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Looking for a proof different from the standard proof(s) of a result

35 votes
17 answers
6k views

Which theorems have Pythagoras' Theorem as a special case?

Loomis famously wrote hundreds of proofs of Pythagoras' Theorem (reference below), but these are all basically proofs "from below". Today on Twitter @panlepan mentioned Carnot's theorem which has Pyt …
3 votes
0 answers
106 views

Examples of "proof by generalising" [duplicate]

In a previous post I asked (Which theorems have Pythagoras' Theorem as a special case?). Are there any compelling examples where it is significantly "easier"/"simpler" to prove a more general or more …
2 votes

Theorems with many proofs

I think two important characteristics are The importance of the theorem itself The extent of connections within the subject These two are not, of course, mutually exclusive! This book is a recent di …
Chris Sangwin's user avatar