A new angle on ancient trigonometry
13 August 2021
For some people, the word “trigonometry” conjures up images of right-angled triangles, or maybe even our old friends sine, cosine and tangent. And that may mean tears of blood, as “trigonometry” is a trigger for many from their school days.
But without “trig”, architects would botch your new extension, GPS wouldn’t exist – and I would hate to see what a CT scan would do to you if we didn’t understand trigonometric functions as we shot X-rays at your flesh.
You may recall an old Greek chap, Pythagoras, and some of the many discoveries attributed to his name. Most famously, perhaps, is Pythagoras’ theorem, which gives us this Pythagorean equation: a2 + b2 = c2 . This tells us that if we have any right-angled triangle, the sum of the squares of the perpendicular sides is equal to the length of the hypotenuse squared.
Any three positive integers that satisfy the Pythagorean equation are known as “Pythagorean triples”. For example, (3,4,5) is a Pythagorean triple because 32 + 42 = 52. A less obvious Pythagorean triple is (140, 171, 221), and we know that, as often happens in maths, there is an infinite number of these things.
However, over a thousand years before Pythagoras even set foot on Earth, the Babylonians were not only aware of Pythagorean triples, they were using them in sophisticated ways.
Ancient Greeks were said to have discovered trigonometry. But Australian detective work gives the kudos to the Babylonians, about a thousand years before Pythagoras.
More:
https://cosmosmagazine.com/science/mathematics/babylonian-tablet-trigonometry-pythagorean-triplets/
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I tried squaring 32 and 42 and added the results together and came up with 2788. 52 squared is 2704.
Oh, now I see- they meant 3 squared (which is a very small number 2) plus 4 squared equals 5 squared.
And the three three-digit numbers check out, also.
RIP and three cheers for the brilliant Babylonian mathematicians and Pythagoras for figuring out these kinds of things in an age of no calculators or computers. 
