Forget trigonometry, 'cos Babylonians did it better 3,700 years ago – by counting in base 60!

Source: The Register
Published: Aug 25, 2017
Author: Simon Sharwood
Post Date: 2017-08-25 11:26:09 by Deckard
Views: 2841

greek vs. babylonian triangles

Greek vs. Babylonian triangle workings-out

Those of you who can remember trigonometry can feel free to forget it, because ancient Babylonian mathematicians had a better way of doing it – using base 60!

That's the conclusion of a new paper, Plimpton 322 is Babylonian exact sexagesimal trigonometry, in the new issue of the journal Historia Mathematica.

The “Plimpton 322” from the title is a clay tablet inscribed with cuneiform script. Discovered in the early 1900s, the tablet has been of interest to mathematicians for years because it describes Pythagoras' theorem, yet is thought to have been created around 1800BC, more than a thousand years before Pythagoras was born and started tinkering with triangles.

The rest of the tablet's four columns and fifteen rows of numbers have been debated for some time, but in the paper Daniel Mansfield and N.J. Wildberger, both of the University of New South Wales' School of Mathematics and Statistics, suggest it was a trigonometric table.

Mansfield explains his work in the video below:

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#1: Tooconservative    To: Deckard (#0)

This doesn't surprise me at all.

Every number base has its peculiar advantages for certain types of problems, just as binary and hexadecimal are so vital to computer work.

Tooconservative posted on 2017-08-25 12:51:52   Reply   Private Reply

#2: Pinguinite    To: Deckard (#0)

The base 10 system we use today really offers no advantages that I know of. I've always imagined base 10 is the human norm because we have 10 fingers. Base 12 would probably be far more advantageous as it's evenly divisible by twice as many numbers as 10 is.

Pinguinite posted on 2017-08-25 12:56:38   Reply   Private Reply

#3: Justified    To: Pinguinite (#2)

Base 10 is best. As an American brought up with Imperial system I can tell you base 10 is the way to go. Easy to understand and manipulate. I like to play around with metal working and thats when I started noticing the advantages of the base 10. I suppose it all comes down to what you are working on to the tool needed.

Even binary system is nice but cumbersome to humans.

Justified posted on 2017-08-25 13:27:16   Reply   Private Reply

#4: Pinguinite    To: Justified (#3)

Base 10 is best. As an American brought up with Imperial system I can tell you base 10 is the way to go. Easy to understand and manipulate. I like to play around with metal working and thats when I started noticing the advantages of the base 10. I suppose it all comes down to what you are working on to the tool needed.

We all have experience with the base 10 system, but none with a base 12 system. I would question the credibility of any claim that 10 is better than 12 based on experience when there is clearly no one with experience with base 12 system.

It's a clear fact that 12 divides much more cleanly much more often than 10 does. For multiplying, either is fine, but when it comes to dividing, it's a different story.

Pinguinite posted on 2017-08-25 13:43:05   Reply   Private Reply

#5: rlk    To: Deckard (#0)

Forget trigonometry, 'cos Babylonians did it better 3,700 years ago – by counting in base 60!

I don't believe it. Just another pipsqueek looking for attention.

rlk posted on 2017-08-25 14:40:12   Reply   Private Reply

#6: Hank Rearden    To: Pinguinite (#2)

Base 12 would probably be far more advantageous as it's evenly divisible by twice as many numbers as 10 is.

Yes, there's a lot of sense in that; we're just used to being able to count on our fingers from the cave days.

A couple more symbols tacked on after the number 9 and it would be just as natural - if we'd grown up with it.

Hank Rearden posted on 2017-08-25 15:54:46   Reply   Private Reply

#7: misterwhite    To: rlk (#5)

I don't believe it. Just another pipsqueek looking for attention.

I agree. It's like they're saying, "Look what we found. It's very important because we say it is."

Base 60. Pffft! They still need a trig table so what good is it?

Ever hear of the ruins of Babylon? There you go. Shows you how much good that Base 60 system did them.

misterwhite posted on 2017-08-25 17:37:50   Reply   Private Reply