List questions from geometric-inequalities

Published on 13 Jul 2020 - 15:50

194

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Proving $\sqrt{x^2-xz+z^2} + \sqrt{y^2-yz+z^2} \geq \sqrt{x^2+xy+y^2}$ algebraically

Published on 23 Feb 2026 - 4:42

72

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In a triangle prove that $\mathrm{cosec}( A) +\mathrm{cosec}(B) +\mathrm{cosec}(C)\le \frac{2\sqrt 3}{9}\left (1+\frac Rr\right)^2$

Published on 14 Jul 2020 - 17:29

119

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Prove that in a triangle $\sum\limits_{cyc}\frac{w_bw_c}{w_a}\geq\frac{3}{4}\left(\sum\limits_{cyc}\frac{a^2w_a}{w_bw_c}\right)\geq\sqrt{3}s$

Published on 25 Mar 2026 - 17:41

95

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Inequality involving medians

Published on 25 Mar 2026 - 17:38

91

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system of inequalities in Mathematica

Published on 13 Jul 2016 - 18:55

116

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A generalization of Barrow's inequality

Published on 24 Jul 2016 - 14:25

294

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Israel tst 2011 geometrical inequality

Published on 27 Jul 2016 - 4:15

72

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Inequality involving lenghts of a triangle's sides

Published on 31 Jul 2016 - 9:39

112

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Inequality with triangle sides

Published on 31 Jul 2016 - 10:22

38

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Open cones in Macaulay2

Published on 25 Mar 2026 - 1:21

99

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Prove a geometric inequality, if 3 numbers are satisfying the condition

Published on 10 Aug 2016 - 11:53

475

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Arbitrary partition of a rectangle into rectangles: algorithms and data structures

Published on 26 Mar 2026 - 0:58

117

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How prove this inequality $a^2m_{b}m_{c}+b^2m_{c}m_{a}+c^2m_{a}m_{b}\ge\frac{1}{4}(a^2+b^2+c^2)^2$

Published on 25 Mar 2026 - 20:36

80

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why exist $a_{i},a_{j},a_{k}(1\le i<j<k\le 4)$ are side lengths of a triangle，if $2(a^4_{1}+a^4_{2}+a^4_{3}+a^4_{4})<33a_{1}a_{2}a_{3}a_{4}$

Published on 22 Aug 2016 - 7:06

List Question

a product of distances inequality of circumscribed polygon

Proving $\sqrt{x^2-xz+z^2} + \sqrt{y^2-yz+z^2} \geq \sqrt{x^2+xy+y^2}$ algebraically

In a triangle prove that $\mathrm{cosec}( A) +\mathrm{cosec}(B) +\mathrm{cosec}(C)\le \frac{2\sqrt 3}{9}\left (1+\frac Rr\right)^2$

Prove that in a triangle $\sum\limits_{cyc}\frac{w_bw_c}{w_a}\geq\frac{3}{4}\left(\sum\limits_{cyc}\frac{a^2w_a}{w_bw_c}\right)\geq\sqrt{3}s$

Inequality involving medians

system of inequalities in Mathematica

A generalization of Barrow's inequality

Israel tst 2011 geometrical inequality

Inequality involving lenghts of a triangle's sides

Inequality with triangle sides

Open cones in Macaulay2

Prove a geometric inequality, if 3 numbers are satisfying the condition

Arbitrary partition of a rectangle into rectangles: algorithms and data structures

How prove this inequality $a^2m_{b}m_{c}+b^2m_{c}m_{a}+c^2m_{a}m_{b}\ge\frac{1}{4}(a^2+b^2+c^2)^2$

why exist $a_{i},a_{j},a_{k}(1\le i<j<k\le 4)$ are side lengths of a triangle，if $2(a^4_{1}+a^4_{2}+a^4_{3}+a^4_{4})<33a_{1}a_{2}a_{3}a_{4}$

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