Questions tagged [proof-without-words]

For questions concerning the creation and understanding of pictorial proofs.

27 questions
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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?

Can anyone provide a geometric proof of $\frac1r = \frac{1}{h_a} + \frac{1}{h_b} + \frac{1}{h_c}$ in a given triangle, if there is one? Here, $h_i$ refers to the distance from the side $i$ to the ...
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Is there anything missing in this proof?

I came with this geometry problem and numerous lengthy solutions were proposed, so I thought there must be something missing in my solution. The problem: Given that $\angle CAB=3x$, $\angle BCA=x$, ...
25 views

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

Can you cut the squares of a right triangle with one cut (cutting all three pieces at the same time) so that it’s possible to arrange them and prove Pythagoras’ theorem?
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Why matrix representation of convolution cannot explain the convolution theorem?

A record saying that Convolution Theorem is trivial since it is identical to the statement that convolution, as Toeplitz operator, has fourier eigenbasis and, therefore, is diagonal in it, has ...
918 views

Intuitive/Visual proof that $(1+2+\cdots+n)^2=1^3+2^3+\cdots+n^3$ [duplicate]

$$(1+2+\cdots+n)^2=1^3+2^3+\cdots+n^3$$ I noticed this only because $\displaystyle \sum_{i=1}^n i = \frac{n(n+1)}{2}$ and $\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}{4}$. But the two things ...