Geometric Series Sum Visually @MathVisualProofs

Uploaded May 2026 | Updated September 2026, 2 weeks ago

Geometric Series Sum Visually

This is a short, animated visual proof demonstrating the infinite geometric series formula for any positive ratio r with r less than 1. This series is important for many results in calculus, discrete mathematics, and combinatorics.

To buy me a coffee, head over to buymeacoffee.com/VisualProofs
Thanks!

If you want to see a slower, wide format version of this animation, check out:

youtu.be/TGUWt5xcB8M

Also, check out my playlist on geometric sums/series: youtube.com/playlist?list=PLZh9gzIvXQUsgw8W5TUVDtF0q4jEJ3iaw

This animation is based on a proof by Benjamin G. Klein and Irl C. Bivens from the October 1988 issue of Mathematics Magazine page 219 (doi.org/10.2307/2689355).

#math #calculus #manim #proofwithoutwords #geometricseries

To learn more about animating with manim, check out:
https://manim.community

$Manim Tutorial: Hilbert Curve and L-Systems This is fifth video in a series inspired by the Talking Maths in Public group, I am trying my hand at showing how I create animations using 3blue1browns (Grant Sandersons) Python library ManimGL. The Talking Maths in Public Group encouraged creators to share how they would animate Hilbert Curves. In this video, I code in real time to create an L-system that draws out a level 4 and level 5 Hilbert Curve. In a previous video, I used this process to animate drawing a level 8 Hilbert Curve: https://youtu.be/xfuvkGSk8hs Let me know if you would like to see more how-to-animate math videos in the future. If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! If you want the code from this video, check out: https://github.com/Tom-Edgar/MVPS/blob/main/HilbertTurtle.py If you are interested in Talking Maths in Public, check out their website: https://talkingmathsinpublic.uk/animation/ Thank you for watching! #MathsAnimationTMiP #turtlegraphics #fractal #math #manim #mathvideo #Lsystem #hilbert #hilbertcurve #planefillingcurve #visualmath #fractalcurves #tutorial #iteration #python #learntocode To learn more about animating with manim, check out: https://manim.community$

Sum Geometric Series with Ratio 1/2 in Rectangles (visual proofs)

$Gosper Curve L-System : Walking a Plane-Filling Curve In this video, we describe two how to draw a plane filling curve called the Gosper curve using an L-system. While the substitution strings are a bit complicated, the rules for this system are easy to implement and use to draw a level 6 Gosper curve (to dramatic music). If you liked this video, consider liking or subscribing. Or you can support me by buying me a coffee at https://www.buymeacoffee.com/VisualProofs Thanks! If you want to see other constructions of like this, see https://youtu.be/GVhLhAXAWoI https://youtu.be/MEzgGGq2l5E https://youtu.be/8Q_zuRKKh2g If you want to know more about L-systems or turtle graphics or the Gosper curve, check out these wikipedia sites: https://en.wikipedia.org/wiki/L-system https://en.wikipedia.org/wiki/Turtle_graphics https://en.wikipedia.org/wiki/Gosper_curve To learn more about animating with manim, check out: https://manim.community #turtlegraphics #fractal #math #manim #mathvideo #Lsystem #Gosper #gospercurve #planefillingcurve #visualmath #fractalcurves Music in this video: Rise Again by Alex-Productions | https://onsound.eu/ Music promoted by https://www.free-stock-music.com Creative Commons / Attribution 3.0 Unported License (CC BY 3.0) https://creativecommons.org/licenses/by/3.0/deed.en_US$

Elementary Derivative Rules Graphically | Synthwave and Math

$Building the Wallis Sieve: What’s the Area? In this short, we show how to build the Wallis Sieve using an iterative procedure of cutting remaining square lengths into the next odd and removing the created central square in the corresponding square grid. The question is: can you determine the area of the resulting limiting shape? If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks! If you want to know more about the Wallis Sieve, check out this wonderful short article by Evelyn Lamb: https://www.scientificamerican.com/blog/roots-of-unity/a-few-of-my-favorite-spaces-the-wallis-sieve/ If you want to see the area computed in terms of the infinite Wallis product, check out this short : https://youtube.com/shorts/s1JORwIzabs?feature=share #mathvideo #math #mtbos #manim #animation #iteachmath #mathematics #dynamicalsystems #fractal #fractals #wallissieve #wallis #wallisproduct #infiniteproduct To learn more about animating with manim, check out: https://manim.community$

Mathematical Visual Proofs |

Geometric Series Sum Visually