Anon
  • Member for 6 years, 2 months
  • Last seen more than a week ago
85 answers
2k votes
575k views
2k bookmarks
Visually stunning math concepts which are easy to explain
164 answers
663 votes
54k views
486 bookmarks
What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)
6 answers
605 votes
83k views
251 bookmarks
Why can you turn clothing right-side-out?
21 answers
572 votes
89k views
306 bookmarks
Mathematical difference between white and black notes in a piano
9 answers
496 votes
251k views
362 bookmarks
Integral $\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right) \mathrm dx$
7 answers
493 votes
20k views
232 bookmarks
"The Egg:" Bizarre behavior of the roots of a family of polynomials.
106 answers
337 votes
32k views
373 bookmarks
Surprising identities / equations
36 answers
334 votes
29k views
229 bookmarks
A challenge by R. P. Feynman: give counter-intuitive theorems that can be translated into everyday language
14 answers
283 votes
12k views
112 bookmarks
Help with a prime number spiral which turns 90 degrees at each prime
5 answers
259 votes
21k views
150 bookmarks
Evaluate $ \int_{0}^{\frac{\pi}2}\frac1{(1+x^2)(1+\tan x)}\:\mathrm dx$
26 answers
246 votes
60k views
106 bookmarks
Does the square or the circle have the greater perimeter? A surprisingly hard problem for high schoolers
36 answers
231 votes
29k views
178 bookmarks
What are some counter-intuitive results in mathematics that involve only finite objects?
2 answers
224 votes
17k views
51 bookmarks
Proving you *can't* make $2011$ out of $1,2,3,4$: nice twist on the usual
6 answers
214 votes
14k views
121 bookmarks
Why does this matrix give the derivative of a function?
1 answers
191 votes
7k views
91 bookmarks
Generalizing $\int_{0}^{1} \frac{\arctan\sqrt{x^{2} + 2}}{\sqrt{x^{2} + 2}} \, \frac{\operatorname dx}{x^{2}+1} = \frac{5\pi^{2}}{96}$
8 answers
181 votes
30k views
116 bookmarks
Are there any series whose convergence is unknown?
4 answers
177 votes
10k views
97 bookmarks
A math contest problem $\int_0^1\ln\left(1+\frac{\ln^2x}{4\,\pi^2}\right)\frac{\ln(1-x)}x \ \mathrm dx$
6 answers
174 votes
8k views
76 bookmarks
Symmetry of function defined by integral
27 answers
173 votes
16k views
78 bookmarks
Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction
13 answers
162 votes
40k views
90 bookmarks
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
6 answers
161 votes
7k views
113 bookmarks
Proof of $\frac{1}{e^{\pi}+1}+\frac{3}{e^{3\pi}+1}+\frac{5}{e^{5\pi}+1}+\ldots=\frac{1}{24}$
4 answers
160 votes
34k views
123 bookmarks
Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$
4 answers
153 votes
9k views
62 bookmarks
Sum of random decreasing numbers between 0 and 1: does it converge??
7 answers
133 votes
16k views
65 bookmarks
$\pi$ in arbitrary metric spaces
44 answers
129 votes
24k views
107 bookmarks
What are some examples of a mathematical result being counterintuitive?
3 answers
119 votes
2k views
53 bookmarks
All real numbers in $[0,2]$ can be represented as $\sqrt{2 \pm \sqrt{2 \pm \sqrt{2 \pm \dots}}}$
19 answers
110 votes
10k views
69 bookmarks
What is the most unusual proof you know that $\sqrt{2}$ is irrational?
0 answers
105 votes
4k views
27 bookmarks
Mondrian Art Problem Upper Bound for defect
4 answers
100 votes
19k views
53 bookmarks
An integral involving Airy functions $\int_0^\infty\frac{x^p}{\operatorname{Ai}^2 x + \operatorname{Bi}^2 x}\mathrm dx$
1 answers
98 votes
3k views
30 bookmarks
Arithmetic-geometric mean of 3 numbers
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