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Interesting and unexpected applications of $\pi$

pi asked Feb 25, 2014 at 2:26

math.stackexchange.com

43 votes

Why the "self-referential number" function eventually fixes every point

combinatorics puzzle asked Sep 7, 2020 at 1:56

math.stackexchange.com

22 votes

Is the Banach-Tarski paradox realistic? Why is Volume not an invariant?

paradoxes asked Apr 14, 2015 at 17:20

math.stackexchange.com

22 votes

A closed $1$-form on a convex open set is exact

real-analysis differential-forms asked Nov 15, 2015 at 23:27

math.stackexchange.com

19 votes

"categorical" proof of a seemingly symmetric statement about Noetherian/Artinian modules

abstract-algebra category-theory modules noetherian artinian asked Sep 22, 2018 at 17:43

math.stackexchange.com

18 votes

Visual explanation of the following statement:

elementary-number-theory visualization asked Mar 20, 2014 at 11:41

math.stackexchange.com

16 votes

Coefficients of a polynomial also are the roots of the polynomial?

algebra-precalculus polynomials roots asked Dec 24, 2013 at 16:04

math.stackexchange.com

14 votes

Change color of lineplot depending on data

python matplotlib asked Jul 10, 2015 at 16:08

stackoverflow.com

11 votes

TypeError constructor returned NULL while importing pyplot in ssh

python windows matplotlib ssh asked Jul 9, 2015 at 21:20

stackoverflow.com

10 votes

If $\sum A_n$ converges, does $\sum A_n x^n$ converge uniformly on $[0,1]$?

real-analysis sequences-and-series uniform-convergence asked Sep 26, 2015 at 19:17

math.stackexchange.com

Top Answers

104

Visually deceptive "proofs" which are mathematically wrong

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A fair coin is flipped 2k times. What is the probability that it comes up tails more often than it comes up heads?

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What are some theorems that currently only have computer-assisted proofs?

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Definition: rational prime, rational integer

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Rolling a die until obtaining the face 6. Whats the expected amout of the sum?

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Doubt regarding divisibility of the expression: $1^{101}+2^{101} \cdot \cdot \cdot +2016^{101}$

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Explanation of a joke on abelian groups (grapes).

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Is $\infty / \infty = 1$?

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Evaluating $\sum_{n=1}^{\infty} \frac{1}{n^2+1}$

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Is it true that $2^n$ is $O(n!)$?

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Can a queue automaton recognize palindromes?

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How many 6 digit numbers are possible with no digit appearing more than thrice?

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How to solve this algorithmic math olympiad problem?

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Is the integer $0$ a deficient number?

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Example of a very simple math statement in old literature which is (verbatim) a pain to understand

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Is $\frac{0}{0}$ different from $\frac{1}{0}$?

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Visual explanation of the following statement:

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Prove that the equation $x^3 + 10000 = y^3$ has no solutions

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Calculate the last digit of $3^{347}$

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Does $p = x^2 + 9y^2$ for some $x$, $y \in \mathbb{Z}$ if and only if $p \equiv 1 \text{ mod }12$?

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Is there a set $A$ such that power set of $A $ has a bijection with $\mathbb{N}$?

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Evaluation of $\lim_{x\to 0} \frac{(1+x)^{1/x}-e+\frac{ex}{2}}{x^2}$

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Let $H\unlhd G$ with $[G:H]=p$, prime. Let $K\le G$ and $K\not\subseteq H$. Then is $G=HK$?

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Divisibility Of $(2^{32} +1)$

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The value of an integral of a piecewise defined function

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Find the value of this series

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In the expansion of $(x_1+x_2+x_3+...+x_k)^n$ , the coefficient of $(x_1^{n_1} x_2^{n_2} ... x_k^{n_k} )$?

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How to figure out if $x,y,z$ are postive reals and $x(1+y)+y(1+z)+z(1+x)=6\sqrt{xyz}$ then $xyz=1$

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Find the value of a+b+c

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What is zero times infinity?

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