Uploaded December 2024 | Updated September 2026, 2 weeks ago
In this video, we see an intriguing fact about the number 2025. This fact is part of the more general theorem called Nicomachus's theorem, and we show visual proofs and a rigorous proof of this theorem.
To see more visual proofs of this same fact, check out the following videos
youtu.be/Gz9DhDHVGy8
Four flat stacks: youtu.be/Ye9OPNqV9FA
Triangular arrays: youtu.be/jWpyrXYZNiI
Overlapping gnomons: youtu.be/d1yM6Rq7Tfw
Cubes to gnomons: youtu.be/YQLicI8R4Gs
Triangular dissection: youtu.be/NxOcT_VKQR0
Two cuboid stacks: youtu.be/i12p4Acb3L4
Summing Odds: youtu.be/LYfKapE_g1Q
To buy me a coffee, head over to buymeacoffee.com/VisualProofs
Thanks!
The first visual proof in this video 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.
The second visual proof in this video 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).
#happynewyear2025 #happynewyear #sumcubes #mathematics #mathproof #2025
#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
In this video, we see an intriguing fact about the number 2025. This fact is part of the more general theorem called Nicomachus's theorem, and we show visual proofs and a rigorous proof of this theorem.
To see more visual proofs of this same fact, check out the following videos
youtu.be/Gz9DhDHVGy8
Four flat stacks: youtu.be/Ye9OPNqV9FA
Triangular arrays: youtu.be/jWpyrXYZNiI
Overlapping gnomons: youtu.be/d1yM6Rq7Tfw
Cubes to gnomons: youtu.be/YQLicI8R4Gs
Triangular dissection: youtu.be/NxOcT_VKQR0
Two cuboid stacks: youtu.be/i12p4Acb3L4
Summing Odds: youtu.be/LYfKapE_g1Q
To buy me a coffee, head over to buymeacoffee.com/VisualProofs
Thanks!
The first visual proof in this video 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.
The second visual proof in this video 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).
#happynewyear2025 #happynewyear #sumcubes #mathematics #mathproof #2025
#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
