Petals, Chords, and Circle Inversion (some SVG/JavaScript and some Mathematica/Wolfram-Cloud)

Published: 22 July 2024
on channel: Thomas Blum

In this video we look at "circle inversion". We start by establishing that the inversion of an arc passing through the origin of the circle used for inversion is a straight line (in this case horizontal). Turning that idea around, we next look at the inversion of chords inside the "circle of inversion." Their inverses turn out to be arcs that if extended to the inside of the circle would pass through the origin. We use Mathematica/Wolfram-Cloud to grind through some of the algebra/trigonometry. We illustrate some of the results using a HTML page with an SVG element and some JavaScript to generate the figures of interest.

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