fifteen-hundred years. For fun, try doing multiplication and/or division using Roman numerals and you will immediately see the problem. How does one write fractions using that system? With the 360-degree system, one almost always arrives at a whole number. One thing puzzles me though: How did the Indians come to develop a 10-base system in lieu of a 12-base one?
Good explanation, but 100 would have been a better choice. 400 even better.
kinda knew the answer still watched it. coz why not
This comment will get 360 likes
PS:52 likes are huge thank you all
PS:HOLY 136 LIKED
PS: THANK
Ohmygoddddddd wow but more than 360?
You forgot the zero
Actually 90degs is actually 100grads. That is being used by metirc system. Its only americans using the degress system. Grads is easier.
@@fqdt9753I don't think anyone uses grads
Remove the “PS” for more likes! 🤡
here's a dislike to balance it out
I'm so used to the decimal way, I totally hadn't realized there is another way to count with your fingers without just lifting each individual finger. That was unexpectedly eye-opening.
My father taught my siblings and I to count using base 2 (binary). 10 fingers allows me to count to 1023. It's still my go to way of finger counting 30 years later. Always have to be careful with the number 4 though, that can be misunderstood.
@@myaccountisntthisone 132 is even worse
@@myaccountisntthisone I used this as a neat Bar Bet. Only lost once in my life. Probably you ;-)
@@myaccountisntthisone I learned another one where the fingers of the right hand count as 1, the thumb counts as 5, the fingers of the left hand are each 10, and the thumb is 50. It's a lot like tally marks, but for fingers. You can only count up to 99, but it's much easier to translate into a decimal number. I still use it in music when there's more than 10 measures of rest.
You can also use the fingers to count in a base 5 system. 5 fingers on the one hand to count 1 through 5, and the other hand counts the iterations. Similar to the video, but using the whole finger instead of each knuckle. I like using this as it allows counting more than 10 and up to 30, but is close enough to the decimal based system most people are used to. I have encountered enough practical situations in life that require counting just a few digits past 10, usually 11 to 17, hence I found it useful. For instance bi-monthly payments-every 15 days-, or biweekly payments-14 days.
I remember being quite flustered when I first learnt about radians. I thought it was incredibly stupid because I KNEW there were 360 degrees in a circle. Just wish the teacher had introduced the subject of radians by pointing out that the 360, and thus the size of a degree, is completely arbitrary.
Just wait until you discover gradians…
400 gradians to a circle…
Which is also why a kilometre is 1/40,000 of the circumference of the earth…(through Paris of course).
Would it help to know that every number system is completely arbitrary, including money?
I didn't think so. You're stuck with it.
Or 360° at the equator where each degree is 60 miles, and one minute is 1 mile (nautical mile). Kind of makes the whole time/speed distance/latitude/longitude thing work out nicely.
@@buckerjungmann Which is where the whole “statute mile” starts looking really arbitrary…
@@allangibson2408 Errr... No. a kilometre is derived from a universal unit of physics, the speed of light.
This makes a lot of sense. But why are the Americans using it then?
The irony here is that imperial units are also based on the value of divisibility... the real question is why hasn't europe switched to a decimal based system for degrees?
Never asked this question myself. But now that you have mentioned it, thanks!
There was an article in the “Journal of Irreproducible Results” between 1980-1985 that had a fabulous, detailed article about how we should switch to ten-based time. It was a very well thought out and explained article, suggesting 100 seconds in a minute, 100 minutes in an hour, etc. They even figured out how to deal with 10 days per week, 10 days per month, everything would be so easy!
Every couple of years I search for that magazine and article, with no luck. I would feel deeply indebted if somebody had a copy, or was able to find it!
The only way to be satiated now is to do it yourself. It's not much difficult.
Now you’ve got me intrigued :)
But the problem with the 10 day week would be the shifting of the weekdays, on which a lot of religious holidays depend :)
@@stylo025 yeah im sure thats the only problem
I would also like to find this.
It also has to do with calendars, time, astronomy, and living on a spherical planet. Before we used the 365 day calendar there were 360 day calendars. The 30 day months tracked the lunar cycle. 360 days/ 30 degrees to a zodiac sign equals 12 months as well. Observing the sky for navigation and charting the seasons gave us the numbers to work with.
360/15 degrees equals 24 hours in a day and the further divisions of minutes and seconds lend to our coordinate for GPS as well.
ну вот, хоть кто-то понимает логику предков
Even better, When chinese hold 365¼ degrees in a circle make their calculation more complex except representing the movement of the sun along the sky.
@@ANoticer Well, if the heavenly bodies were cubes instead of spheres then none of the math would work out the same. The video is talking about why a circle has 360 degrees so the shape of the planet is highly relevant.
