Base 60 (sexagesimal) - Numberphile
video description
Date: 2022-04-08
Related videos
Comments and reviews: 9
Lord
Why don, t we use 2520 degrees in a circle. 2520 is the smallest number divisble by all the numbers from (1-10) whereas using 360 degrees you can divide it by all numbers between (1-10) except 7.
360/1 = 360
360/2 = 180
360/3 = 120
360/4 = 90
360/5 = 72
360/6 = 60
360/7 = 51. 428.
360/8 = 45
360/9 = 40
360/10 = 36
If we use 2520 we can easily draw septagons
2520/1 = 2520
2520/2 = 1260
2520/3 = 840
2520/4 = 630
2520/5 = 504
2520/6 = 420
2520/7 = 360
2520/8 = 315
2520/9 = 280
2520/10 = 252
reply
Why don, t we use 2520 degrees in a circle. 2520 is the smallest number divisble by all the numbers from (1-10) whereas using 360 degrees you can divide it by all numbers between (1-10) except 7.
360/1 = 360
360/2 = 180
360/3 = 120
360/4 = 90
360/5 = 72
360/6 = 60
360/7 = 51. 428.
360/8 = 45
360/9 = 40
360/10 = 36
If we use 2520 we can easily draw septagons
2520/1 = 2520
2520/2 = 1260
2520/3 = 840
2520/4 = 630
2520/5 = 504
2520/6 = 420
2520/7 = 360
2520/8 = 315
2520/9 = 280
2520/10 = 252
reply
TheKurikid
Yes and no. 12 has been brought up (see Numberphile's -base 12- video, but not as a replacement for 60.
As for replacing it: We know that 60 is the smallest number to be divisible by all numbers 1-6. The smallest number to be divisible by all the numbers 1-7 is 420. A base 420 counting system is ridiculous.
If you just mean in terms of dividing time, then also remember that 60 is good because 60 x 60 x 24 seconds is 1 day, whereas the aforementioned 420 doesn't fit as nicely into a day.
reply
Yes and no. 12 has been brought up (see Numberphile's -base 12- video, but not as a replacement for 60.
As for replacing it: We know that 60 is the smallest number to be divisible by all numbers 1-6. The smallest number to be divisible by all the numbers 1-7 is 420. A base 420 counting system is ridiculous.
If you just mean in terms of dividing time, then also remember that 60 is good because 60 x 60 x 24 seconds is 1 day, whereas the aforementioned 420 doesn't fit as nicely into a day.
reply
BadHombre
The Babylonian counting system evolved around an economy based on poppy. Ten plants are efficiently stacked 1, 2, 3, 4 in a 60 degree arc segment, of which 6 completes a circular plot. This is reflected in the symbols; for the digits 1-9 plants and then 10 is folded into the arc segment. These plots can then be efficiently stacked with hexagonal packing, where each is surrounded by 6 others.
So, from planting, harvesting and trading, they could very efficiently count their product.
reply
The Babylonian counting system evolved around an economy based on poppy. Ten plants are efficiently stacked 1, 2, 3, 4 in a 60 degree arc segment, of which 6 completes a circular plot. This is reflected in the symbols; for the digits 1-9 plants and then 10 is folded into the arc segment. These plots can then be efficiently stacked with hexagonal packing, where each is surrounded by 6 others.
