An experiment from an old physics textbook: trace a convex shape on a piece of paper, wet its contour with a brush and drip some water on it until it beads up. You then place the paper on a still water surface and touch the surface of the bead with a needle. The surface tension will move the shape under the needle until it points at the geometric center of the shape.
My favourite field-improvised planimeter consists of (a) tracing out the figures and cutting them out of paper, then (b) weighing the paper shapes with an analytical balance and dividing out by the weight of a unit area's worth of paper.
I always trip on the ability of English has to turn nouns into verbs so after my first parse of the sentence I thought "w.t.f does the verb to planimeter mean?". Then I realized that "can" is not a verb here....
Noun phrases can be arbitrarily long in English and don't require connecting words or hyphens. This can be very confusing to people whose first language doesn't have this feature. Classic example: "Heathrow airport customer car park", a five word noun phrase (IE, noun noun noun noun noun) that native speakers find completely normal.
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.
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.
"He shows that
with two basic mechanisms, the harmonic transformer
and the three-bar linkage, it is possible to perform
the fundamental operations of arithmetic, addition,
subtraction, multiplication and division, and to
generate ballistic functions."
- JOHN WOMERSLEY (https://www.nature.com/articles/162085a0.pdf)