Your explanation make much more sense than the one presented here. To me the heavens lunar cycles, and time keeping seem like they would be the basis for 360 degrees.
Correct
A good and informative video. I especially liked the point about highly composite numbers. A reminder too that the old British or 'Imperial' measurements of inches and feet, ounces and pounds and stones, pints and gallons are more easily divisible into halves, quarters, eighths etc - as in dry measures of wheat and liquid measures of beer etc.
Remember the great schism of 22 yards to the chain of 100 links or 4 rods.
I struggled with math in school, but I actually guessed that was going to be the reasoning because I could see that so many numbers went into 360 evenly. 👍🏻
If you get cold, stand in the corner of your home. It's always 90°.
you are very optimistic.
by this i mean it's bold to assume construction workers know what a right angle is.
Get the heck out of here
@@windhelmguard5295 Never explain your joke. Express the joke better.
Well, which degrees you mean? Because in Celsius scale (which I use daily because Europe) I would be boiled
I wanna say you're wrong, but it's right
6 circles of the same size also fit perfectly around a circle. If you use a compass you can further divide from the centers of those and make a protractor.
This is why you're THE Louis Sankey baby!
noice
Hexagons are the bestagons
@@stigcc sorry to break this to you but they are not, triangles are way better than them
4 equal circles have the same surface area as one with a diameter twice as big, also works with a circumference twice as big. 8 equal Spheres have the same volume as 1 with a diameter twice as big, etc etc. But it all reverts back to some decimal, fraction, or percental system when scaling individual measurements like having 3.561652 circles and converting to a larger one. Still a useful concept in the right aplication.
Why do parts of this video look like educational Family Guy?
Astoundingly informative!
Glad you think so!
I would make a video on this topic, but this outperforms anything I could do. Bravo!
I will definitely show this to my math class!
West doesn't necessarily Explain Best
Lol true, not with everything!
Cool teacher
East mostly sucks;)
I still think you can add to it if you would have a go at it. This video mostly explains how many dividers 360 has, and how Babylonians enjoyed their fingers. No mentions of why many circle calculations are actually done with radians and why 360 isn't better here. Also no mention of gradians either (400 degrees around the circle).
It feels so trippy to realize that other cultures used to do math in a manner so different (yet still made perfect sense!) from what we use today. Math is like the language of the universe or something.
Perhaps the pyramid builders used a more versatile mathematical system than we are assuming. Maybe that system has the answers to how the pyramids were built. Among many other "ancient mysteries"
Is it really trippy? How is it different from normal languages? They are also different yet make perfect sense.
Every mathematical statement can be expressed with a regular language. However, the inverse is not true. Human languages are actually supersets of mathematics.
Maybe that is why observations by the JWST are turning out ideas of the universe inside out. The theory, defined by mathematics, seems to be crumbling before observation.
It's just a representation system though, doesn't really affect the mathematics itself. Naturals are always the naturals.
@@PaulHarris-sl1ct
the flaws of mathematics are rather well-known, the Gödel's incompleteness theorem was a shocker in the last century but now I think people got used to it and just treat mathematics as it should be treated - a product of human very limited brain which was never meant to deal with the secrets of the universe in the first place. It is a good-enough approach and a robust language, or rather languages.
The real question is why doesnt school teach this kind of stuff
never thought of it to ask but intriguing answer
thanks
Thank God for this video!! I've thought about this issue so many times! (Although, I've usually always been too lazy to look through Google for possible answers lol) I'm glad for the first time that my Google phone must be listening to my conversations and/or reading my mind and this just happened to show up in my feed lmao. Great explanation!
Google does record a lot of your stuff you may leave online. So google does know about a lot about you.
When I was in high school, I spent about a month trying to really train myself to learn the Base 12 multiplication table. One subtle advantage of Base 10 is that it takes care of the number 5, which is actually quite "unintuitive" in division. So while 12 has more factors, 10 has the advantage of "consuming" a weird number and making it easy to divide or multiply by 5. In base 12, you face similar problems with 5 as you do with 7 in base 10 (and retain the same difficulties of 7), for only the advantage of making multiples of 3 easier to count out (which they are already quite simple in base 10).
Which’s why the best system is seximal: it has 2 and 3 as factors, and it has 5 and 7 as neighbors. This means the two most common factors are trivial, and the next prime, 5, is as easy as 3 and 9 in decimal: the divisibility test is just adding all the digits, and the inverse is just one repeating digit. It also turns 7 into 11, which’s much more convenient to work with than in decimal or dozenal: you add pairs of digits instead of single digits, and the inverse is 0.(05) repeating.
