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Anon
  • Member for 6 years, 11 months
  • Last seen more than a week ago
1548 votes
86 answers
584k views

Visually stunning math concepts which are easy to explain

  • 821
662 votes
164 answers
55k views

What was the first bit of mathematics that made you realize that math is beautiful? (For children's book) [closed]

  • 101
613 votes
6 answers
84k views

Why can you turn clothing right-side-out?

  • 6,133
581 votes
21 answers
91k views

Mathematical difference between white and black notes in a piano

  • 5,697
509 votes
10 answers
261k views

Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$

503 votes
7 answers
21k views

"The Egg:" Bizarre behavior of the roots of a family of polynomials.

  • 26.2k
348 votes
108 answers
34k views

Surprising identities / equations

  • 60.8k
335 votes
36 answers
30k views

A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language

  • 6,102
285 votes
14 answers
12k views

Help with a prime number spiral which turns 90 degrees at each prime

  • 4,653
264 votes
5 answers
21k views

Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$

  • 50.3k
249 votes
26 answers
62k views

Does the square or the circle have the greater perimeter? A surprisingly hard problem for high schoolers

  • 4,243
234 votes
36 answers
31k views

What are some counter-intuitive results in mathematics that involve only finite objects?

  • 3,616
225 votes
2 answers
17k views

Proving you *can't* make $2011$ out of $1,2,3,4$: nice twist on the usual

219 votes
6 answers
15k views

Why does this matrix give the derivative of a function?

  • 8,771
193 votes
1 answer
7k views

Generalizing $\int_{0}^{1} \frac{\arctan\sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \, \frac{\operatorname dx}{x^{2}+1} = \frac{5\pi^{2}}{96}$

187 votes
8 answers
33k views

Are there any series whose convergence is unknown?

  • 2,141
181 votes
28 answers
17k views

Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction

179 votes
4 answers
11k views

A math contest problem $\int_0^1\ln\left(1+\frac{\ln^2x}{4\,\pi^2}\right)\frac{\ln(1-x)}x \ \mathrm dx$

174 votes
6 answers
9k views

Symmetry of function defined by integral

  • 135k
166 votes
7 answers
8k views

Proof of $\frac{1}{e^{\pi}+1}+\frac{3}{e^{3\pi}+1}+\frac{5}{e^{5\pi}+1}+\ldots=\frac{1}{24}$

  • 1,795
165 votes
4 answers
36k views

Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$

164 votes
14 answers
42k views

How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?

155 votes
4 answers
10k views

Sum of random decreasing numbers between 0 and 1: does it converge??

137 votes
7 answers
16k views

$\pi$ in arbitrary metric spaces

  • 1,910
132 votes
44 answers
24k views

What are some examples of a mathematical result being counterintuitive?

  • 5,346
121 votes
3 answers
2k views

All real numbers in $[0,2]$ can be represented as $\sqrt{2 \pm \sqrt{2 \pm \sqrt{2 \pm \dots}}}$

  • 30.5k
112 votes
19 answers
10k views

What is the most unusual proof you know that $\sqrt{2}$ is irrational?

109 votes
0 answers
4k views

Mondrian Art Problem Upper Bound for defect

  • 19.8k
103 votes
4 answers
20k views

An integral involving Airy functions $\int_0^\infty\frac{x^p}{\operatorname{Ai}^2 x + \operatorname{Bi}^2 x}\mathrm dx$

  • 17.3k
100 votes
1 answer
4k views

Arithmetic-geometric mean of 3 numbers

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