User CuriousMind - Mathematics Stack Exchange

11 votes

3 answers

515 views

Prove that $2-\cfrac{\pi^2}{6-\cfrac{\pi^2}{10-\cfrac{\pi^2}{14-\cfrac{\pi^2}{...}}}} = 0$

asked Sep 25, 2021 at 23:58

9 votes

3 answers

1k views

Prove two angles add up to 90 degrees

asked Aug 17, 2020 at 1:45

9 votes

1 answer

323 views

$N$ kids with $k$ balls. Reshuffle. Find distribution of number of balls brought back by same kids when $N \rightarrow \infty$

asked Oct 15, 2020 at 2:43

8 votes

3 answers

228 views

simple looking but hard to prove geometrical problem: prove that 4 points on the same circle.

asked Dec 22, 2018 at 14:07

7 votes

1 answer

96 views

n-th order polynomial with all roots where all coefficients are 1 or -1, highest order of n?

asked Dec 25, 2018 at 3:45

7 votes

2 answers

176 views

Find maximum $k \in \mathbb{R}^{+}$ such that $ \frac{a^3}{(b-c)^2} + \frac{b^3}{(c-a)^2} + \frac{c^3}{(a-b)^2} \geq k (a+b+c) $

asked Jun 14, 2020 at 14:10

5 votes

1 answer

755 views

Why do we usually not need to find the eigenvalues of non-symmetric matrix

asked Aug 5, 2021 at 23:43

4 votes

2 answers

284 views

Prove that $\int_0^{\infty} \frac{1-\cos(at)}{t^{1+\alpha}} dt = \frac{\pi}{2 \Gamma(\alpha+1) \sin (\alpha \pi /2 )} |a|^{\alpha}$

asked Jul 25, 2021 at 13:39

4 votes

1 answer

89 views

Intuitive explanation of "Information Filter" formation of Kalman filter

asked May 22 at 2:32

3 votes

0 answers

125 views

Proving the matrix is positive semidefintie through integrals

asked Jul 25, 2021 at 23:05

3 votes

1 answer

99 views

Find minimum value of $(ab-2a+4)^2 + (bc-2b+4)^2+ (ca-2c+4)^2$ where $0 \leq a,b,c \leq2$

asked Jan 14, 2023 at 14:59

3 votes

1 answer

65 views

Acute triangle $\triangle ABC$ has $(\sin A - 2 \sin 2B) = 2 - 2 \cos 2B$ Find the range of $\frac{\sin B + \sin C}{\sin A}$

asked Jan 25, 2023 at 0:04

3 votes

2 answers

697 views

Sum of Liouville's function

asked Sep 14, 2019 at 3:37

3 votes

1 answer

409 views

The intuition behind the definition of the definiteness of a matrix

asked Oct 18, 2019 at 0:14

3 votes

2 answers

129 views

$16$ people around a round table

asked Oct 20, 2019 at 13:25

3 votes

2 answers

148 views

$\omega$ satisfies $a \omega^3 + b \omega^2 + c \omega + d = 0$, Prove that $ |\omega| \leq \max( \frac{b}{a}, \frac{c}{b}, \frac{d}{c})$

asked Dec 6, 2019 at 12:44

3 votes

1 answer

466 views

How do I prove that $x^n+x^{n-1}+...+x^2-nx+1=0$ ($n>2$) has one and only one root in $(0,1)$

asked Aug 4, 2019 at 1:12

3 votes

3 answers

139 views

simplify $\sqrt[3]{x \sqrt[3]{ x \sqrt[3]{x ...}} }$ -- if $x$ is negative?

asked Apr 12, 2020 at 1:24

2 votes

1 answer

193 views

Let $a_{i,i+1} = c_i$ for $i=1,...n$, Prove that the determinant of $I + A + A^2 + ... + A^n = (1-c)^{n-1}$ where $c = c_1...c_n$

asked Dec 17, 2019 at 21:55

2 votes

4 answers

320 views

Linear Algebra question on positive definite matrix

asked Mar 9, 2015 at 18:54

2 votes

1 answer

786 views

Drawing n intervals uniformly randomly, probability that at least one interval overlaps with all others

asked Apr 20, 2015 at 1:04

2 votes

1 answer

1k views

Does Rayleigh quotient iteration always find the largest eigenvalue in magnitude? If not, what are the applications?