So, from planting, harvesting and trading, they could very efficiently count their product.
reply
Gary
Actually, the place to start is Sumerian astrology. Their cosmology believed the circle was the -perfect shape, - that the earth was a circle (disk, and the planets traveled circles. They observed the -365 days of a year. Since 365 lacks symmetry it can't be -perfect. - 360 has periods of 60, and 90. The Sumerian idea that a temple Holy Day didn't -count- as a day was the answer. The obvious Holy Days (the equinox, and solstice days, + one or two more) made the -real- 360 day year work.
reply
Actually, the place to start is Sumerian astrology. Their cosmology believed the circle was the -perfect shape, - that the earth was a circle (disk, and the planets traveled circles. They observed the -365 days of a year. Since 365 lacks symmetry it can't be -perfect. - 360 has periods of 60, and 90. The Sumerian idea that a temple Holy Day didn't -count- as a day was the answer. The obvious Holy Days (the equinox, and solstice days, + one or two more) made the -real- 360 day year work.
reply
0623kaboom
um it is not that 360 is nearly a seasonal year but the actual calendar they used like the Mayans. a 360 minor parts with 260 major parts. to get the long count. all civilizations prior to chirstians conquering peoples and enforcing their dogmatic date system on them they all had a seasonal 365. 25 day calendar for taxation and planting and used a 360 day and a 260 day count. a little basic research and you would have known that instead of propagating the lie of modern science
reply
um it is not that 360 is nearly a seasonal year but the actual calendar they used like the Mayans. a 360 minor parts with 260 major parts. to get the long count. all civilizations prior to chirstians conquering peoples and enforcing their dogmatic date system on them they all had a seasonal 365. 25 day calendar for taxation and planting and used a 360 day and a 260 day count. a little basic research and you would have known that instead of propagating the lie of modern science
reply
Mehul
Interestingly, Indian children were taught to count on their knuckles but in base 60 until my father's generation, following which we began to learn to count on our fingers. As a boy, I would find it strange that my father counted on his knuckles in trying to teach me, while I just couldn't get the hang of it. And then, of course, I could calculate mentally and didn; t need to bother. Thank you for a great video!
reply
Interestingly, Indian children were taught to count on their knuckles but in base 60 until my father's generation, following which we began to learn to count on our fingers. As a boy, I would find it strange that my father counted on his knuckles in trying to teach me, while I just couldn't get the hang of it. And then, of course, I could calculate mentally and didn; t need to bother. Thank you for a great video!
reply
Gary
A circle divided in half (with a -count- of 360 degrees) gives straight 180 degree lines, and in quarters a right angle of 90 degrees. The application to piling up mud bricks, and laying lines for the first cities are obvious. They also had a 10 day market calendar, and you can imagine the interesting combinations. We owe the mathematics of trigonometry to the Sumerians and their circle obsession.
reply
A circle divided in half (with a -count- of 360 degrees) gives straight 180 degree lines, and in quarters a right angle of 90 degrees. The application to piling up mud bricks, and laying lines for the first cities are obvious. They also had a 10 day market calendar, and you can imagine the interesting combinations. We owe the mathematics of trigonometry to the Sumerians and their circle obsession.
reply
Jake
Actually, the Babylonians didn't choose base 60 because of its many factors, it was created because two different cultures (one that uses base 10 and the other uses base 6) were combined, and they created the base 60 system so everyone from both cultures could understand the number system. When you look at how they wrote numbers, you can see how it feels like a combination of base 10 and base 60.
reply
Actually, the Babylonians didn't choose base 60 because of its many factors, it was created because two different cultures (one that uses base 10 and the other uses base 6) were combined, and they created the base 60 system so everyone from both cultures could understand the number system. When you look at how they wrote numbers, you can see how it feels like a combination of base 10 and base 60.
reply
TheKurikid
Yes, but it would have hindered the discoveries that they DID make, because the calculations would be more complicated with such a dreadful counting system. Also, the Babylonians lived thousands of years ago, not hundreds (well, somewhere from -1000 to 4000 years ago; not sure where the culture disintegrated exactly. They would have had to discover electricity first.
reply
Yes, but it would have hindered the discoveries that they DID make, because the calculations would be more complicated with such a dreadful counting system. Also, the Babylonians lived thousands of years ago, not hundreds (well, somewhere from -1000 to 4000 years ago; not sure where the culture disintegrated exactly. They would have had to discover electricity first.
reply
Add a review, comment
Other channel videos
