4 ms·
for completeness, here is a reference to the AMS presentation. https://meetings.ams.org/math/spring2023se/meetingapp.cgi/Paper/23621 https://meetings.ams.org/ma
by nolamark 4y ago
for completeness, here is a reference to the AMS presentation. https://meetings.ams.org/math/spring2023se/meetingapp.cgi/Paper/23621 https://meetings.ams.org/math/spring2023se/meetingapp.cgi/Pa...
[my post updated to include abstract]
Abstract
In the 2000 years since trigonometry was discovered it's always been assumed that any alleged proof of Pythagoras’s Theorem based on trigonometry must be circular. In fact, in the book containing the largest known collection of proofs (The Pythagorean Proposition by Elisha Loomis) the author flatly states that “There are no trigonometric proofs, because all the fundamental formulae of trigonometry are themselves based upon the truth of the Pythagorean Theorem.” But that isn’t quite true: in our lecture we present a new proof of Pythagoras’s Theorem which is based on a fundamental result in trigonometry—the Law of Sines—and we show that the proof is independent of the Pythagorean trig identity \sin^2x + \cos^2x = 1.
- hgsgm 4y agoNote that in math "flatly" means "asserted without proof", not "incontrovertible". "Trigonometry" is not formally defined, so Loomis's statement is merely tautological.
- dullcrisp 4y agoMaybe this is my mathematical background, but is that not the common meaning of “flatly” stating something?
- deleted 4y ago[deleted]
- alex_smart 4y agoThe trigonometry thing is simply a marketing gimmick for this proof. There is no more or less trigonometry in this proof than there is in Einstein's proof. In fact, they could just as well have taken Einstein's construction and reformulated that proof in their language by using sine rule instead of similar triangles. But then the gimmick would be too obvious. Somehow the second gimmick (the infinite series construction instead of Einstein's elegant and simple construction) makes our monkey brains not notice the first gimmick.