Talk:Test for Vectors as Sides of Equilateral Triangle

I thought to make it a Theorem. --Telliott99 (talk) 10:05, 5 November 2023 (UTC)

It is suboptimal to copy one page and move it into another. Someone then has to go and decommission the other page, with all the irritation that goes with it.

Besides, it needs a better name.

Does this actually have any use outside of Napoleon's Theorem? --prime mover (talk) 10:19, 5 November 2023 (UTC)

The general test (for sides of regular polygons) would be applicable to many similar constructions. Perhaps this is better as the Lemma that it was. --Telliott99 (talk) 10:52, 5 November 2023 (UTC)

Well as for me, I can't see its intrinsic worth in the first place. --prime mover (talk) 12:39, 5 November 2023 (UTC)

I'm thinking you're not a fan of vector proofs, at least not the way I've been doing them. But there are others on ProofWiki.

The main reason I've pushed this instead of bailing out is that the method can give a very simple proof for the Variant of Napoleon's Theorem. In fact it's the identical proof, down to the components of the paths. I suspect that means there's some sophisticated way of showing that the main Theorem and the Variant are the same problem.

All very well, but if a simple proof requires endless fiddly detail like this, then it's not really simple. --prime mover (talk) 16:35, 5 November 2023 (UTC)

There may well be a standard proof for the Variant from the Law of Cosines, but I haven't really tried yet. It gets to be such a mess with everything in the same region. --Telliott99 (talk) 14:57, 5 November 2023 (UTC)