Talk:Archimedes' Limits to Value of Pi

I have worked up Archimedes actual calculations for this, but not sure how to integrate them into a proof. I have also written a sketch of a proof for the lower bound. It's at User:Telliott99/Sandbox. Not sure if this is like what you're looking for. --Telliott99 (talk) 02:48, 22 October 2023 (UTC)

Someone else may have to do this because I have other things planned today, sorry --prime mover (talk) 06:17, 22 October 2023 (UTC)

As to the objection that the proof is inelegant, I am simply following Archimedes. --Telliott99 (talk) 14:44, 26 October 2023 (UTC)

A lot of the inelegance stems from the excess wordage: "Archimedes said this", "Archimedes said that", etc. It is sufficient, once it has been established in a Historical Note that this proof is directly attributable to Archimedes, just to get on with the job of presenting it. --prime mover (talk) 14:56, 26 October 2023 (UTC)

OK, think I've done that. But the statement was: "Upper bound perimeter is $\pi$ and lower bound perimeter is $2 \pi$ - make consistent". Two problems with that, we need right angles, and I would prefer to follow Archimedes proof. The reason the upper bound proof uses a central angle is so you can get one side of the hexagon by doubling the angle, and the tangent. --Telliott99 (talk) 23:51, 27 October 2023 (UTC)

Worth adding a note to explain that then. Set up a lemma? --prime mover (talk) 23:52, 27 October 2023 (UTC)

The ancient way of estimating $\pi$ was insanely tedious. --Robkahn131 (talk) 20:50, 29 October 2023 (UTC)

It's those square roots. Not hard with a calculator. Thanks for the enormous effort you put into this. --Telliott99 (talk) 01:40, 30 October 2023 (UTC)

Those who have a dog in this particular fight: might it make it less unwieldy to extract bits of this into lemmata? Not it, sorry. --prime mover (talk) 21:23, 29 October 2023 (UTC)

The improve tag is misguided, at best. I tried to do what I thought you might want as a comment, and I get three words. Done here. --Telliott99 (talk) 01:51, 29 November 2023 (UTC)

Restructured the historical note so as to make the structure consistent and tight. This should now satisfy everybody. --prime mover (talk) 01:22, 2 December 2023 (UTC)