The main problem with dozenalim is, I think, is that they talk about repeating digits like they make calculations horrible and imprecise, but they’re quite simple to deal with in reality. What’s actually really annoying is when a number has a long period, like 1/7 which’s 0.(142857) in decimal and 0.(186A35) in dozenal, which are very hard to remember. Like, does anyone actually know that 1/13 in decimal is 0.(076923)? No, but it’s very obvious that 1/20 is 0.05, and that 4/9 is 0.(4)
@@felipevasconcelos6736 this is woke!!!!!
Why base 12 and not base 16 which has more use in computer stuff? :D
@@felipevasconcelos6736 most repeating decimals have 6 repeating numbers. Its not that hard to remember them.
The only problem is in some repeating decimals of fractions with denominators greater than 24 and are multiples of 3. Ex: 1/21 where it changes from 0.0476190 to 0.0952380 to 0.14285 and eventually 0.33333. (And other variations of these. like how 1/7 functions, the first digit in 1/21 moves around depending on the fraction). Numbers like x/21 are really annoying because you would need to know 3 sets of 6 numbers to memorize repeating decimals of fractions with denominators that are multiples of 3.
Aside from these numbers, most repeating decimals are very easy to memorize.
@@melonenlord2723 base 16 is used in programming but like thats just because it's base 2^4, it doesnt have anything else that makes it a good base, it's only divisible by the powers of 2 before itself [i.e. 2, 4, 8]
I feel a little more educated now. Thank you!
never questioned this, but very nice to know! thx =)
This proves how clever the Babylonians were. Yes, they didn't have the convenience of Arabic numerals. However, they were smart enough to calculate out base 60 (which we also base our notion of minutes and hours off of). Also they helped invent beer. We owe a great deal to this 6,000 year old civilization.
Agreed, just one (pedantic) correction though, it is not arabic numerals, it is Decimal / Hindu / Indian numeral. Photocopy is not xerox.
@@nyxawesome9409 photocopy is xerox
@@someonejustsomeone1469 Xerography / Photocopy is the actual invention and process. Xerox is just another company / brand using that process and commercialized it.
@@nyxawesome9409 photocopy is xerox
Well, if you check an image at 2:28, you can see that symbols were base 10. They repeat every 10 numbers.
I always thought 360 got the nod not only because it was so highly composite (I guessed that part correctly), but also because it happens to be very close to the number of days in a year, so that we have 1 second or arc being 1/60th of a minute, 1 minute of arc being 1/60th of a degree, 1 degree of arc being 1/360th of an Earth revolution (i.e., a day) and 1 Earth revolution being (roughly) 1/360th of a Solar orbit (i.e., a year). I'm sure that would have been a useful metric for early navigators to predict star positions and plot vectors therefrom.
Thanks for the video, it's a question I have many times wondered about.
Thanks for that. It’s always been something that I wondered about.
as a surveyor I'm used to grads. A full circle has 400g , each grad has 100cents and each cent has 100ccs (cents of cents)
Kinda reminds me of the arcsecond unit used in astronomy
@@givrally7634 yeah astronomy uses degrees, so does cartography and higher geodesy (elleipsoid geometry). We use grads for surveying
the kilometer is based on the grads system like the nautical mile on the degrees
I have a surveyors magnetic compass in a wooden box; it is calibrated in Grads.
I wasn't aware that grads were broken down like that.
1:35 man hit puberty instantly 💀
💀
What?
🗿
The decimal system which has become the universally adopted system for doing maths was developed in India.
I thought I would just learn some math trivia, but I actually learned something practical. I know know an easy way to count on my fingers past 10 and keep track of the tally. Thanks!
This video doesn't explain why we use 360. It explains the convenience of 360.
Exactly. It's a poor video given it's title. Furthermore, the Babylonian system also involved base 10. Every number up to 59 involves the "
convenience has its own usefulness. if it works it sticks or if it ain't broke don't fix it.
that's why we use 360. because it's convenient.
We use it because it is convenient
It does at the end. If you divide the side of an equilateral triangle by sixty which was the base for the babylonians their number system and exactly 6 equilateral triangles fit into a circle then 6x60= 360.
0:09 Us mathematicians don't even use 360°, we use 2π.
We never describe angles with degrees, but with fractions of π.
?
@@polanski2399 π=3.14159...
If you go around a sphere with a radius of 1, you cover a distance of 6.28318..., which is exactly two times pi, so it makes more sense to describe angles with fractions of this number than introducing a unit like degrees and having to convert every result in trigonometry from radians to degrees whenever you happen to encounter a circle.
