Coke can planimeter
durealeyes.comAn 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.
Am I correct in thinking that the wet contour is made within the boundaries of the convex 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.
Not surprisingly, this technique is used for numerical integration of complex graphs.
My advisor’s thesis had an entire section on that for computing complex integrals.
That's Galileo's method of integration.
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....
"Coke can" is a phrasal adjective here and ought to be hyphenated, which removes the ambiguity: "Coke-can planimeter"
I don't think that's mandatory.
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.
Proper capitalization would have made it clearer.
Right. Coke can can planimeter
What's the difference between a piano and a fish?
You can tune a piano, but you can tuna fish.
You can tune a file system, but you cannot tune a fish.
I mean, we verb nouns all the time, but this is just a homonym, can and can are different words that sound and spell the same.
Yes I was referring to the verbing of "planimeter" which wasn't
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.
I can't pass the opportunity to post https://neal.fun/perfect-circle/
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/
This YouTube channel is worth a peek if you find physical computation interesting: https://www.youtube.com/@ChrisStaecker
3 bar linkage computing by Svoboda. MIT rad labs, ww2. Cams and drums did a lot of work plotting bomb angle, gunnery, rate of descent.
Computing Mechanisms and Linkages By Antonín Svoboda https://archive.org/details/computingmechani00anto
"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)