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Babylonians by degrees

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1168004.  Thu Jan 07, 2016 4:04 pm Reply with quote

I have long had a quibble with the easy assertion (also made by mr. Fry on Series M episode 5) that 360 degrees in a circle are because of the Babylonian sexagecimal system.

The problem is that a sexagecimal system should work with factors of 60, and 60^2= 3600, not 360 which equals 6x60. Some sort of explanation is needed as to why the Babylonians would have chosen to multiply 60 by the number 6, which in this context is rather random. It would have been a much more comfortable fit if they had called a full circle 60 degrees or 3600 degrees.

Personally, I can only assume it has to do with trying to use regular hexagons to approximate and measure the circumference of a circle. They must have used the equilateral triangle as their standard, making its internal angles the standard angle and therefore calling such an angle the easiest thing they knew, 60 (equally, had I invented trig and decided that an equilateral triangle was the standard, I would have called its internal angles 10 or 100 degrees each). Subsequently, when inscribing shapes into circles, they found the hexagon to be the best fit and a regular hexagon is partitioned in six equilateral triangles, so six of those standard angles.

In any case the assertion that 360 degrees is due to a sexagesimal system surely takes some explaining...

1168013.  Thu Jan 07, 2016 4:49 pm Reply with quote

You're correct that the number of degrees is a circle does not come directly from their use of a sexagesimal system. I mentioned this before in the M series discussion thread somewhere:

There are 360 in a circle because the Babylonians were avid astronomers. With there being 365 days in a year, the sun moves about 1 per day with respect to the stars.

It certainly wouldn't surprise me though if they went for 360 over a more accurate measurement because it was, to them, a nice round number.

In fact, the Babylonians did not apply degrees to angle measurement. Whilst they did do some geometry (obviously, to invent the Pythagorean theorem!), they concerned themselves only with ratios of sides in triangles, rather than the sizes of the angles.

1168018.  Thu Jan 07, 2016 5:23 pm Reply with quote

@Zziggy Thank you for your reply. I'm afraid I find some parts of your explanation not too convincing. Firstly I don't think someone who has gone to the trouble and has the accuracy to note that the sun moves one degree per day will then round up the number for convenience sake. And the statement that they did not concern themselves with degrees seems to me a contradiction for a people who measured the movement of the sun.

But then again, your guess is as good as mine all these centuries later. I for one wasn't there when it happened!

1168019.  Thu Jan 07, 2016 5:32 pm Reply with quote

Sorry, but it isn't a guess! :-P

An interesting book you might like to read (try a library though, since it's bloody expensive!) is From Eudoxus to Einstein: A History of Mathematical Astronomy, by C M Linton.

Don't forget, they didn't 'note that the sun moves one degree per day', they noted that it moves about the same amount every day and called that a 'degree' (except in ancient Babylonian).

(NB I'm not saying it's beyond contestation - but it's not me guessing.)

Last edited by Zziggy on Thu Jan 07, 2016 6:01 pm; edited 1 time in total

1168022.  Thu Jan 07, 2016 5:55 pm Reply with quote


Page 12 :)


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