@@lucahermann3040 I see, so that's what the radians mean on my calculator
@@polanski2399 exactly, it makes the calculator show the angles as the ratio to the radius of a circle.
Thats highschool level math
That the task of dividing up the circle in equal parts is so common in têchnology is probably the reason the unit for angle has resisted decimalisation. In most other measuring tasks, dividing in equal parts is not quite so common. (Adherers to systems of units based on a monarchs body parts notwithstanding)
Not surprisingly, the field where the 100° to the right angle unit 'gradian' could establis itself, surveying, does not often have to divide the circle, but measures relative angles between points on the earth.
I really loved that part about degrees from the start, it is so easily devisable. I always wondered though if the clock follows the same rule. I mean is it 12 hours and 60 minutes, because it's easily divisible, or is there another reason?
The guy at the beach at 3:36 looks like he is from Family Guy / American Dad.
A lot of people don't know about grads (gradians). It dividea a circle into 400 degrees, with a right angle being 100 degrees. It never really caught on with popularity. The 2 most popular are still standard (360) degrees and radians (multiplea of PI).
PI/2=90deg
PI=180deg
2PI=360deg
etc.
But, I would have to agree: The 360-degree system is best in a lot of ways. It is also standard in electrical engineering, with phase angles in for example inductive and capacitive circuits being measured in standard degrees.
grads did not catch on because it is a worse system than the one invented some 6000+ years ago
it had nothing to do with popularity . and yes the 6000+ years is right because it
was the sumerians and not the babylonians who came up with it
military use grads, it is easier to divide and understand i your head
@@bjorneriksson6480 I am not sure about that, we here used the which are basically aproximating miliradians and the circle was 6400. I think in English its called "mils".
I wonder why radianes were not used more...
On physics we constantly used them...
Very cool, informative and well-explained video.
Thanks for this. Appreciate it.
60 was popular with ancient mathematicians because it was the smallest number that can be divided into decades ( 10 ) and dozens (12)
60 is "5 Dozen" or "6 Decads."
The Ancients would switch between decades and dozens depending on which was easier to use in a specific situation.
Here's how they approached math.
"Multiply 7 × 49"
Instead of factoring that the way we did in school , they would see this as
7× ( 4 dozen +1 ) = ( 28 dozen and 7 )
7x ( 5 decades - 1) = ( 35 decades minus 7 )
And they would use which one was most convenient for them.
It also makes division a lot easier to do in your head.
"Divide 77 by 4"
( 6 dozen + 5 ) ÷ 4
(3 per dozen × 6 dozen ) + 5/4
18 + 5/4
"Divide 77 by 3"
( 6 dozen + 5 ) ÷ 3
2 dozen + 5/3
*Degrees:* I've got 360° for a circle.
*Everyone:* That's... an unusual number. Anyone else?
*Radians:* What about 2π? Will that work?
*Everyone:* Ugh, that's even worse. Sounds like something a math nerd came up with.
*Radians:* [shuffles nervously]
*Gradians:* Ooh, ooh, I have one. It's based on 100.
*Everyone:* Oh, that sounds easy and very metric. So 100 gradians, right?
*Gradians:* Yes! 100 gradians in a right angle.
*Everyone:* Wai.. what? In a right angle? So that means...
*Gradians:* 400 in a circle! Neat, huh?
*Everyone:* ಠ_ಠ
*Gradians:* Sooo... when do we start using it?
*Everyone:* Alright, we're going with the 360° thing... goddamn I hate math.
With 400 gradiens in a circle you don't went down so fast in a under 1 gon angle for small angles. 230 gon you can easy think about. These are 2 right angles and 30% of another added together.
The irony is that radial are way more convenient and also used a lot in science.
It's funny, how you can go through life just accepting many things without giving them much thought. This topic is one of those things for me. I never once wondered or thought about why there were 360 degrees in a circle. Thanks for piquing my interest and showing me this. It's very interesting.
Thanks. Great video. I look forward to checking out your channel. Subscribed. Cheers
Awesome, thank you!
I always asked the same question. I came up with a theory that this is the count of days for the Eart to full round the Sun. It is 365.25 days. But, it is smplified into 360 since is every month is usually 30 days (30×12=360).
Not enough convincable proofs, but that was the best I came up with.
I think this is actually more true. This is what I always heard.
The Indo-Arabic positional decimal notation system has become so fundamental to our thinking that we've forgotten how difficult and clumsy were all previous systems. For example, try doing astronomical calculations using Roman numerals and one will quickly realize why the Ancients wanted to be able to write results in whole numbers wherever possible rather than having to resort to fractions. Hence, the use of 360.
