Using spaced repetition systems to see through a piece of mathematics (2019)
If you want to see how some very simple notations greatly simplifies some math, check out J. H. Conway's proof of Morley's theorem.<p>Background: Morley's theorem is a non-trivial theorem in planar euclidean geometry stated in 1899 (first proof appeared 15 years later). The proofs are not easy. One can use complicated trignometry identities to prove it. Even the "simple" proofs are sometimes quite involved.<p>Conway introduced some notation and almost trivialized it. The notation he introduced was just a* := a + 60 where a is the degree of an angle. No one would believe this notation can do anything good, but with them (and some other insight) Conway can explain the proof in just a few sentences! (One might think anyone who understand that the interior angles of a triangle will always have a sum of 180° can come up with this simple proof, but that just didn't happen for 100 years until Conway revealed it.)<p>See page 3-6 here: <a href="http://thewe.net/math/conway.pdf" rel="nofollow noreferrer">http://thewe.net/math/conway.pdf</a>