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...

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

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...

this proof was not accepted by all mathematicians because the computer-assisted proof was infeasible for a human to check by hand. The proof has gained...

(PDF) from the original on 2021-05-27. Swain, Stuart G. (2018). "Proof Without Words: Gabriel's Staircase". Mathematics Magazine. 67 (3): 209. doi:10...

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

new point A can be chosen so that case b occurs for each of the new lines Proof. For the case a, three points must be on one line: the new point A, the...

{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...

perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square...

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...

Proof without words of the arithmetic progression formulas using a rotated copy of the blocks....

difference between two inscribed angles as discussed in the first part of this proof. Given a circle whose center is point O, choose three points V, C, D on...

that their product equals the right hand side of the equality. A proof without words is also possible based on multiple applications of the Pythagorean...

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

n + 1 ) / 2 {\displaystyle n(n+1)/2} can be illustrated using a visual proof. For every triangular number T n {\displaystyle T_{n}} , imagine a "half-rectangle"...

Proof without words that the volume of a cone is a third of a cylinder of equal diameter and height...

on the Art of MATLAB, Matlab Central. Kanim, Katherine (2004), "Proofs without words: The sum of cubes—An extension of Archimedes' sum of squares", Mathematics...

though similar to the area of the circle – and hence admitted less rigorous proofs before the advent of calculus, with the ancient Greeks using the method...

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

semicircle in P. ("Arbelos - the Shoemaker's Knife") Nelsen, R B (2002). "Proof without words: The area of an arbelos". Math. Mag. 75 (2): 144. doi:10.2307/3219152...

independently proved by Orrin Frink and Paul Smith, also in 1930, but their proof was never published. The special case of cubic planar graphs (for which...

for hypervolume. Coxeter labels it the γ4 polytope. The term hypercube without a dimension reference is frequently treated as a synonym for this specific...

Additionally, the RMS value of various waveforms can also be determined without calculus, as shown by Cartwright. In the case of the RMS statistic of a...

that do not have formal meaning. Proofs without words have existed since antiquity, as in the Pythagorean theorem proof found in the Zhoubi Suanjing Chinese...

"Parallelogram Law". MathWorld. The Parallelogram Law Proven Simply at Dreamshire blog The Parallelogram Law: A Proof Without Words at cut-the-knot...

Chinese astronomical and mathematical text Zhoubi Suanjing indicating a proof of the Pythagorean theorem. Zhoubi Suanjing is one of the oldest Chinese...

which B 1 − = − 1 2 . {\textstyle B_{1}^{-}=-{\frac {1}{2}}.} A rigorous proof of these formulas and Faulhaber's assertion that such formulas would exist...

there is no way to make all nine connections without any of the lines crossing each other. In other words, the graph K 3 , 3 {\displaystyle K_{3,3}} is...

CS1 maint: DOI inactive as of April 2025 (link) ProjMath Mamikon Proof without Words from MathWorld Wolfram Interactive Demonstration of Mamikon's theorem...

Press. ISBN 978-0-19-853171-5. Kanim, Katherine (1 October 2004). "Proof without Words: The Sum of Cubes: An Extension of Archimedes' Sum of Squares". Mathematics...