You are on the right track.
12x30 day months.
But add 1 day between every season =360+4=364.
Then have Enoch calender.
Add leap week every 7th year. And also every jubliee (50). Will keep year in synchronisation with 365.2522 solar day year.
The Babylonians (and greeks) used moon 354 days. Romans used 365. (in use today)
But the biblical year uses 364. Adam, Enoch, Noah, Abraham, Moses, David. Daniel, Jesus, John.
Good luck Brother.
One of my high school math teachers said that there were 360 degrees in a circle because it was based on 365 days in a year. He's the only person I've ever met that said that, though. Could Mr. Phillips have been right back in 1979? I've never seen it in a book!
I heard the same thing on a documentary I think. It was about the stars on the night sky which were positioned 1 constant unit apart each night same hour until the circle was completed 365 units later.
*This was easy to comprehend, nice job*
This interesting channel popped up in my feed! I’m gonna subscribe!
Awesome, thank you!
Around 5th grade we were introduced to some thing call The New Math which in essence was mathematics in different bases. It prepared us to work in binary, octal, and hexadecimal which of course are used in computer science, binary being fundamental.
It's really amazing.. You answered the question that I never think about...👍🏻
Glad you liked it 🙂
Another often overlooked argument is that 360 is very close to 365. That means de sun moves - almost - exactly 1 degree each day against the sky. That is useful for navigating at sea. And for setting dates. You just count de number of degrees the sun has moved, and you know how many days have passed.
You just commented what approximately one sixth the top commenters already commented. Good work. Very overlooked indeed.
I thought that also as a commonly admitted fact.
This comment section is the best!!!! I’m learning so much. I was a Straight A math student my entire life but I took the path towards science and I often think about what my life would be like if I’ve gotten a math degree instead.
Thanks. Well done.and very interesting.
Excellent detailing, analysis and conclusions. This short video is interesting and informative....
Glad you liked it!
This is a great video. I was wondering why 120 or 240 didn’t do the job since they’re both numbers that are fairly divisible and it’s nice to keep the number low. I wasn’t not familiar with why you would want to divide 360 by 60 degrees or anything bigger like that. Now I know that it comes from having 6 triangles.
The bit about 6 triangles of each 60 degrees is a bit circular, since the angles for an equilateral triangle is 60 degrees because you defined a whole circle to be 360 degrees. If you defined a whole circle to be 100 degrees then each angle of an equilateral triangle would be about 16.7 degrees and then you could still fit 6 equilateral triangles in a full circle with their angles adding up to a 100 degrees...
@@smittymcjob2582 but why would you want such an ugly number when you could leave yourself with a number that’s still highly composite? I don’t know the advantage of keeping the relationship between the two but at least it has an origin
@@smittymcjob2582You want to be able to divide the circle by 6
@smitty Actually, the reason 60 was picked for triangles and 360 for circles is because they are both good numbers.
@@francisluglio6611 it may look ugly represented in decimal, but in a 60 base system its not. Considering the importance of being divisible by 6 in a 60 base system, 6 * 60 is actually a super neat number to choose.
Thank you for this video!!!
I always thought 360 was better for dividing into lots of numbers, nice to have my thoughts confirmed.
One connection for 360 is that each day we travel approximately 1 degree around the sun (365 days in a year). 30 degrees per month on average gets us 360 degrees in 12 months exactly.
3:30 Hexagons are the bestagons.
Because (bonnie) bees are the best, and they make only the bestagon.
정말 흥미롭고 재밌었어요! 감사합니다❤
An interesting question would be how this might change or if it stays the same in a different base, like base 8 or base 16. I wonder about this because I know there were a number of different bases used before the decimal base became standard and that we could have had a different base become standard, and I think hexadecimal probably would have been a better base to use than decimal, but now it is too hard to change. Let's see if I can figure this out, ending numbers in "d" for decimal and "h" for hexadecimal.
360d = 168h
168h÷2h = B4h = 180d
168h÷3h = 78h = 120d
168h÷4h = 5Ah = 90d
168h÷5h = 48h = 72d
168h÷6h =3Ch = 60d
168h÷8h = 2Dh = 45d
168h÷9h = 28h = 40d
168h÷Ah = 24h = 36d
168h÷Ch = 1Eh = 30d
168h÷Fh = 18h = 24d
168h÷12h = 14h = 20d
Looks like it stays the same even when changing to hexadecimal base. I find that interesting.
Cyfry i liczby to tylko symbole graficzne reprezentujące ilość. Zmiana podstawy systemu liczbowego nie zmienia rzeczywistej ilości. "10" zapisane jako "10" lub "A" lub "1010" to dalej dziesięć inaczej zapisane.
