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#Desmos

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Stupid #math of the day: graphing the distance to the floor according to the stretching of the muscle when doing a split.

If I didn't mess anything, the green curve hints that the distance to the floor remains roughly linearly correlated with the stretch of the muscle as we get closer and closer to the ground.

Which means if progress slows down it's essentially due to the muscle being harder to stretch and not because of angle illusion or something :(

desmos.com/calculator/atvvdeod
#fitness #desmos

A few seconds after I finally managed to hack a gradient in #desmos the website crashed my session (can't access the website anymore unless logged of)

Anyway, that's starting to be a pretty good sandbox for debugging 1D signed distances.

The gradient trick: rgb() and hls() create colors but you can't use a continuous value such as x, so you sample them like a cavem^Wengineer on the x-axis. Then you use t for a constant continuous y-axis value: (G,t), which you can then move around

glhf

I've made some updates to my simulation of two-source wave .

desmos.com/calculator/p21l3jxr

It now has...
* optional shading to smoothly illustrate the net amplitude in different areas.
* the choice between exact hyperbolic solutions for the maxima or the approximate linear maxima regions typically discussed in double-slit interference
* a single curve/ray at an order/path-difference of your choice even if it's not an extremum

For my students I threw together a simulation to illustrate field cancelation inside a spherical shell, a la Newton's "shell theorem".

For visual simplicity this is 2D only! It uses a ring and 1/r force rule as an *analogy* for a spherical shell in our 3D universe with a 1/r^2 force.

As you increase the number of particles in the ring, the results approach the theoretical limit as described by the shell theorem with a zero net field on the interior.

desmos.com/calculator/5huw6ylq

Alright folks, I've finished(?) the graph I've been working on during spare moments for a couple weeks:

desmos.com/calculator/pfzedtpi

It illustrates torque & cross product ideas with three corresponding diagrams that you can choose between: (1) a force vector at the point of application with optional component displays, (2) a "flat" common-origin diagram with dot-IN/x-OUT symbol for the torque, and (3) an in-perspective common-origin diagram to help with the 3D-ness of it all.