User joriki

45 votes

5 answers

2k views

How to evaluate $\int_0^1\frac{\log^2(1+x)}x\mathrm dx$?

asked Feb 28, 2013 at 10:19

35 votes

2 answers

7k views

necessary and sufficient condition for trivial kernel of a matrix over a commutative ring

linear-algebra abstract-algebra matrices commutative-algebra

asked Oct 11, 2011 at 16:07

25 votes

1 answer

6k views

A proof of Wolstenholme's theorem

number-theory binomial-coefficients alternative-proof

asked Jul 16, 2012 at 10:43

22 votes

2 answers

858 views

an integer sum of products of tangents

sequences-and-series trigonometry

asked Jul 21, 2012 at 21:38

18 votes

5 answers

2k views

Generalised inclusion-exclusion principle

combinatorics reference-request inclusion-exclusion

asked Jun 1, 2016 at 10:52

17 votes

1 answer

760 views

At what rate does the entropy of shuffled cards converge?

probability permutations entropy card-games

asked Mar 5, 2016 at 20:45

16 votes

2 answers

791 views

Arnol'd's trivium problem #68

optimization calculus-of-variations

asked Oct 14, 2012 at 13:19

16 votes

3 answers

2k views

What's up with Plouffe's inverter? Is there an alternative?

online-resources

asked Oct 24, 2012 at 9:58

15 votes

3 answers

608 views

definite and indefinite sums and integrals

soft-question integration summation

asked Oct 14, 2012 at 12:55

13 votes

1 answer

447 views

Can we qualitatively predict the strategy of the German and US teams in today's World Cup soccer match?

probability ordinary-differential-equations markov-chains game-theory

asked Jun 26, 2014 at 13:00

13 votes

2 answers

258 views

Why are all subset sizes equiprobable if elements are independently included with probability uniform over $[0,1]$?

probability uniform-distribution binomial-distribution

asked Jan 19, 2020 at 13:13

12 votes

4 answers

379 views

The case of the missing ninth of a $2$€ coin

probability soft-question expected-value paradoxes

asked Nov 29, 2019 at 20:49

12 votes

2 answers

355 views

Why do the triangular numbers initially form long cycles mod $2^k$?

elementary-number-theory permutations modular-arithmetic permutation-cycles triangular-numbers

asked Dec 30, 2019 at 6:35

12 votes

2 answers

565 views

Does the Riemann hypothesis guarantee that integer factorization is difficult?

prime-numbers factoring computational-complexity cryptography riemann-hypothesis

asked Jun 1, 2020 at 7:59

10 votes

1 answer

3k views

variable bounds on definite integrals in Wolfram|Alpha

wolfram-alpha

asked Jul 13, 2011 at 11:24

10 votes

1 answer

374 views

What is the minimal isoperimetric ratio of a polyhedron with $5$ vertices?

optimization polyhedra solid-geometry

asked Apr 20, 2013 at 12:35

9 votes

1 answer

394 views

expansion of $\int_0^\infty\left(\frac{\sin t}t\right)^p\mathrm dt$ in inverse powers of $p$

sequences-and-series convergence-divergence asymptotics definite-integrals

asked May 8, 2012 at 16:07

9 votes

1 answer

754 views

How is the number of points in the convex hull of five random points distributed?

geometric-probability

asked Jan 19, 2013 at 18:14

8 votes

1 answer

254 views

A lawn, a flower, a pipe and the neighbours

probability geometric-probability

asked Mar 13, 2013 at 8:41

8 votes

1 answer

218 views

Probability that one part of a randomly cut equilateral triangle covers the other

probability triangles geometric-probability

asked Mar 9, 2016 at 10:06

7 votes

0 answers

363 views

Is there a connection between the 3D random walk constant and the partition function?

stochastic-processes integer-partitions random-walk

asked Dec 26, 2011 at 1:13

6 votes

1 answer

476 views

What's the probability for two points to lie on the same side of the line joining two other points?

geometric-probability

asked Jan 19, 2013 at 14:07

6 votes

2 answers

115 views

How to refer to the "sign" of the dependence of events?

probability probability-theory terminology

asked Sep 11, 2015 at 20:23

6 votes

0 answers

156 views

Probability that one part of a randomly cut equilateral triangle covers the other without flipping

probability triangles geometric-probability

asked Mar 9, 2016 at 18:31

6 votes

0 answers

177 views

Coupon collection with trading of doubles

probability combinatorics coupon-collector

asked Jun 14, 2016 at 6:25

6 votes

2 answers

713 views

Probability that a stick randomly broken in three places can form a triangle

probability alternative-proof inclusion-exclusion geometric-probability

asked Jul 25, 2018 at 16:33

6 votes

1 answer

117 views

Succinct proof that $\frac\pi4+\frac\pi6+\log2\gt2$

inequality definite-integrals approximation pi rational-functions

asked Apr 17, 2020 at 6:50

6 votes

1 answer

160 views

What is the expected volume of the simplex formed by $n+1$ points independently uniformly distributed on $\mathbb S^{n-1}$?

probability geometry volume spheres geometric-probability

asked Feb 24, 2020 at 16:05

5 votes

0 answers

100 views

More elegant derivation of the shift in median bin occupancy

combinatorics asymptotics alternative-proof balls-in-bins

asked Apr 21, 2016 at 11:38

5 votes

0 answers

176 views

Symmetric proof for the probability of real roots of a quadratic with exponentially distributed parameters

probability probability-distributions roots quadratics alternative-proof

asked Oct 13, 2015 at 7:21

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48 Questions

How to evaluate $\int_0^1\frac{\log^2(1+x)}x\mathrm dx$?

necessary and sufficient condition for trivial kernel of a matrix over a commutative ring

A proof of Wolstenholme's theorem

an integer sum of products of tangents

Generalised inclusion-exclusion principle

At what rate does the entropy of shuffled cards converge?

Arnol'd's trivium problem #68

What's up with Plouffe's inverter? Is there an alternative?

definite and indefinite sums and integrals

Can we qualitatively predict the strategy of the German and US teams in today's World Cup soccer match?

Why are all subset sizes equiprobable if elements are independently included with probability uniform over $[0,1]$?

The case of the missing ninth of a $2$€ coin

Why do the triangular numbers initially form long cycles mod $2^k$?

Does the Riemann hypothesis guarantee that integer factorization is difficult?

variable bounds on definite integrals in Wolfram|Alpha

What is the minimal isoperimetric ratio of a polyhedron with $5$ vertices?

expansion of $\int_0^\infty\left(\frac{\sin t}t\right)^p\mathrm dt$ in inverse powers of $p$

How is the number of points in the convex hull of five random points distributed?

A lawn, a flower, a pipe and the neighbours

Probability that one part of a randomly cut equilateral triangle covers the other

Is there a connection between the 3D random walk constant and the partition function?

What's the probability for two points to lie on the same side of the line joining two other points?

How to refer to the "sign" of the dependence of events?

Probability that one part of a randomly cut equilateral triangle covers the other without flipping

Coupon collection with trading of doubles

Probability that a stick randomly broken in three places can form a triangle

Succinct proof that $\frac\pi4+\frac\pi6+\log2\gt2$

What is the expected volume of the simplex formed by $n+1$ points independently uniformly distributed on $\mathbb S^{n-1}$?

More elegant derivation of the shift in median bin occupancy

Symmetric proof for the probability of real roots of a quadratic with exponentially distributed parameters