@@szczeczaczoszczeczek5077 that is what I showed. But, there is a degree of error that often comes into converting decimal numbers into binary numbers within a computer system, because some of the conversions involve floating point operations that go beyond the the capabilities of finite binary system to deal with. This in general happens with some floating point operations where some rounding must take place at some point.
Makes programming some mathematical functions in discrete limited bit binary systems tricky.
@@MusingsFromTheJohn00 I agree in 100%. And this is beautiful.
2:22 I always thought this with time. Why is there 60 seconds in a minute (or 60 minutes in an hour)? It would be easier to make a second faster, so there are 100 in a minute (or slower, so there are 10 in a minute). I love that idea you mentioned about cutting a circle into different parts, and the 60 is nice because you can cut a clock in 3 parts with whole numbers.
Anyways, thanks for the video! LOL, the 60 seconds in a minute (60 minutes in an hour) might not even relate to this idea of divisors, and there is some other reason, but it's interesting!
A 12-base would have been the better system then the current 10-base system. Then the 60 system or 50 in 12 base would have had more usable fractions before getting into decimals. Just look how easy it is to divide a day, hour or minute into fractions.
@@Sander-zj3wi i don't think many people say "one-thirds of a day" or "one-fourth of a day", though.
@@user-pv8ob2uc6s Why would you say "one-third of a day" when "8 hours" is simpler?
But if you would like to divide a day into 5 for some reason, it could be better to say "one fifth of a day" instead of actually counting how many hours and minutes that is.
I always have a doubt. 1 min= 60 seconds, similarly 1 hour= 60 min but why is millisecond, microsecond and nanosecond different. As 1 second= 1000 millisecond. 1 millisecond= 1000 microsecond and 1 microsecond = 1000 nanosecond.
@@pokechannel9758 fractions of seconds are different. The part in front is a decimal prefix.
Milli = one thousands
Nano = one millionth
...
You can technically use them with every measure. That's why it's called kilometer and kilogramm, just 1000 times meter or gramm
I just find it amazing that our day is ALMOST 1 degree of a circle.
This idea would sound much more conclusive to me.
it's almost as if there used to be 360 days in a year but then someone corrected it when they had some kind of accurate way to measure it with a telescope
very insightful
Thanks for the video 😊
In the military, we used mils instead of degrees. 6400 mils in a circle. Mils calibration has the advantage of working well with artillery calculations, as the same unit is used to calculate distance, vertical angles and horizontal angles.
Mils for distance? I'm quite intrigued! Tell me more about this system, maybe a crash course in artillery? :)
Please explain how it works.
@@darkfrei2 probably the same thing as degrees just 17.777 times smaller
@@poruzu Is it just 1/1000 of radian? Than ok, the distance can be an angle with factor 1000.
1 radian is 57.29578 degrees, 1000 times smaller is 0.05729578 and it's just 1/17.45329252 degrees, not 17.7777, but very near.
The only advantage of certain units is, people are used to integral numbers and dislike too many digits after the decimal. It's easier to speak and to memorize.
10.000 you can remember, but just speaking 0.0003 verbally is hard. (people tend to multipliy with 1 million, and call it 300 micro-units in this case, to be back to integral numbers).
Nice video !
Which software r u using to make maths animation videos
I was super confused in school in trig and calculus particularly about all the symbols. None of the courses ever explained where and how the symbols came to be. I was stuck not understanding how everyone else seemed to move through math so easily. It is true that everyone learns differently and I happen to need to understand things in detail before I can move on. One day I realized that it's all made up and that mathematics is a set of symbols manipulated via a group of standardized processes and procedures. 🤔
I like how I knew this answer without actually knowing it yet. When I read the title I thought, "100 sucks when dividing a bunch of numbers from it"
Division is why the Metric System sucks. The metric system rocks when multiplying. Standard Units suck when multiplying, but are great for dividing.
1/3 of a Meter is 33.3333333333333 cm Sucks using math after. 3 meters is 300cm easy.
1/3 of a yard is 12 Inches (aka foot). 3 yards is 108 inches (9 feet).
FYI, a mile is approx what an army can march in 15 minutes (1/4 hour) and brisk pace, and 20 Minutes (1/3 hour) at leisurely pace. Things aren't as random as it appears.
360 is a much more "simple number" than 100 because it is much more divisible, and many more numbers divide evenly into it, like the number 60.
It's also pretty close to the number of days in the year, so each day represent One degree in the motion of earth around the Sun.(approximation)
@@Altinget It was accurate enough for a lunar month/year cycle. Those calendars are wonky.
