achille hui's user avatar
achille hui's user avatar
achille hui's user avatar
achille hui
  • Member for 11 years, 2 months
  • Last seen this week
  • Hong Kong
101 votes
Accepted

Conjecture $\int_0^1\frac{\mathrm dx}{\sqrt{1-x}\ \sqrt[4]x\ \sqrt[4]{2-x\,\sqrt3}}\stackrel?=\frac{2\,\sqrt2}{3\,\sqrt[8]3}\pi$

74 votes
Accepted

Is $0.1010010001000010000010000001 \ldots$ transcendental?

74 votes

Does non-symmetric positive definite matrix have positive eigenvalues?

70 votes
Accepted

Integral $\int_0^1\frac{\ln\left(x+\sqrt2\right)}{\sqrt{2-x}\,\sqrt{1-x}\,\sqrt{\vphantom{1}x}}\mathrm dx$

66 votes

What are some examples of mathematics that had unintended useful applications much later?

57 votes
Accepted

Conjecture $\int_0^1\frac{dx}{\sqrt[3]x\,\sqrt[6]{1-x}\,\sqrt{1-x\left(\sqrt{6}\sqrt{12+7\sqrt3}-3\sqrt3-6\right)^2}}=\frac\pi9(3+\sqrt2\sqrt[4]{27})$

53 votes

Find $xy+yz+zx$ given systems of three homogenous quadratic equations for $x, y, z$

52 votes
Accepted

Why does Wolframalpha think that this sum converges?

51 votes
Accepted

Prove that there exists a triangle which can be cut into 2005 congruent triangles.

50 votes
Accepted

Is there a fast way to prove a symmetric tridiagonal matrix is positive definite?

48 votes
Accepted

How does one [easily] calculate $\sum\limits_{n=1}^\infty\frac{\mathrm{pop}(n)}{n(n+1)}$?

47 votes
Accepted

Evaluating $\int_{0}^{1}\cdots\int_{0}^{1}\bigl\{\frac{1}{x_{1}\cdots x_{n}}\bigr\}^{2}\:\mathrm{d}x_{1}\cdots\mathrm{d}x_{n}$

47 votes

A strange integral: $\int_{-\infty}^{+\infty} {dx \over 1 + \left(x + \tan x\right)^2} = \pi.$

40 votes

Conflicting limit answers using calculator and wolfram alpha

39 votes

Can you complete the expression $2 \underline{ }\, \underline{ }\, \underline{ } \,\underline{ } 5 = 2015$?

37 votes
Accepted

Is Tolkien's Middle Earth flat?

37 votes
Accepted

Find large power of a non-diagonalisable matrix

35 votes
Accepted

A very different property of primitive Pythagorean triplets: Can number be in more than two of them?

35 votes
Accepted

How prove this matrix $\det (A)=\left(\frac{1}{\ln{(a_{i}+a_{j})}}\right)_{n\times n}\neq 0$

34 votes
Accepted

Gauss-divergence theorem for volume integral of a gradient field

34 votes

Geometry problem involving infinite number of circles

33 votes

What's the limit of $\sqrt{2 + \sqrt{2-\sqrt{2+\sqrt{2-\sqrt{2-\sqrt{2 + ...}}}}}} $?

32 votes
Accepted

Find $x,y,z>0$ such that $x+y+z=1$ and $x^2+y^2+z^2$ is minimal

30 votes

An exotic sequence

29 votes
Accepted

Can multiples of two reals stay separated?

29 votes
Accepted

How to evaluate $\int_{0}^{+\infty}\exp(-ax^2-\frac b{x^2})\,dx$ for $a,b>0$

28 votes
Accepted

How to compute $\int_{-\infty}^\infty\exp\left(-\frac{(x^2-13x-1)^2}{611x^2}\right)\ dx$

27 votes

Summation of an infinite Exponential series

26 votes
Accepted

A way to find this shaded area without calculus?

26 votes
Accepted

How would you find the exact roots of $y=x^3+x^2-2x-1$?

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