Uploaded November 2024 | Updated September 2026, 2 weeks ago
This video is a compilation of seven different visual proofs showing the sum formula for the sum of the first n positive cubes that can be found on my channel. This is a new style of video for me inspired by @ThatsAmazing 's trick shots at various levels and @dudeperfect 's soundtracks. I hope you enjoy it. If these visual proofs are too fast to follow completely in this format, the originals are linked below.
If you like this video, consider subscribing to the channel or consider buying me a coffee: buymeacoffee.com/VisualProofs. Thanks!
For the original animations, see here:
Level 1, Four flat stacks: youtu.be/Ye9OPNqV9FA
Level 2, Triangular arrays: youtu.be/jWpyrXYZNiI
Level 3, Overlapping gnomons: youtu.be/d1yM6Rq7Tfw
Level 4, Cubes to gnomons: youtu.be/YQLicI8R4Gs
Level 5, Triangular dissection: youtu.be/NxOcT_VKQR0
Level 6, Two cuboid stacks: youtu.be/i12p4Acb3L4
Level 7, Summing Odds: youtu.be/LYfKapE_g1Q
Original sources:
Level 1: This animation is based on a visual proofs by Warren Lushbaugh (from an article by Solomon Golomb) in the May 1965 issue of the Mathematical Gazette (doi.org/10.2307/3612319) and, independently, Antonella Cupillari from the October 1989 issue of Mathematics Magazine page 259 (doi.org/10.2307/2689765).
Level 2: This animation is based on a visual proof by Parames Laosinchai from the December 2012 issue of Mathematics Magazine (jstor.org/stable/10.4169/math.mag.85.5.360 page 360).
Level 3: This animation is based on a visual proofs by Warren Lushbaugh (from an article by Solomon Golomb) in the May 1965 issue of the Mathematical Gazette (doi.org/10.2307/3612319).
Level 4: This animation is based on independently discovered, separate visual proofs by J. Barry Love from the March 1977 issue of Mathematics Magazine (jstor.org/stable/2689727), page 74, and Alan L. Fry from the January 1985 issue of Mathematics Magazine (jstor.org/stable/2690228) , page 11.
Level 5: This animation is based on a visual proof by Georg Schrage from the June 1992 issue of Mathematics Magazine (doi.org/10.2307/2691330 - page 185).
Level 6: This animation is based on a visual proof by Tom Edgar from the September 2024 issue of Mathematics Magazine (doi.org/10.1080/0025570X.2024.2379213 page ??).
Level 7: This animation is based on a visual proof by Alfinio Flores from the January 1998 issue of The College Mathematics Journal (jstor.org/stable/2687639 page 61).
#mathshorts #mathvideo #math #calculus #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #finitesums #discretemath #calculus #sum #induction #faulhaber #sumofcubes #cubes
To learn more about animating with manim, check out:
https://manim.community
This video is a compilation of seven different visual proofs showing the sum formula for the sum of the first n positive cubes that can be found on my channel. This is a new style of video for me inspired by @ThatsAmazing 's trick shots at various levels and @dudeperfect 's soundtracks. I hope you enjoy it. If these visual proofs are too fast to follow completely in this format, the originals are linked below.
If you like this video, consider subscribing to the channel or consider buying me a coffee: buymeacoffee.com/VisualProofs. Thanks!
For the original animations, see here:
Level 1, Four flat stacks: youtu.be/Ye9OPNqV9FA
Level 2, Triangular arrays: youtu.be/jWpyrXYZNiI
Level 3, Overlapping gnomons: youtu.be/d1yM6Rq7Tfw
Level 4, Cubes to gnomons: youtu.be/YQLicI8R4Gs
Level 5, Triangular dissection: youtu.be/NxOcT_VKQR0
Level 6, Two cuboid stacks: youtu.be/i12p4Acb3L4
Level 7, Summing Odds: youtu.be/LYfKapE_g1Q
Original sources:
Level 1: This animation is based on a visual proofs by Warren Lushbaugh (from an article by Solomon Golomb) in the May 1965 issue of the Mathematical Gazette (doi.org/10.2307/3612319) and, independently, Antonella Cupillari from the October 1989 issue of Mathematics Magazine page 259 (doi.org/10.2307/2689765).
Level 2: This animation is based on a visual proof by Parames Laosinchai from the December 2012 issue of Mathematics Magazine (jstor.org/stable/10.4169/math.mag.85.5.360 page 360).
Level 3: This animation is based on a visual proofs by Warren Lushbaugh (from an article by Solomon Golomb) in the May 1965 issue of the Mathematical Gazette (doi.org/10.2307/3612319).
Level 4: This animation is based on independently discovered, separate visual proofs by J. Barry Love from the March 1977 issue of Mathematics Magazine (jstor.org/stable/2689727), page 74, and Alan L. Fry from the January 1985 issue of Mathematics Magazine (jstor.org/stable/2690228) , page 11.
Level 5: This animation is based on a visual proof by Georg Schrage from the June 1992 issue of Mathematics Magazine (doi.org/10.2307/2691330 - page 185).
Level 6: This animation is based on a visual proof by Tom Edgar from the September 2024 issue of Mathematics Magazine (doi.org/10.1080/0025570X.2024.2379213 page ??).
Level 7: This animation is based on a visual proof by Alfinio Flores from the January 1998 issue of The College Mathematics Journal (jstor.org/stable/2687639 page 61).
#mathshorts #mathvideo #math #calculus #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #finitesums #discretemath #calculus #sum #induction #faulhaber #sumofcubes #cubes
To learn more about animating with manim, check out:
https://manim.community