The smallest whole numbers you can use to get a right angle triangle are 3, 4, & 5. 3*4 = 12 and 12*5 = 60. Also, each day is divided into 24 hours with 60 degrees of minutiea (minutes), each of which have 60 degrees of second order minutiae (seconds).
Yes, all of which came from the ancient Mesopotamians and their base 12 counting system.
This presentation is an excellent example of human post-justification. It's predicated on the assumption of using a base 10 numeric system. Our organic creators were frequently limited in similar way, as their measuring systems were originally based on their bodies and redefined using the properties of matter shortly before they became extinct.
there happens to be roughly 360 days in a year, useful for celestial navigation.
And 24 hours a day which 24 is....1 2 3 4 6 8 12 and 24.....all can equally divide into 360. For navigating too.
this is such a good video and the explanation is brilliant but the fact that the characters depicted here look like they’re from family guy makes me crack up every time
Excellent.
Well explained
This is a very good explanation of why is it useful to have 360 degrees, but not a very good one to answer the title question: "Why is a circle 360 degrees?" Yes, it comes from Babylonians and yes they used a sexagesimal system, but this is not the core reason why. The reason for this division is their astronomical observations of the sky and their practical astrological applications. Also, it's not "one theory", the oldest written evidence of sky division into 360 'steps' comes from Babylonians, so we simply have no other evidence to the contrary.
There doesn’t need to be an explanation for a circle being 360 but rather a definition that the angle between two vectors in the same direction is 360. This helps define that a full rotation is 360 degrees and that all angles are based of the 360 degree benchmark. The video aims to make sense why 360 was the best choice rather than why 360 is a circle because by definition, the circle is one full rotation. I guess what I’m saying is that a rotation is being defined and the circle is dependent on what a rotation is.
🤓🤓🤓🤓🤓
Though I know 360 is highly divisible, I always thought it also had something to do with the Earth's rotation around the sun. Would have been nice if a year was 360 days, instead of 365.2425 days. Then each day would be one degree around the sun.
rotation isn't a fixed number anyway, so 360 would be accurate only 1 year XD but yeah, many stuff could be improved with those numbers
At some point in the history this is actually true.
Wow in India we have similar story but moon involved in it.
Reg Veda 1: 164- 11&48 says time of wheel has360 spoke.
This was the question I asked as a kid.
Finally it is answered
The first time I recall coming across the number 360 as a kid, was, when I was doing sick moves in Tony Hawks Pro Skater from `99.
I can't help wondering if someone, in ancient times, miscalculated the number of days in a year (or made up a crude 'rule of thumb' based on an approximation of that number).
Seems too much of a coincidence that the numbers are so close.
Even if they did know that 360 wasn't entirely correct, the number 360 would still be close enough, and at the same time convenient due to its number of divisors.
Fact is, from the viewpoint of early astronomers, the stars would go full circle in one year. In other words, they would move 1 degree per day. Well, really only 0.9856 degrees per day, but that difference is not noticeable to the bare eye.
Well, to a bank, when calculating interest, they usually assume a month has 30 days and a year has 360 to make things easier to process.
It is only when talking about large sums and potential gains for the bank that they remember precission.
I believe 360° , must have relation to number of days in a year on rough scale. Month to number of days between one new moon to next new moon.
It has to do with the moon cycle. After 12 lunar months you get roughly the same season and the celestial bodies are close enough. So it's easy to make that mistake in approximation of solar year.
.....or they just used lunar calendar and not a mistake.
That was probably the case, until a new king came into power after his father died, and he noticed that his birthday celebration was significantly more summery than spring-y. Those missing 5 (.24blahblahblah) days unaccounted for over a lifetime will shift the calendar off-season.
For a while I wondered why a circle was chosen to have 360° and not 100° and eventually I came up with a plausible reason (which is different than yours). There are 365 days in a year and in ancient times people thought there were 360. I think they chose to divide a circle into 360° because the Earth would then move 1° per day. (I know back then many people believed the sun revolved around the Earth but there were some people who correctly believed the Earth revolves around the sun.)
Maybe you should question your own desire for everything to be based on 10 or 100 instead. The most efficient number is 240.
You are correct. In fact, the Babylonians were able to determine that there were 365 and 1/4 days in a year, but they used 360 for a Circle because it is highly composite.
There actually were 360 days in a year, until a cataclysm slowed earth's orbit. Ancient people were neither stupid nor sloppy.
@@sixchuterhatesgoogle3824 Wow! Do you know any other things that never really happened?
