Questions tagged [geometry]
For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, and angles.
52,618 questions
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Why does $\,\lim_{b\to \infty}\left(\sqrt{c}-b\right)=\frac{a}{2}\;$ when $\;c=b^2+ab\;?$ [closed]
Why does $\,\lim\limits_{b\to \infty}\left(\sqrt{c}-b\right)=\frac{a}{2}\;$ when $\;c=b^2+ab\;?$
I've been studying the properties of rectangles for a little while on my own so I don't know what are ...
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Showing positive definite quadratic forms give the "most symmetrical" metrics over $\mathbb{R}^n$
I was unsatisfied with the many proofs of the Pythagorean theorem in which it's not clearly apparent which axioms are specifically needed, or because said axioms seem too geometrically motivated in ...
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Average distance between all the points on 3d surface
I am trying to calculate the average distance a particle passing through a cylinder experiences. There is both a top and a bottom and the dimensions of the cylinder are known. Particles can exit any ...
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Divide a right triangle into three quadrilaterals of equal area .
The goal is to find the point $M$ inside a given right triangle $ABC$ such that $\operatorname{Area}(APMN)=\operatorname{Area}(CQMP)=\operatorname{Area}(BQMN)$, where $N$, $P$, and $Q$ are the ...
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Finding coordinates of a point on a parabola given a rotated triangle condition
I am working on a geometry problem involving a parabola and coordinate transformations. I have solved the preliminary parts, but I am looking for a more elegant or geometric solution for the final ...
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Collinearity of $M', H, N'$ where $M', N'$ are reflections of midpoints across sides of the intouch triangle
Problem Statement:
Let $ABC$ be a triangle. Let $AH$ be the internal angle bisector of $\angle BAC$ (with $H \in BC$). Let $M$ and $N$ be the midpoints of the sides $AB$ and $AC$, respectively. Let ...
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Perpendicular from vertex in square - angle problem
Let ABCD be a square and Z the midpoint of BC. From vertex A, draw a perpendicular to line DZ with foot E. Draw segment EC. Find ∠ZEC.
Context:
I was studying parallelograms and their properties, ...
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Using geometric constructions to solve algebraic problems (in Euclid and Descartes)
Long-time listener, first-time caller here. I've got what I guess is a history of math question. I've been teaching a college course on Euclid's Elements (surprisingly fun, btw). I've been using David ...
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Relation between cuts of ellipsoid by lines and the ellipsoid itself
I stumbled across a problem regarding ellipsoids and got stuck trying to prove this relation between ellipsoids and their sections. Consider an ellipsoid $E$ written as
$$
E = \left\{x \in \mathbb{R}^...
- 1,870
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Three ways of finding x yield different results (basic circle question)
Say there is a circle P. The line XE is tangent to circle P, with E being the point of tangency. There is the line XP. The measures of angle EXP is 30º, and the measure of arc EW (W is the second ...
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Dissecting a "Line-Perpendicular Triangle" (side ratio 1:2) and finding the distance relationship.
I came across a geometry problem from a Chinese Grade 9 math exam that involves a specific type of triangle defined as a "Line-Perpendicular Triangle" (线垂三角形). I am stuck on the construction ...
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Is my proof wrong? The length of AE seems to be 64/11 but i got 6 [closed]
[A triangle ABC circumscribes a circle with center O and radius 4,the point of contact between the incircle and AB is at F and at AC it is E and at BC it is D,the lengths of BD is 6,CD=10, find AE]
$$(...
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generalizing space diagonals to all (or most) geometric solids
While writing about diagonals of shapes, I defined a space diagonal as a diagonal of a 3D shape connecting vertices that are not on the same face of the shape. I then realized that this definition ...
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How to prove that the locus of point $Q$ is a circle?
I've encountered the following problem:
Segment $AB$ is a diameter of the black circle $M$. The blue circle $T$ passes through point $B$, and $P$ is a point on the blue circle $T$. Draw line $BP$, ...
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Question about the inscribed square problem
I am reading The discrete square peg problem by Igor Pak (arXiv:0804.0657), where it is shown, among other things, that every simple polygon in the plane has an inscribed square.
If you were to use a ...
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