Product of chords?
This short animation shows chords connecting n equally space points to one of those points on a unit circle and computes the product of the chord lengths. Do you have a conjecture based on this? Can you prove it?
If you’re interested, check out the related video at • Products of Chords in a Circle (math ... .
This animation is based on a famous problem that has been discussed in numerous places. In particular, a great reference for this problem and related ones (with a fantastic bibliography) is the source Chords of an Ellipse, Lucas Polynomials, and Cubic Equations in Issue 8 of the 2020 American Mathematical Monthly (https://doi.org/10.1080/00029890.2020...) by Ben Blum-Smith and Japheth Wood. You can also find the source here: https://arxiv.org/abs/1810.00492.
#math #mathvideo #manim #circle #chords #visualproof #trigonometry #sine #cosine #tangent #rootsofunity #complexanalysis #complexnumbers #products #geometry
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