In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident...

Nicomachus's Theorem, Matlab Central. Kanim, Katherine (2004), "Proofs without words: The sum of cubes—An extension of Archimedes' sum of squares", Mathematics...

most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years...

above works, and then projecting back into the plane. The last step of the proof fails if the projective space has dimension less than 3, as in this case...

{x_{i}x_{j}}{\beta }}={\frac {(\beta -x_{i})(x_{j}-\beta )}{\beta }}>0} . The proof then follows along similar lines as in the earlier replacement. Of the non-negative...

mathematical literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written fully in symbolic language without the involvement...

with the finite sums. Ajose, Sunday; Nelsen, Roger (June 1994). "Proof without Words: Geometric Series". Mathematics Magazine. 67 (3): 230. doi:10.2307/2690617...

more general inequality Popoviciu's inequality Law of averages A proof without words of Jensen's inequality Jensen, J. L. W. V. (1906). "Sur les fonctions...

the Varignon parallelogram is half the area of the quadrilateral. Proof without words (see figure): An arbitrary quadrilateral and its diagonals. Bases...

given number of straight slices Carter, Larry; Wagon, Stan (1994a), "Proof without Words: Fair Allocation of a Pizza", Mathematics Magazine, 67 (4): 267,...