- Trigonometric proofs of the Pythagorean theorem are rare, because many trigonometric identities depend on the Pythagorean theorem, so it's easy to end up with an argument that is in fact circular.
- Nevertheless, there have been a handful of trigonometric proofs in recent decades.
- These two students have come up with a new trigonometric proof, and it is a nice one too (“could well be the most beautiful and simplest trigonometric proof we have seen to date”). That is the novelty/notability.
Note that this is consistent with the talk abstract (quoted in https://news.ycombinator.com/item?id=35498423) — they don't claim to have the first trigonometric proof, just that “in our lecture we present a new proof […] based on a fundamental result in trigonometry—the Law of Sines—and we show that the proof is independent of the Pythagorean trig identity”. Pretty cool work IMO.
- Trigonometric proofs of the Pythagorean theorem are rare, because many trigonometric identities depend on the Pythagorean theorem, so it's easy to end up with an argument that is in fact circular.
- Nevertheless, there have been a handful of trigonometric proofs in recent decades.
- These two students have come up with a new trigonometric proof, and it is a nice one too (“could well be the most beautiful and simplest trigonometric proof we have seen to date”). That is the novelty/notability.
Note that this is consistent with the talk abstract (quoted in https://news.ycombinator.com/item?id=35498423) — they don't claim to have the first trigonometric proof, just that “in our lecture we present a new proof […] based on a fundamental result in trigonometry—the Law of Sines—and we show that the proof is independent of the Pythagorean trig identity”. Pretty cool work IMO.