User Đào Thanh Oai

18 votes

3 answers

1k views

An ellipse through 12 points related to Golden ratio

asked Jun 24, 2018 at 0:34

17 votes

2 answers

2k views

Is every odd positive integer of the form $P_{n+m}-P_n-P_m$?

asked Jun 28, 2018 at 10:58

15 votes

2 answers

1k views

Do two new special points in any triangle exist?

asked Sep 30, 2018 at 17:09

14 votes

2 answers

684 views

Can four integer numbers $x$, $y$, $x-y$, $x+y$ be powerful numbers where $\gcd(x,y)=1$?

asked Jul 3 at 2:43

13 votes

2 answers

2k views

Is it a new discovery on conic section?

asked May 8, 2021 at 12:14

11 votes

3 answers

713 views

An open triangle problem in plane geometry

asked Nov 14, 2021 at 11:50

10 votes

1 answer

2k views

Is new $n$-conjecture as follows correct?

asked Jul 7, 2020 at 7:38

10 votes

0 answers

4k views

Is the conjecture A+B=C following correct?

asked Jun 19, 2018 at 4:00

9 votes

2 answers

595 views

Strengthened version of Isoperimetric inequality with n-polygon

asked Apr 30, 2018 at 8:08

9 votes

2 answers

496 views

In arbitrary cyclic polygon then $\sum_{i<j} x_{ij}^\alpha \ge \sum_{i<j} y_{ij}^\alpha $

asked Jul 12, 2018 at 5:39

9 votes

0 answers

911 views

A new theorem (discovered in 2013) equivalent to Brianchon theorem (the old theorem) discovered in XIX century?

asked Jun 14, 2020 at 4:03

9 votes

1 answer

1k views

Possible new theorem in plane geometry encompassing 5 famous geometry theorems

asked Oct 24, 2020 at 3:31

8 votes

0 answers

576 views

Are there at least one of $a$, $b$, $c$, $a+b$, $b+c$, $c+a$ have h(P) $\le 3$? (was checked up to $10^{18}$)

asked Oct 3, 2019 at 14:58

8 votes

1 answer

543 views

A Muirhead Like Inequality

asked Jun 17, 2018 at 13:34

8 votes

2 answers

394 views

Can exist a positive integer number $x$ such that $a_1=x$ and $a_n=2a_{n-1}+1$ are not prime for all $n \ge 1$?

asked Jul 3 at 9:52

7 votes

1 answer

660 views

Prove: If $P_n$ is $n$-$th$ prime number then $P_{n+m} \ge P_n+P_m$

asked Jun 27, 2018 at 2:24

7 votes

1 answer

201 views

Distributing $N$ points on the sphere so that the sum of their mutual distances is maximized?

asked Jul 11, 2018 at 9:39

7 votes

1 answer

679 views

A problem of four conics

asked Dec 12, 2018 at 15:36

6 votes

2 answers

399 views

An inequality related to area and sidelengths of a polygon $Area(A_1A_2....A_n) \le \frac{1}{n}cotg{\frac{\pi}{n}} \sum_{i=1}^nA_iA_{i+1}^2$

asked Jul 10, 2018 at 3:12

6 votes

2 answers

1k views

$\pi((n+1)^2)-\pi(n^2) \le \pi(n)$ for all $n \ge 370$?

asked Jun 26, 2018 at 2:11

6 votes

1 answer

365 views

Like Bradley’s conjecture (Four incenters lie on a circle) [closed]

asked Jun 12, 2020 at 5:18

6 votes

1 answer

307 views

Is min exponents of three positive integers $n$, $n+1$ and $n+2$ $=1$ true or false?

asked Sep 22, 2019 at 6:26

6 votes

0 answers

321 views

Does this plane geometry theorem have a name (well-known)?

asked Feb 5, 2021 at 3:55

6 votes

2 answers

723 views

Does always exist a prime number between $n(n+1)$ and $(n+1)(n+2)$?

asked Jun 15, 2021 at 1:59

5 votes

1 answer

1k views

Is this a new result about hexagon?

asked Aug 29 at 9:20

5 votes

1 answer

434 views

Golden ratio as a property of conic section (is it known?)

asked May 10, 2021 at 0:11

5 votes

1 answer

358 views

Discovered 240 new circles associated with Pascal's line

asked Oct 22, 2020 at 2:31

5 votes

1 answer

268 views

Is it a known property of positive integers $n> 2 $ that one must have $n < \mathrm{rad}(n(n-1)(n-2))$?

asked Sep 26, 2019 at 15:41

5 votes

0 answers

343 views

$N$-$th$ closed chain of six circles

asked Jul 4, 2018 at 9:54

4 votes

1 answer

388 views

$\sum_{k=1}^n\frac{\sin kx}{k^\alpha} >0\quad\text{for all}\ n=1,2,3,\ldots\ \text{and}\ 0<x<\pi, \text{and}\ \alpha \ge 1$

asked Jun 27, 2018 at 11:17

Stack Exchange Network

102 Questions

An ellipse through 12 points related to Golden ratio

Is every odd positive integer of the form $P_{n+m}-P_n-P_m$?

Do two new special points in any triangle exist?

Can four integer numbers $x$, $y$, $x-y$, $x+y$ be powerful numbers where $\gcd(x,y)=1$?

Is it a new discovery on conic section?

An open triangle problem in plane geometry

Is new $n$-conjecture as follows correct?

Is the conjecture A+B=C following correct?

Strengthened version of Isoperimetric inequality with n-polygon

In arbitrary cyclic polygon then $\sum_{i<j} x_{ij}^\alpha \ge \sum_{i<j} y_{ij}^\alpha $

A new theorem (discovered in 2013) equivalent to Brianchon theorem (the old theorem) discovered in XIX century?

Possible new theorem in plane geometry encompassing 5 famous geometry theorems

Are there at least one of $a$, $b$, $c$, $a+b$, $b+c$, $c+a$ have h(P) $\le 3$? (was checked up to $10^{18}$)

A Muirhead Like Inequality

Can exist a positive integer number $x$ such that $a_1=x$ and $a_n=2a_{n-1}+1$ are not prime for all $n \ge 1$?

Prove: If $P_n$ is $n$-$th$ prime number then $P_{n+m} \ge P_n+P_m$

Distributing $N$ points on the sphere so that the sum of their mutual distances is maximized?

A problem of four conics

An inequality related to area and sidelengths of a polygon $Area(A_1A_2....A_n) \le \frac{1}{n}cotg{\frac{\pi}{n}} \sum_{i=1}^nA_iA_{i+1}^2$

$\pi((n+1)^2)-\pi(n^2) \le \pi(n)$ for all $n \ge 370$?

Like Bradley’s conjecture (Four incenters lie on a circle) [closed]

Is min exponents of three positive integers $n$, $n+1$ and $n+2$ $=1$ true or false?

Does this plane geometry theorem have a name (well-known)?

Does always exist a prime number between $n(n+1)$ and $(n+1)(n+2)$?

Is this a new result about hexagon?

Golden ratio as a property of conic section (is it known?)

Discovered 240 new circles associated with Pascal's line

Is it a known property of positive integers $n> 2 $ that one must have $n < \mathrm{rad}(n(n-1)(n-2))$?

$N$-$th$ closed chain of six circles

$\sum_{k=1}^n\frac{\sin kx}{k^\alpha} >0\quad\text{for all}\ n=1,2,3,\ldots\ \text{and}\ 0<x<\pi, \text{and}\ \alpha \ge 1$