[mauvehaus]

I can't pass up this opportunity to mention "How Round is Your Circle". It's nerd shit about geometry applied to, among other things, steam engines.

There's a chapter or three about planimeters, the introduction to which is the hatchet planimeter.

Worth a read if you're into geometry and Industrial Revolution stuff, and honestly, probably worth working through with pencil and paper, though I never have.

[theyinwhy]

I can't pass the opportunity to post https://neal.fun/perfect-circle/

[jasomill]

Nice. After five minutes: 95.6% with a mouse; 96.2% with a Wacom tablet; trackpad (Apple Magic 2), hopeless.

As for opportunistically relevant posting: see the first chapter of Felix Klein's Elementary Mathematics from an Advanced Standpoint: Geometry[1] for a bit on the geometric theory behind the planimeter.

[1] https://archive.org/details/elementary_mathematics_geometry/