Скачать или смотреть A New Year 2025 Math Fact

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

   • Seven Proofs Without Words for Summing Cubes  
Four flat stacks:    • Visual Sum of Cubes II  
Triangular arrays:    • Sum Cubes with Triangles (visual proof wit...  
Overlapping gnomons:    • Visual Sum of Cubes III  
Cubes to gnomons:    • Sum of Cubes IV (Nicomachus's Theorem)  
Triangular dissection:    • Sum Of Cubes I (visual proof)  
Two cuboid stacks:    • Sum of Cubes VII (visual proof without words)  
Summing Odds:    • Sum of Cubes as Sum of Odds and more (visu...  

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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 (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.

The second visual proof in this video 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).

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