Uploaded August 2026 | Updated September 2026, 2 weeks ago
Sum Cubes with Triangles
This is a short, animated (wordless) visual proof demonstrating the sum of the first n positive cubes by rearranging triangular arrays into a larger triangular array.
If you like this video, consider subscribing to the channel or consider buying me a coffee: buymeacoffee.com/VisualProofs. Thanks!
Here are four other visual proofs of sum of cubes formulas:
youtu.be/YQLicI8R4Gs
youtu.be/Ye9OPNqV9FA
youtu.be/NxOcT_VKQR0
youtu.be/d1yM6Rq7Tfw
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).
To learn more about animating with manim, check out:
https://manim.community
#mathshorts #mathvideo #math #calculus #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #finitesums #discretemath #calculus #sum #induction
Sum Cubes with Triangles
This is a short, animated (wordless) visual proof demonstrating the sum of the first n positive cubes by rearranging triangular arrays into a larger triangular array.
If you like this video, consider subscribing to the channel or consider buying me a coffee: buymeacoffee.com/VisualProofs. Thanks!
Here are four other visual proofs of sum of cubes formulas:
youtu.be/YQLicI8R4Gs
youtu.be/Ye9OPNqV9FA
youtu.be/NxOcT_VKQR0
youtu.be/d1yM6Rq7Tfw
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).
To learn more about animating with manim, check out:
https://manim.community
#mathshorts #mathvideo #math #calculus #mtbos #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #finitesums #discretemath #calculus #sum #induction
