Talk:Napoleon's Theorem
There is a simple proof using "vectors" without coordinates.
$v$ (like a standard vector $\mathbf{v}$), is specified by two points drawn in the plane and a direction drawn as an arrow representing the vector. But there's no coordinate system.
If the two points coincide $v = 0$.
$-v$ is $v$ with reversed direction: $a + (-a) = 0$
A closed path is $0$ since if $a + b + c = - d$ then $a + b + c + d = 0$.
Rotations are transformations defined, for example, as one-third of a full turn in a given direction. Then $v' ' ' = v$, for example.
I don't know if there's anything like that already here or whether it's too sloppy to be rigorous. But the proof of Napoleon's Theorem is very simple (and pretty) using this approach.
Broken Link
I'm trying to understand the links that go through books like David Wells. These link in this order:
Napoleon's Theorem/Historical Note
which doesn't exist. Likely my fault. Note that next in the first one is listed as something different. --Telliott99 (talk) 02:09, 8 November 2023 (UTC)
- No, it just hasn't been posted up yet. Can't do everything all at once. I don't understand the comment about the first one. --prime mover (talk) 06:12, 8 November 2023 (UTC)
- To see the problem, look at the source for Morley's Trisector Theorem:
- 1991: David Wells: Curious and Interesting Geometry ... (next): Morley's triangle
- next links to Napoleon's Theorem/Historical Note --Telliott99 (talk) 11:47, 8 November 2023 (UTC)
- What is it about this which makes it a problem? --prime mover (talk) 11:55, 8 November 2023 (UTC)
- The mismatch in: next = Napoleon's Theorem/Historical Note|entry = Morley's triangle. --Telliott99 (talk) 12:00, 8 November 2023 (UTC)
- There is no mismatch. I'm confused. What do you think it should be? --prime mover (talk) 14:45, 8 November 2023 (UTC)