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Beautifully irrational
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321 votes
31 answers
34k views

Nice examples of groups which are not obviously groups

286 votes
24 answers
25k views

Is mathematics one big tautology?

  • 2,859
146 votes
19 answers
67k views

What is the difference between a point and a vector?

  • 1,565
100 votes
9 answers
9k views

Divisibility by 7 rule, and Congruence Arithmetic Laws

  • 5,157
80 votes
9 answers
63k views

What is the meaning of the third derivative of a function at a point

  • 1,073
60 votes
14 answers
8k views

Choice of $q$ in Baby Rudin's Example 1.1

  • 2,754
53 votes
4 answers
5k views

How many "super imaginary" numbers are there?

  • 649
43 votes
6 answers
4k views

What do cones have to do with quadratics? Why is $2$ special?

  • 5,914
39 votes
7 answers
7k views

Intuition behind normal subgroups

  • 5,873
32 votes
1 answer
791 views

Geometric representation of Euler-Maclaurin Summation Formula

30 votes
6 answers
3k views

Why isn't $\int \frac{1}{x}~dx = \frac{x^0}{0}$?

  • 767
29 votes
2 answers
3k views

Where is axiom of regularity actually used?

28 votes
4 answers
3k views

How to prove those "curious identities"?

  • 7,978
27 votes
4 answers
3k views

What are the applications of finite calculus

24 votes
2 answers
13k views

On the vector spaces of Taylor Series and Fourier Series

23 votes
4 answers
6k views

Use of partial derivatives as basis vector

  • 411
19 votes
1 answer
552 views

Differential forms without derivatives?

  • 58.9k
17 votes
2 answers
5k views

Why does partial differentiation give centre of a conic?

  • 1,287
16 votes
1 answer
16k views

Discriminant of a Conic Section

  • 189
16 votes
4 answers
23k views

Squaring both sides of an inequality of opposite signs

  • 826
15 votes
6 answers
40k views

Simple proof that equilateral triangles have maximum area

  • 79k
15 votes
3 answers
25k views

Does $\sqrt{a+b} \le \sqrt a + \sqrt b$ hold for all positive real numbers a and b?

  • 195
15 votes
3 answers
42k views

Equation of ellipse, hyperbola, parabola in complex form

  • 3,095
13 votes
3 answers
537 views

Find $\int_0^1 \frac{f(x)}{\sqrt{1+x^2}}dx$

12 votes
5 answers
2k views

Reflection inside spherical mirror

  • 2,762
11 votes
1 answer
158 views

What does Heron's formula naturally deform?

  • 1,706
11 votes
4 answers
23k views

Show $\max{\{a,b\}}=\frac1{2}(a+b+|a-b|)$

  • 406
10 votes
1 answer
492 views

Solve: $2^{\cos^{2014}x} - 2^{\sin^{2014} x} = \cos^{2013} (2x)$

  • 931
9 votes
3 answers
378 views

A sum of series with the inverse squared central binomial coefficient

  • 22.1k
9 votes
1 answer
199 views

How to find this $\prod_{k=-\infty}^{+\infty}\frac{x^2+(4k+1-y)^2}{x^2+(4k+3-y)^2}$