That is actually indeed the reason. Ancient Egyptians had the year be 360 days + 5 extra special days that were not considered part of the year. They also had a 10 days week, which they lined up with 36 small constellations to keep track of time. There is still the factor that 360 being a convenient number, I don't recall exactly why, but it involved calculations about the size of an individual degree, and the size being divisible by 30 was the ideal solution.
Nice video.
The Babylonian approach is also the reason our clocks are running the way they are.
Hours and minutes are not made up of 60 minutes/ seconds by chance but are based on exactly the same 5x12 concept as explained in the video.
Quite cool I say.
I love Number Theory. It is just amaizing what people came up with and it is also amaizing how many dorks are still aroung
I personally prefer base 12. not that different from decimal but also a highly composite number.
despite not all divisions ending in a natural number, the only divisions that cause repeating decimals are 5, 7 and 11. (I'm not including 10 since it's dividing by 5) since 8 and 9 just need a single decimal place.
If you're trying to minimize confusing sequences like 0.142857... and what not, then why not base 6? Dividing by 1, 2, 3, 4, 6, 8, or 9 yield numbers without repeating decimals, and dividing by 5 or 7 yield numbers with repeating decimal sequences no longer than two digits (0.111... and 0.050505... respectively).
The sumerian way of counting is brilliant. The first time I heard about it I suddenly felt enlightened and understood why we have 60 seconds, 60 minutes and 360 degrees. It's also a far more useful way of counting
One of the big benefits is in crop accounting. Counting produce in sets of 60 makes them very easy to divide between 4 or 6 villages.
Minute literally means one sixtieth and second is short for second order minute (the minute of a minute).
i think is useful for circle related calculation
And a year is about 360 days…
That's one of my big questions in my younger years. Thank you.
Did they invent 60 minutes with that base 60 system as well?
Wow! Mind blowing!
I always thought that the main reason for 360° is that it is the nearest highly composite number to 365.25, number of days in a solar year. Thus the celestial dome shifts by about 1° every day.
Moreover, in Greek the words "degree" and "day" sound similar, so I thought 1 day is a rotation of 1 degree around sun, not sure if it is the case, though.
@@user-uc5tq7gh2e I don't think that's an accident, that was the assumption most pre-Julian calendars worked on, with an extra 5 or 6 leap days to stick in at some point, which was often done as part of some religious festival. It actually only moves about 59 minutes 8 seconds per day (360/365.25), hence the need for the leap days, but the difference really wasn't measurable on any reasonable time before Kepler in the 17th century and was not measurable for any practical purposes (like navigation) until the invention of the sextant in the 18th century, only then were more precise tables really necessary. In the ancient and even through the medieval world, one degree per day would have been the assumption pretty much all navigators worked with.
You are correct.
Could you imagine a numbering system based PI, just to make circles friendly.
So basically Radians but as a numbering system
i have thought a lot about this lately. i have concluded its impossible because Pi is irrational. i think this also why its impossible to square a circle.
@@markwelschmeyer2426 That's not the problem. You can have irrational bases, like the golden ratio. The statement that it's impossible to square a circle is actually a statement about straightedge and compass constructions, and those can bisect angles, so they can make many irrational lengths and areas.
So if we take a number like 2520 which is divisible by all number from 1 to 10 then will it be better than 360, right?
I think so. The way I look at it is the more degrees you have in the circle, the more accurate you could be. Especially dividing a circle or trying to do equations
Actually yeah...but 360 has been very well established alredy that there is no chance for that to change...
and us surveyors use grads, full circle is 400, then 1 grad is 100 grad minutes, 1 minutes is 100 grad seconds. Way easier to compute and count :) Plus its more accurate
it is 2 pi
calculations are not done by degrees
degree is just representation after the caculations are done
you could do them in degrees tho.
But then if f(x)=sin(x)
then f'(x)=cos(x)*360/(2π)
which is inconvinient
This is the most amazing explaination about "why full circle/angle is 360" that I have ever heard
What was the worst and what was the runner up?
Also, that after degrees, minutes and seconds are used in lat/long, which are also in 60s.
I always thought it was because of the yearly cycle -- the solstices and equinoxes divide the year up into 4, and the lunar cycle divides each of those sections, roughly, into, 3. So I at least thought the factor of 12 stemmed from that, and then a month was roughly 30 days, so round 365.25 to 360 to make the math simpler. Not sure if that even contradicts what is said in the video, but I was surprised this aspect wasn't mentioned.
I used to think that 365 days in a year roughly translated to 360 degrees, that the movement of earth in one day is approximately 1 degree.
Me to 😅
that's correct though
yeah, 360 is cool and all... but 2pi is the king 👑
I enjoyed this article 😀.
Thanks for sharing team 😊
Our pleasure!