asked Aug 7, 2021 at 1:53

2 votes

2 answers

301 views

Geometry question: Find the area of blue-shared area inside this isosceles

asked Jun 26, 2020 at 21:32

2 votes

1 answer

146 views

Find $x_1 + x_2 + \dots+ x_{n}$ and $1^{n+1}x_1 + 2^{n+1}x_2 + \dots + {n}^{n+1}x_{n}$ given a set of linear constraints

asked Jan 7, 2022 at 22:09

2 votes

1 answer

67 views

minimizing $| x x^T - A |^2$ for a covariance matrix $A$

asked May 23 at 2:24

2 votes

0 answers

62 views

How exactly is Sherman-Morrison-Woodbury formula used in Kalman Filter

asked Jul 13 at 16:02

1 vote

2 answers

282 views

Number of binary matrices whose rows/columns are weakly monotone

asked Nov 29, 2018 at 19:00

1 vote

3 answers

80 views

Is there a closed-form analytical solution to: Maximize $y^T (X \beta) $ s.t. $(X \beta)^T (X \beta) = y^T y$.

asked Dec 26, 2022 at 1:48

1 vote

1 answer

74 views

Maximum of $\prod_{k=1}^{n} { f(c_k) }$ where $f(m) = \sum_{k=1}^{m} k^2, \sum_{i=1}^{n} c_i = 2020$.

asked Dec 28, 2020 at 15:40

1 vote

5 answers

99 views

Find $\lim_{t \rightarrow 0} \int_{0}^{t} \frac{\sqrt{1+\sin(x^2)}}{\sin t} dx$

asked Dec 29, 2020 at 19:10

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51 Questions

Prove that $2-\cfrac{\pi^2}{6-\cfrac{\pi^2}{10-\cfrac{\pi^2}{14-\cfrac{\pi^2}{...}}}} = 0$

Prove two angles add up to 90 degrees

$N$ kids with $k$ balls. Reshuffle. Find distribution of number of balls brought back by same kids when $N \rightarrow \infty$

simple looking but hard to prove geometrical problem: prove that 4 points on the same circle.

n-th order polynomial with all roots where all coefficients are 1 or -1, highest order of n?

Find maximum $k \in \mathbb{R}^{+}$ such that $ \frac{a^3}{(b-c)^2} + \frac{b^3}{(c-a)^2} + \frac{c^3}{(a-b)^2} \geq k (a+b+c) $

Why do we usually not need to find the eigenvalues of non-symmetric matrix

Prove that $\int_0^{\infty} \frac{1-\cos(at)}{t^{1+\alpha}} dt = \frac{\pi}{2 \Gamma(\alpha+1) \sin (\alpha \pi /2 )} |a|^{\alpha}$

Intuitive explanation of "Information Filter" formation of Kalman filter

Proving the matrix is positive semidefintie through integrals

Find minimum value of $(ab-2a+4)^2 + (bc-2b+4)^2+ (ca-2c+4)^2$ where $0 \leq a,b,c \leq2$

Acute triangle $\triangle ABC$ has $(\sin A - 2 \sin 2B) = 2 - 2 \cos 2B$ Find the range of $\frac{\sin B + \sin C}{\sin A}$

Sum of Liouville's function

The intuition behind the definition of the definiteness of a matrix

$16$ people around a round table

$\omega$ satisfies $a \omega^3 + b \omega^2 + c \omega + d = 0$, Prove that $ |\omega| \leq \max( \frac{b}{a}, \frac{c}{b}, \frac{d}{c})$

How do I prove that $x^n+x^{n-1}+...+x^2-nx+1=0$ ($n>2$) has one and only one root in $(0,1)$

simplify $\sqrt[3]{x \sqrt[3]{ x \sqrt[3]{x ...}} }$ -- if $x$ is negative?

Let $a_{i,i+1} = c_i$ for $i=1,...n$, Prove that the determinant of $I + A + A^2 + ... + A^n = (1-c)^{n-1}$ where $c = c_1...c_n$

Linear Algebra question on positive definite matrix

Drawing n intervals uniformly randomly, probability that at least one interval overlaps with all others

Does Rayleigh quotient iteration always find the largest eigenvalue in magnitude? If not, what are the applications?

Geometry question: Find the area of blue-shared area inside this isosceles

Find $x_1 + x_2 + \dots+ x_{n}$ and $1^{n+1}x_1 + 2^{n+1}x_2 + \dots + {n}^{n+1}x_{n}$ given a set of linear constraints

minimizing $| x x^T - A |^2$ for a covariance matrix $A$

How exactly is Sherman-Morrison-Woodbury formula used in Kalman Filter

Number of binary matrices whose rows/columns are weakly monotone

Is there a closed-form analytical solution to: Maximize $y^T (X \beta) $ s.t. $(X \beta)^T (X \beta) = y^T y$.

Maximum of $\prod_{k=1}^{n} { f(c_k) }$ where $f(m) = \sum_{k=1}^{m} k^2, \sum_{i=1}^{n} c_i = 2020$.

Find $\lim_{t \rightarrow 0} \int_{0}^{t} \frac{\sqrt{1+\sin(x^2)}}{\sin t} dx$