Questions tagged [geometry]
For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, and angles.
50,580
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how to prove that two line segments are perpendicular
I encountered with a pretty simple geometry problem, but I'm totally stuck. Can somebody help?
Let a quadrilateral $ABCD$ is inscribed in a circle with center $O$.
Two opposite edges $AB$ and $CD$ ...
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Where is the pentagon in the Fibonacci sequence?
It is common wisdom that "When you see $\pi$, there is a circle close at hand". For example:
The periods of sine and cosine equal $2\pi$? Properly constructed, the right triangles that ...
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How do you find the intersection between 2 complex shapes?
One thing I've done to find if two perfect circles intersect is to compare the radii of both circles to the distance between them, which isn't complicated at all. However, for non-circle shapes, I don'...
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Knowing that the area of the shaded region is 2π, find the length of the chord PQ [closed]
Diagram
The diagram shows two circles contained within a larger circle. The shaded region is the area of the larger circle minus the area of the the two enclosed circles. A chord PQ is tangent to both ...
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Prove that a loin with it's boundaries is closed
So, I'm not very advanced in topology, but I've noticed that lines on manifolds can have interesting properties. But I don't know if and how lines are defined on general topological spaces (is extra ...
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Continuous Course Deviation. [closed]
It's been a long time since I took geometry, analytic geometry, etc. This problem and how to solve it must be explained to the laymen (including me). I solved a similar problem in high school (1976) ...
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Golden ratio points in ellipse
This is a property of the ellipse. The sum of distances to the foci is constant:
In particular, some of these points must satisfy the golden ratio relationship:
Given the equation of the ellipse in ...
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If a Banach manifold satisfies the Heine-Borel property, then does it have finite dimension?
Suppose $C$ is a topological Banach manifold, that is also a closed convex subset of a Banach space $E$, also, $C$ satisfies the Heine-Borel property:
Every closed and bounded (with respect to the ...
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horizontal cross section area of egg in terms of the depth [closed]
how to get the horizontal cross sectional area of egg in terms of the depth where the cross section area reduces with decrease in the depth.
(here I need to calculate the surface area of water in the ...
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solution-verification | ind the measures of the angles $(AD',A'M)$ and $((A'MN),(ABC))$
The problem
Consider the cube $ABCDA'B'C'D'$ with $M$ in the middle of $BC$ and $N$ in the middle of $DC$. Find the measures of the angles $(AD',A'M)$ and $((A'MN),(ABC))$
My solution
drawing
For the ...
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Can i express $\arg(z_3)$ as a combination of $\arg(z_1)$ and $\arg(z_2)$? [closed]
if $z_1$ and $z_2$ are two complex numbers and $z_3=z_1+z_2$, can I express $\arg(z_3)$ in terms of $\arg(z_1)$ and $\arg(z_2)$. I want to do this so that I can see the individual contributions of $\...
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How to draw more precise of iterations in this type of constructions?
In this question I made this construction
Given a non-regular pentagon $A_1B_1C_1D_1E_1$ with no two adjacent angle having a sum of 360 degrees, from the pentagon $A_nB_nC_nD_nE_n$ construct the ...
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Question from the Proof of the Classification of Finite Subgroups of SO(3)
On page 14 here, the author sets up the following situation: say we have an order 12 subgroup $G$ of $SO(3)$ acting on the poles of $G$ (i.e. on the set of vectors on $S^2$ fixed by some non-identity ...
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Intersect polytopes defined by half-planes
Is there a quick way to find this region or its convex hull? $N$ is large, $M=d=5$ or so
$$
\bigcap_{n=1}^N \bigcup_{m=1}^M \{x \in \mathbb{R}^d :a_{nm}'x \geq 1\}
$$
The slow way to do it (the only ...
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Pieces of a regular octagon [closed]
Given regular octagon ABCDEFGH, is it always true that AD is parallel to BC is parallel to HE is parallel to GF?
In order to prove this, it also needs to be proven that the diagonals of an even sided ...
