Скачать или смотреть Seven Proofs Without Words for Summing Cubes

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.

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For the original animations, see here:
Level 1, Four flat stacks:    • Visual Sum of Cubes II  
Level 2, Triangular arrays:    • Sum Cubes with Triangles (visual proof wit...  
Level 3, Overlapping gnomons:    • Visual Sum of Cubes III  
Level 4, Cubes to gnomons:    • Sum of Cubes IV (Nicomachus's Theorem)  
Level 5, Triangular dissection:    • Sum Of Cubes I (visual proof)  
Level 6, Two cuboid stacks:    • Sum of Cubes VII (visual proof without words)  
Level 7, Summing Odds:    • Sum of Cubes as Sum of Odds and more (visu...  

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 (https://doi.org/10.2307/3612319) and, independently, Antonella Cupillari from the October 1989 issue of Mathematics Magazine page 259 (https://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 (https://www.jstor.org/stable/10.4169/... 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 (https://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 (https://www.jstor.org/stable/2689727), page 74, and Alan L. Fry from the January 1985 issue of Mathematics Magazine (https://www.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 (https://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 (https://doi.org/10.1080/0025570X.2024... page ??).

Level 7: This animation is based on a visual proof by Alfinio Flores from the January 1998 issue of The College Mathematics Journal (https://www.jstor.org/stable/2687639 page 61).

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