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 ... .
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 (doi.org/10.1080/00029890.2020...) by Ben Blum-Smith and Japheth Wood. You can also find the source here: arxiv.org/abs/1810.00492.
#math #mathvideo #manim #circle #chords #visualproof #trigonometry #sine #cosine #tangent #rootsofunity #complexanalysis #complexnumbers #products #geometry
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[@muffinmainia4340]

I’d love to see an explanation/proof for this!

[@Living_Murphys_Law]

ruclips.net/video/8GPy_UMV-08/видео.htmlsi=8I89MK0V8FCePpXx

[@MathVisualProofs]

See linked video. 😀

[@YouTube_username_not_found]

Check also this video!
Title: Proving Grant's little theorem.

[@thenationalist8845]

​@@MathVisualProofsit is called the power of point with respect to circle
Am I correct??

[@brendankoelsch4461]

The Chanel name covers it, but for anyone who’s wondering the bottom number says “chord length product”

[@MathVisualProofs]

Ugh. One day I’ll figure out how to optimize for all the RUclips shorts clutter. Thanks.

[@quantumbuddha777]

Wow! Very cool! I was not aware of this property of chords.

[@YouTube_username_not_found]

Grant's liitle theorem!

[@GovindShukla-cc6ul]

Best content creator 😎❤

[@bradleyday2777]

At first I thought you said best concert creator, and I’m like, well yes, with the music, and the “chords”, absolutely.

[@GovindShukla-cc6ul]

@@bradleyday2777 🤣🤣🤣🤣🤣🤣🤣🤣

[@catmacopter8545]

I wonder if there is a proof for this using roots of unity! Each chord would have length of abs(1-[root]).

[@MathVisualProofs]

Yes!

[@GenericInternetter]

Huh???

[@vennstudios9885]

Wait so
4 points has
2×(√2)² soo maybe which us 4 chords
So if we back track
The chord would be a triangle with a base of 1+|cos120| or 3/2 and a height of √3/2 so Pythagorean theorem it comes out as 9/4+3/4 which comes down to 3sq
Then √3
Then realization kicks in
I'm not smart enough to conclude anything with this
Google is my trusted navigator

[@user-yh9kk6kz3b]

😎🆒🆒