A Nonstandard Geometric Series (visual proof)

This is a short, animated visual proof showing the sum of the infinite geometric series with first term 1/8 and ratio 1/2. #manim #math​​ #mathshorts​ #mathvideo​ #trisect #trisectangle #impossible #geometry #chords #mtbos​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #calculus #series #geometricseries #infiniteseries

This animation is based on a visual proof from the wonderful book Charming Proofs by Claudi Alsina and Roger Nelsen:

To learn more about animating with manim, check out:
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Licensed under Creative Commons BY Attribution 4.0 License

[cheeseburgermonkey]

You can actually figure this out easily from 1+1/2+1/4+1/8+...=2 by just dividing everything by 8

[SridharGajendran]

Great video as usual.. very interesting..

[David-bhhs]

An infinite series of recursively inscribed right triangles will have a sum of all the perimeters (only counting a shared segment once) that is finite and related to the original side length. Is there an angle that one could choose instead of 90 degrees from the hypotenuse (or 45 degrees from the base) that results in a sum of perimeters that has a limit of infinity?