I am looking for examples of three dimensional constructible proofs. By this I mean activities such as steps in proving $1^2+2^2+\cdots+n^2=n(n+1)(2n+1)/6$. In this construction the identity is proven by assembling 6 special pyramids that interlock to make a box.
2026-02-24 07:02:47.1771916567
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Examples of 3d visual proofs
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- Some geometric proofs using series: http://www.maa.org/external_archive/joma/Volume7/Styer/Series3.html
- Article Geometric Progressions - A Geometric Approach by Michael Strizhevsky, in Nov.2001 edition of College Mathematics Journal
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Here's the best 3d proof. There is a bijection between the following two kinds of combinatorial objects:
The proof is by lookin':