List questions from geometric-inequalities

Published on 28 Feb 2015 - 7:41

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How prove this geometry inequality $R_1^4+R_2^4+R_3^4+R_4^4+R_5^4\geq {4\over 5\sin^2 108^\circ}S^2$

Published on 14 Apr 2015 - 17:01

589

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Find maximum width of a rectangle contained with another (diagonally)

Published on 23 Apr 2015 - 2:53

857

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How to prove that $ \sin \angle{GAB}+\sin \angle{GBC}+\sin \angle{GCA} \le \frac{3}{2} $ for a triangle $ABC$ with centroid $G$?

Published on 25 Apr 2015 - 6:07

92

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Inequality involving lengths and triangles

Published on 31 May 2015 - 13:24

353

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The inequality $\frac{MA}{BC}+\frac{MB}{CA}+\frac{MC}{AB}\geq \sqrt{3}$

Published on 05 Jul 2015 - 2:36

162

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Point on the Plane, a Triangle, and a Lower Bound of a Ratio Sum

Published on 26 Jul 2015 - 8:52

146

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O.I.M. polygon inequality

Published on 31 Jul 2015 - 17:49

1.2k

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An inequality about the sum of distances between points : same color $\le$ different colors?

Published on 05 Aug 2015 - 13:05

190

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Area of quadrilateral: $S \leq \frac{(a+b)(c+d)}4 $

Published on 19 Aug 2015 - 21:48

684

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Inequality between altitude and sides in triangle

Published on 20 Aug 2015 - 3:17

1.2k

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Find the min and max distance from origin of the curve $\vert z+\frac{1}{z}\vert=a$

Published on 23 Aug 2015 - 1:40

124

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Can we relax the triangle inequality for $\| v \|$ = $\|v - v_0 + v_0\|$?

Published on 26 Aug 2015 - 6:05

385

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In tetrahedron ABCD, prove that $r<\frac{AB\cdot CD}{2AB+2CD}$

Published on 15 Sep 2015 - 5:25

508

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How can we explain $e^{\pi}-\pi\approx20$?

Published on 06 Oct 2015 - 10:08

List Question

Proof of a geometric statement

How prove this geometry inequality $R_1^4+R_2^4+R_3^4+R_4^4+R_5^4\geq {4\over 5\sin^2 108^\circ}S^2$

Find maximum width of a rectangle contained with another (diagonally)

How to prove that $ \sin \angle{GAB}+\sin \angle{GBC}+\sin \angle{GCA} \le \frac{3}{2} $ for a triangle $ABC$ with centroid $G$?

Inequality involving lengths and triangles

The inequality $\frac{MA}{BC}+\frac{MB}{CA}+\frac{MC}{AB}\geq \sqrt{3}$

Point on the Plane, a Triangle, and a Lower Bound of a Ratio Sum

O.I.M. polygon inequality

An inequality about the sum of distances between points : same color $\le$ different colors?

Area of quadrilateral: $S \leq \frac{(a+b)(c+d)}4 $

Inequality between altitude and sides in triangle

Find the min and max distance from origin of the curve $\vert z+\frac{1}{z}\vert=a$

Can we relax the triangle inequality for $\| v \|$ = $\|v - v_0 + v_0\|$?

In tetrahedron ABCD, prove that $r<\frac{AB\cdot CD}{2AB+2CD}$

How can we explain $e^{\pi}-\pi\approx20$?

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