Question

Does ONLY the ellipse have these properties?

score 446 · Answer 1 · 2026-03-30 13:20:58

446

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Does ONLY the ellipse have these properties?

Published on 30 Mar 2026 - 13:20

score 287 · Answer 2 · 2020-08-20 22:14:26

287

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If $D$ is inside an acute triangle $ABC$ s.t. $\angle ADB=\angle ACB+\pi/2$ and $AC\cdot BD=AD\cdot BC$, then find $\frac{AB\cdot CD}{AC\cdot BD}$.

Published on 20 Aug 2020 - 22:14

score 622 · Answer 3 · 2026-03-29 03:36:32

622

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There are given $n$ points on plane. Prove that there are not more than $n$ pairs of vertices, distance between which is exactly $d$

Published on 29 Mar 2026 - 3:36

score 161 · Answer 4 · 2026-03-28 06:06:58

161

Views

Building "oppositely bitten rectangles" with consecutive squares

Published on 28 Mar 2026 - 6:06

score 54 · Answer 5 · 2020-08-24 12:16:41

54

Views

Plane Fitting, why everbody set c = 1?

Published on 24 Aug 2020 - 12:16

score 68 · Answer 6 · 2026-02-23 11:41:25

68

Views

How to compute a particular sum of ratios in a triangle?

Published on 23 Feb 2026 - 11:41

score 104 · Answer 7 · 2020-08-26 17:57:28

104

Views

Reference request: Where does this proposition about ellipses appear in the literature?

Published on 26 Aug 2020 - 17:57

score 169 · Answer 8 · 2020-08-27 00:36:10

169

Views

True or False: An equation of the form $ax_1 + bx_2 + cx_3 = d$ can be visualized as a line in $R^3$.

Published on 27 Aug 2020 - 0:36

score 158 · Answer 9 · 2026-03-30 10:37:46

158

Views

Existence of regular $n$-gon whose vertices are arbitrarily close to integer coordinates

Published on 30 Mar 2026 - 10:37

score 64 · Answer 10 · 2026-03-25 23:35:34

64

Views

Pick's theorem and the gamma function?

Published on 25 Mar 2026 - 23:35

score 45 · Answer 11 · 2020-09-01 03:44:34

45

Views

Sine of the angle made by two intersecting lines

Published on 01 Sep 2020 - 3:44

score 39 · Answer 12 · 2020-09-01 13:22:56

39

Views

Which of the following sets are planes(in their various n-spaces)?

Published on 01 Sep 2020 - 13:22

score 38 · Answer 13 · 2020-09-08 23:03:00

38

Views

$n$ amount of lines make $m$ amount of intersection points. How many values of $m$?

Published on 08 Sep 2020 - 23:03

score 109 · Answer 14 · 2020-09-12 00:31:37

109

Views

Tangent of $Ax^2+By^2+2Hxy+2Gx+2Fy=0$

Published on 12 Sep 2020 - 0:31

score 91 · Answer 15 · 2020-09-12 17:33:57

91

Views

Showing $\frac{|\vec{A_1B}|}{|\vec{A_1C}|}\frac{|\vec{B_1C}|}{|\vec{B_1A}|}\frac{|\vec{C_1A}|}{|\vec{C_1B}|}=1$ implies $AA_1$, $BB_1$, $CC_1$ concur

Published on 12 Sep 2020 - 17:33

List Question

Does ONLY the ellipse have these properties?

If $D$ is inside an acute triangle $ABC$ s.t. $\angle ADB=\angle ACB+\pi/2$ and $AC\cdot BD=AD\cdot BC$, then find $\frac{AB\cdot CD}{AC\cdot BD}$.

There are given $n$ points on plane. Prove that there are not more than $n$ pairs of vertices, distance between which is exactly $d$

Building "oppositely bitten rectangles" with consecutive squares

Plane Fitting, why everbody set c = 1?

How to compute a particular sum of ratios in a triangle?

Reference request: Where does this proposition about ellipses appear in the literature?

True or False: An equation of the form $ax_1 + bx_2 + cx_3 = d$ can be visualized as a line in $R^3$.

Existence of regular $n$-gon whose vertices are arbitrarily close to integer coordinates

Pick's theorem and the gamma function?

Sine of the angle made by two intersecting lines

Which of the following sets are planes(in their various n-spaces)?

$n$ amount of lines make $m$ amount of intersection points. How many values of $m$?

Tangent of $Ax^2+By^2+2Hxy+2Gx+2Fy=0$

Showing $\frac{|\vec{A_1B}|}{|\vec{A_1C}|}\frac{|\vec{B_1C}|}{|\vec{B_1A}|}\frac{|\vec{C_1A}|}{|\vec{C_1B}|}=1$ implies $AA_1$, $BB_1$, $CC_1$ concur

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