Question

Finding the range of $\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}$, for $a$, $b$, $c$ the sides of a triangle

score 259 · Answer 1 · 2016-11-21 06:42:09

259

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Finding the range of $\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}$, for $a$, $b$, $c$ the sides of a triangle

Published on 21 Nov 2016 - 6:42

score 251 · Answer 2 · 2016-11-27 21:38:42

251

Views

Variation of Triangle Inequality

Published on 27 Nov 2016 - 21:38

score 340 · Answer 3 · 2016-12-06 14:42:17

340

Views

Find the minimum of $\sqrt{(x+1)^2+(y-1)^2}+\sqrt{(x+2)^2+(y+2)^2}+\sqrt{(x-1)^2+(y+1)^2}$ For real $x,y$

Published on 06 Dec 2016 - 14:42

score 94 · Answer 4 · 2016-12-11 19:09:43

94

Views

Weighted distances from the barycentre

Published on 11 Dec 2016 - 19:09

score 1.1k · Answer 5 · 2026-03-25 12:49:50

1.1k

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Let $a,b,c$ be the length of sides of a triangle then prove that $a^2b(a-b)+b^2c(b-c)+c^2a(c-a)\ge0$

Published on 25 Mar 2026 - 12:49

score 96 · Answer 6 · 2016-12-12 16:01:31

96

Views

Prove that $\tan(πx/4) + (1 - x) \sin(πx/2) > x$ for $x \in (0,1)$

Published on 12 Dec 2016 - 16:01

score 1.1k · Answer 7 · 2016-12-26 03:02:57

1.1k

Views

Oppenheim's Inequality for triangles, American Mathematical Monthly problems

Published on 26 Dec 2016 - 3:02

score 123 · Answer 8 · 2026-03-26 03:08:21

123

Views

Prove the inequality $(x+y+z)^2\ge 4(x^2y^2+y^2z^2+z^2x^2)$

Published on 26 Mar 2026 - 3:08

score 309 · Answer 9 · 2016-12-31 06:27:07

309

Views

Prove that: $ m_a + m_b + m_c \le 4R + r $

Published on 31 Dec 2016 - 6:27

score 253 · Answer 10 · 2026-03-26 03:06:09

253

Views

Geometric (Trigonometric) inequality $\frac{(a+b+c)^3}{3abc}\leq1+\frac{4R}{r}$

Published on 26 Mar 2026 - 3:06

score 118 · Answer 11 · 2017-01-04 05:04:00

118

Views

weaker than isoperimetric inequality for surfaces in $\mathbb{R}^3$

Published on 04 Jan 2017 - 5:04

score 31 · Answer 12 · 2017-01-05 07:39:19

31

Views

Inequality satisfied by coefficients

Published on 05 Jan 2017 - 7:39

score 194 · Answer 13 · 2017-01-05 16:18:54

194

Views

Inequality for Hardy-Littlewood type function

Published on 05 Jan 2017 - 16:18

score 108 · Answer 14 · 2017-01-12 23:41:37

108

Views

How to prove this geometric inequality and find the equality cases?

Published on 12 Jan 2017 - 23:41

score 202 · Answer 15 · 2017-01-15 05:54:41

202

Views

How can I prove this inequality in a triangle: $\frac{1}{(b+c-a)} +\frac{1}{(c+a-b)} +\frac{1}{(a+b-c)} \gt \frac{1}{a} +\frac{1}{b} +\frac{1}{c}$?

Published on 15 Jan 2017 - 5:54

List Question

Finding the range of $\frac{a}{b+c} + \frac{b}{c+a} + \frac{c}{a+b}$, for $a$, $b$, $c$ the sides of a triangle

Variation of Triangle Inequality

Find the minimum of $\sqrt{(x+1)^2+(y-1)^2}+\sqrt{(x+2)^2+(y+2)^2}+\sqrt{(x-1)^2+(y+1)^2}$ For real $x,y$

Weighted distances from the barycentre

Let $a,b,c$ be the length of sides of a triangle then prove that $a^2b(a-b)+b^2c(b-c)+c^2a(c-a)\ge0$

Prove that $\tan(πx/4) + (1 - x) \sin(πx/2) > x$ for $x \in (0,1)$

Oppenheim's Inequality for triangles, American Mathematical Monthly problems

Prove the inequality $(x+y+z)^2\ge 4(x^2y^2+y^2z^2+z^2x^2)$

Prove that: $ m_a + m_b + m_c \le 4R + r $

Geometric (Trigonometric) inequality $\frac{(a+b+c)^3}{3abc}\leq1+\frac{4R}{r}$

weaker than isoperimetric inequality for surfaces in $\mathbb{R}^3$

Inequality satisfied by coefficients

Inequality for Hardy-Littlewood type function

How to prove this geometric inequality and find the equality cases?

How can I prove this inequality in a triangle: $\frac{1}{(b+c-a)} +\frac{1}{(c+a-b)} +\frac{1}{(a+b-c)} \gt \frac{1}{a} +\frac{1}{b} +\frac{1}{c}$?

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