Talk:Test for Vectors as Sides of Equilateral Triangle
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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)