A question about the 'Thales' theorem

[Kyriakos]

The theorem usually attributed to Thales (for example by Aristotle and Eucleid) was the 7th century BC theorem (and proof) that if a triangle has its hypothenuse be the diameter of a circle, then the angle formed by its two other sides will always be 90 degrees (ie a right angle).



I tried to search for the background enabling this, and wiki mentions that the known background was:

-The (proof/axiomatic/both) setting of the degrees of a circle at 360
-The (proof/axiomatic/both) conclusion that a triangle has a total of 180 internal angle degrees.

So i would like to ask if anyone can direct me to info about how the two above were established They might have been pre-Greek, unlike the Thalesian theorem, for example they could be Babylonian (or even Indian originally).

[Aulus]

Mathematical proofs aren't my forte, but I did find these handy sources, I hope they help you in what you're seeking.

Euclid's Elements with nifty Java applets: http://aleph0.clarku.edu/~djoyce/java/elements/toc.html (specifically Books 1 (Angles,Triangles) and 3 (Circles))

Regarding 360 degrees in a circle: http://mathforum.org/library/drmath/view/59075.html and http://mathforum.org/library/drmath/view/52546.html

It appears you are spot on about the Babylonians introducing 360 degrees. Thank you for asking the question ; I wouldn't have thought to look it up, and would have just assumed it was a proof Euclid once did.

[Kyriakos]

Thank you for the info

Setting 360 as the degrees creates a rather interesting (probably by chance, but it is elegant/useful) property, that the outer angles (entire outer angles, not just the ones formed by the expansion of each line) of a triangle now is set to 900 degrees
It should be noted that the ancient Greek number system also was 9-digit, like the later Arabic was. Not sure what the Babylonian one was.