List questions from euclidean-geometry

Published on 06 Dec 2019 - 14:20

61

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If point $P$ varies on a circle about the center of rectangle $\square ABCD$, then $PA^2+PB^2+PC^2+PD^2$ remains constant

Published on 06 Dec 2019 - 23:47

135

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Find the value of $x$ in the figure

Published on 07 Dec 2019 - 16:27

315

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No bounded set in $\mathbb{R}$ is isometric to a proper subset

Published on 25 Mar 2026 - 23:53

69

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$[0,1]$ is equidecomposable with $(0,1]$

Published on 08 Dec 2019 - 9:32

106

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Line joining the intersections of perpendicular bisectors of opposite sides of a quadrilateral

Published on 08 Dec 2019 - 10:06

112

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Equivalent metric for Euclidean space in 3dimension other than usual Euclidean metric

Published on 23 Feb 2026 - 1:22

218

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Shows that $EFD$ is also equilateral.

Published on 08 Dec 2019 - 19:02

38

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Point of intersection of two lines given colinearity

Published on 01 Apr 2026 - 18:49

27

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Intuitive meaning of the theorem "Every continuous odd map $f∶S^2⟶\mathbb{R}^2$ has a zero in $S^2.$"

Published on 11 Dec 2019 - 10:21

297

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Asymptotic number of lattice points in an annulus

Published on 26 Mar 2026 - 13:01

72

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The intersection of $w = x / \beta$ and a line parallel to $w = \beta x$.

Published on 23 Feb 2026 - 2:47

128

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What additional assumptions, if any, that we need to derive transitivity of parallel lines in plane geometry from strong version of Playfair's axiom?

Published on 13 Dec 2019 - 14:05

51

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Forcing some random points to be on a circle via optimization

Published on 26 Mar 2026 - 6:03

23

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Pasture in the field

Published on 29 Mar 2026 - 16:24

List Question

What fraction is shaded?

If point $P$ varies on a circle about the center of rectangle $\square ABCD$, then $PA^2+PB^2+PC^2+PD^2$ remains constant

Find the value of $x$ in the figure

No bounded set in $\mathbb{R}$ is isometric to a proper subset

$[0,1]$ is equidecomposable with $(0,1]$

Line joining the intersections of perpendicular bisectors of opposite sides of a quadrilateral

Equivalent metric for Euclidean space in 3dimension other than usual Euclidean metric

Shows that $EFD$ is also equilateral.

Point of intersection of two lines given colinearity

Intuitive meaning of the theorem "Every continuous odd map $f∶S^2⟶\mathbb{R}^2$ has a zero in $S^2.$"

Asymptotic number of lattice points in an annulus

The intersection of $w = x / \beta$ and a line parallel to $w = \beta x$.

What additional assumptions, if any, that we need to derive transitivity of parallel lines in plane geometry from strong version of Playfair's axiom?

Forcing some random points to be on a circle via optimization

Pasture in the field

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