List questions from geometric-inequalities

Published on 23 Apr 2020 - 16:48

69

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How to analyze the equation $(x-y)^2=2\big( (x+y)-2\sqrt{xy} \big)$?

Published on 24 Apr 2020 - 12:53

80

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Does this inequality hold with some constant factor $c>0$?

Published on 25 Apr 2020 - 18:03

39

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Is this "constrained" infimum zero?

Published on 27 Apr 2020 - 16:21

94

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Prove that $AD\cdot BD \cdot CD \leq \dfrac{32}{27}$ where $ABC$ is a triangle of circumradius 1 and $D\in (BC)$.

Published on 20 May 2020 - 19:24

175

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BMO1 2010-11 Q6

Published on 23 May 2020 - 16:46

611

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Minimize area of n-gon circumscribed around unit circle

Published on 25 May 2020 - 19:55

116

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Lipschitz maps cannot increase the volume of a Borel set by a factor greater than $k^n$.

Published on 27 May 2020 - 22:44

88

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Triangular Inequality: Want resolution of the following discrepancy?

Published on 02 Jun 2020 - 15:28

118

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Prove that $21(a^2+b^2+c^2)\ge 20 +9(a^3+b^3+c^3)$

Published on 25 Mar 2026 - 11:13

170

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Cauchy–Schwarz inequality intuition

Published on 23 Jun 2020 - 17:28

156

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Does the least value of $\cos A + \cos B + \cos C$ exist, where $A$, $B$, $C$ are angles of a triangle?

Published on 28 Jun 2020 - 6:15

245

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Showing that $\sin^2x\cdot\sin^22x\cdot\sin^24x\cdot\sin^28x\cdots\sin^22^nx\leq\frac{3^n}{4^n}$

Published on 08 Jul 2020 - 8:44

276

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For any complex $z$, $|z-1|\leq |z-j|+|z-j^2|$

Published on 11 Jul 2020 - 8:37

36

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Inequality of $( y_1 \cdot y_2 \cdot \ldots \cdot y_M )\log ( y_1 \cdot y_2 \cdot \ldots \cdot y_M )$?

Published on 11 Jul 2020 - 11:31

List Question

Inequality $a^ab^bc^c \geq (a+b-c)^a(b+c-a)^b(c+a-b)^c$

How to analyze the equation $(x-y)^2=2\big( (x+y)-2\sqrt{xy} \big)$?

Does this inequality hold with some constant factor $c>0$?

Is this "constrained" infimum zero?

Prove that $AD\cdot BD \cdot CD \leq \dfrac{32}{27}$ where $ABC$ is a triangle of circumradius 1 and $D\in (BC)$.

BMO1 2010-11 Q6

Minimize area of n-gon circumscribed around unit circle

Lipschitz maps cannot increase the volume of a Borel set by a factor greater than $k^n$.

Triangular Inequality: Want resolution of the following discrepancy?

Prove that $21(a^2+b^2+c^2)\ge 20 +9(a^3+b^3+c^3)$

Cauchy–Schwarz inequality intuition

Does the least value of $\cos A + \cos B + \cos C$ exist, where $A$, $B$, $C$ are angles of a triangle?

Showing that $\sin^2x\cdot\sin^22x\cdot\sin^24x\cdot\sin^28x\cdots\sin^22^nx\leq\frac{3^n}{4^n}$

For any complex $z$, $|z-1|\leq |z-j|+|z-j^2|$

Inequality of $( y_1 \cdot y_2 \cdot \ldots \cdot y_M )\log ( y_1 \cdot y_2 \cdot \ldots \cdot y_M )$?

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