Proof without words of the Nicomachus theorem (Gulley (2010)) that the sum of the first n cubes is the square of the nth triangular number
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 by a diagram without any accompanying explanatory text. Such proofs can be considered more elegant than formal or mathematically rigorous proofs due to their self-evident nature.[1] When the diagram demonstrates a particular case of a general statement, to be a proof, it must be generalisable.[2]
A proof without words is not the same as a mathematical proof, because it omits the details of the logical argument it illustrates. However, it can provide valuable intuitions to the viewer that can help them formulate or better understand a true proof.
^Dunham 1994, p. 120
^Weisstein, Eric W. "Proof without Words". MathWorld. Retrieved on 2008-6-20
and 23 Related for: Proof without words information
In mathematics, a proofwithoutwords (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident...
most for any mathematical theorem. The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years...
Nicomachus's Theorem, Matlab Central. Kanim, Katherine (2004), "Proofswithoutwords: The sum of cubes—An extension of Archimedes' sum of squares", Mathematics...
mathematical literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written fully in symbolic language without the involvement...
the Varignon parallelogram is half the area of the quadrilateral. Proofwithoutwords (see figure): An arbitrary quadrilateral and its diagonals. Bases...
figure on the right is a proofwithoutwords of this formula. Laisant does not discuss the hypotheses necessary to make this proof rigorous, but this can...
adjacent to every other – in the SVG image, move the mouse to rotate it Proofwithoutwords that the number of colours needed is unbounded in three or more dimensions...
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"...
1 {\displaystyle P=({\sqrt {a^{2}r^{n}}})^{n+1}} , which concludes the proof. A clay tablet from the Early Dynastic Period in Mesopotamia (c. 2900 –...
Mathematical Association of America. ISBN 9781614442103. ProjMath Mamikon ProofwithoutWords from MathWorld Wolfram Interactive Demonstration of Mamikon's theorem...
semicircle in P. ("Arbelos - the Shoemaker's Knife") Nelsen, R B (2002). "Proofwithoutwords: The area of an arbelos". Math. Mag. 75 (2): 144. doi:10.2307/3219152...
any polyhedron with 12 faces. Dodecagram See also Kürschák's geometric proof on the Wolfram Demonstration Project Plane Geometry: Experiment, Classification...
given number of straight slices Carter, Larry; Wagon, Stan (1994a), "ProofwithoutWords: Fair Allocation of a Pizza", Mathematics Magazine, 67 (4): 267,...
that do not have formal meaning. Proofswithoutwords have existed since antiquity, as in the Pythagorean theorem proof found in the Zhoubi Suanjing Chinese...
in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing...
Reading: Addison-Wesley, LCCN 76087042 Roger B. Nelsen (1997). ProofswithoutWords: Exercises in Visual Thinking, The Mathematical Association of America...
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...
x_{n}\}} Proof of lim p → 0 M p = M 0 {\textstyle \lim _{p\to 0}M_{p}=M_{0}} (geometric mean) For the purpose of the proof, we will assume without loss of...
theorem – Relation between sides of a right triangle R. B. Nelsen, ProofWithoutWords: A Reciprocal Pythagorean Theorem, Mathematics Magazine, 82, December...
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