Đào Thanh Oai's user avatar
Đào Thanh Oai's user avatar
Đào Thanh Oai's user avatar
Đào Thanh Oai
  • Member for 5 years, 10 months
  • Last seen this week
18 votes
3 answers
1k views

An ellipse through 12 points related to Golden ratio

17 votes
2 answers
2k views

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

13 votes
2 answers
2k views

Is it a new discovery on conic section?

11 votes
2 answers
1k views

Do two new special points in any triangle exist?

11 votes
3 answers
648 views

An open triangle problem in plane geometry

10 votes
1 answer
2k views

Is new $n$-conjecture as follows correct?

9 votes
0 answers
866 views

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

9 votes
2 answers
568 views

Strengthened version of Isoperimetric inequality with n-polygon

9 votes
0 answers
4k views

Is the conjecture A+B=C following correct?

8 votes
1 answer
516 views

A Muirhead Like Inequality

8 votes
0 answers
575 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 $10^{18}$)

8 votes
1 answer
993 views

Possible new theorem in plane geometry encompassing 5 famous geometry theorems

7 votes
1 answer
651 views

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

7 votes
1 answer
198 views

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

7 votes
1 answer
625 views

A problem of four conics

6 votes
2 answers
378 views

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

6 votes
2 answers
1k views

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

6 votes
0 answers
310 views

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

6 votes
1 answer
338 views

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

6 votes
1 answer
300 views

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

6 votes
2 answers
690 views

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

5 votes
1 answer
265 views

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

5 votes
1 answer
412 views

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

5 votes
1 answer
323 views

Discovered 240 new circles associated with Pascal's line

5 votes
0 answers
298 views

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

5 votes
0 answers
327 views

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

4 votes
1 answer
239 views

Inequality $\frac{C}{d_{max}} \le \pi $ relating perimeter and diameter of planar convex body

4 votes
2 answers
416 views

Combination power elementary symmetric polynomial inequality

4 votes
1 answer
367 views

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

4 votes
1 answer
236 views

A closed chain of $2n+1$-gon around $2n+1$-points