@DavidKButlerUoA So in the end we’ll have a dust/fractal, but maybe we can quantify how far away from “flat” we are at each step? I guess I’m claiming that this will flatten out in the limit because we’ve cut out all the bits that could tear…
@DavidKButlerUoA And then inside that triangle, we find its incircle, and cut that out. So our figure so far is a “triangle” minus its “incircle”, which is three “triangle” “legs”. And now repeat that for each of the three legs, and so on; I guess this is an Apollonian gasket on the sphere?
@DavidKButlerUoA I recently watched a talk where a noted mathematician exposited that there were many things we can prove that he felt we do not understand.
@DavidKButlerUoA Another thought, perhaps provoked by lunch being a bit late: how do you feel about writing some version of 1-variable FTC like this: F some antiderivative of f (really F is an equivalence class, and f=dF for some suitable “derivative”), I an interval, dI its endpoints/boundary
@DavidKButlerUoA Anyway, idle thoughts provoked by noticing things in the different ways engineering, mcc, probability, and maths Ia/b all seem to tackle (multiple) integration subtly differently
@DavidKButlerUoA When we have I think THING and it has partial derivatives inside it, I wonder about how to keep some sort of unit or “speed” or velocity in mind. Like thinking of a determinant as a gadget for volumes or areas, normalised for the cross product by inserting unit vectors in the top
@DavidKButlerUoA Also I wonder if being able to play with a physical planimeter—a machine that calculates areas via greens theorem—might be interesting
@rantyben Read this (after learning about bike fitting), thought “to avoid cramped writing hand select nib suitable to your height” 🤔 (then looked at the image, all became clear)