List questions from proof-without-words

Published on 24 Feb 2026 - 5:33

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Is there a sufficiently reachable plausibility argument that $\pi$ is irrational?

Published on 24 Feb 2026 - 5:35

92

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Is there a dissection proof of the Pythagorean Theorem, such that a single cut makes the needed pieces from the squares?

Published on 24 Feb 2026 - 5:37

71

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Is there anything missing in this proof?

Published on 24 Feb 2026 - 5:31

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Is there a geometric proof of $\frac1r = \frac{1}{h_a} + \frac{1}{h_b} + \frac{1}{h_c}$ in a given triangle?

Published on 24 Feb 2026 - 5:37

322

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On equilateral triangles

Published on 24 Feb 2026 - 5:30

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Are pictures legitimate as a proof in mathematics?

Published on 24 Feb 2026 - 5:34

82

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An intuitive approach to a Lemma related to subgroups of quotient groups.

Published on 24 Feb 2026 - 5:36

67

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How to prove an equilateral triangle ABC having first brocard point with angles 30, 30, 30

Published on 24 Feb 2026 - 5:35

42

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geometric series diagram query.

Published on 24 Feb 2026 - 5:32

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Prove $\sum_{n\geq1}\frac{2^n (1-\cos\frac{x}{2^n})^2}{\sin\frac{x}{2^{n-1}}}=\tan\frac{x}{2}-\frac{x}{2}$

Published on 24 Feb 2026 - 5:37

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What is the explanation for this visual proof of the sum of squares?

Published on 24 Feb 2026 - 5:36

214

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Proof without words for Stirling formula

Published on 24 Feb 2026 - 5:31

366

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Proof of four triangles with equal area.

Published on 24 Feb 2026 - 5:33

848

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Is it possible to explain geometrically why $\arctan (1/2) +\arctan (1/3) = 45$ degrees?

Published on 24 Feb 2026 - 5:35

List Question

Quadrilateral in a Parallelogram - Interesting Proofs!

Is there a sufficiently reachable plausibility argument that $\pi$ is irrational?

Is there a dissection proof of the Pythagorean Theorem, such that a single cut makes the needed pieces from the squares?

Is there anything missing in this proof?

Is there a geometric proof of $\frac1r = \frac{1}{h_a} + \frac{1}{h_b} + \frac{1}{h_c}$ in a given triangle?

On equilateral triangles

Are pictures legitimate as a proof in mathematics?

An intuitive approach to a Lemma related to subgroups of quotient groups.

How to prove an equilateral triangle ABC having first brocard point with angles 30, 30, 30

geometric series diagram query.

Prove $\sum_{n\geq1}\frac{2^n (1-\cos\frac{x}{2^n})^2}{\sin\frac{x}{2^{n-1}}}=\tan\frac{x}{2}-\frac{x}{2}$

What is the explanation for this visual proof of the sum of squares?

Proof without words for Stirling formula

Proof of four triangles with equal area.

Is it possible to explain geometrically why $\arctan (1/2) +\arctan (1/3) = 45$ degrees?

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