Questions tagged [geometry]
For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, and angles.
52,821 questions
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Radical Axis and a Fixed Point
Let $ABC$ be a triangle inscribed in $(O)$. A point $P$ moves on the angle bisector of $\angle BAC$. Let $D,E,F$ be the feet from $P$ to $BC, CA, AB$, respectively.
(1) Let $K$ be the second ...
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Probability that 5 shots are fired in the same region and different region. [closed]
Five shots are fired randomly within a circle of radius R. The circle contains an inscribed square, which divides the circle into five distinct regions: the square itself (R1) and and four identical ...
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Inscribed ellipse in a triangle that has a known orientation and a known tangent point
Given a triangle, you want to determine the inscribed ellipse in it, which has a known orientation, specified by a known rotation matrix, and in addition, one of its tangent points with the three ...
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The area of a rectangle containing a curved line of a known length
Let's suppose we have a line with a known length $L$ that we transform from a straight line to a curved one matching a semi-circle.
Is there a way to find a formula for the height of the smallest ...
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Ellipsoid inscribed in a tetrahedron. Does this problem have a unique solution?
Given the four vertices of a tetrahedron. You want to find the equation of the ellipsoid that is inscribed inside the tetrahedron, given the orientation of its three axes which are specified by a ...
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How best to divide a straight line-segment on a stereographic projection into sub-segments of equal real length?
Assume we have a pair of points, $A_r$ and $B_r$, on the surface of a unit sphere. We may translate them into coordinates on a stereographic projection, $A_s$ and $B_s$, and then draw a straight line ...
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New shape? Any literature on a cuboid with proportions of $1: \sqrt{2}:2-\frac {1} {\sqrt {2}} $?
I found a 3d shape that shares properties similar to the golden rectangle or root 2 rectangle. It is a rectangular prism that has a repeating self symmetry when subdivided, somewhat similar to the ...
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proofs of Centroid Theorem and Commandino's Theorem
The Centroid Theorem says that when the medians of a triangle intersect at the triangle's centroid (its point of concurrency), each median is split into two subsegments which are $\frac{1}{3}$ and $\...
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Trying to understand a portfolio of geometric Brownian assets through approximating the LogSumExp function
Trying to understand a portfolio of geometric Brownian variables through approximating the LogSumExp function.
Intro
This is a continuation of this deleted question: there I explored the 2 variables ...
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Prove two interior alternate angles are equal [closed]
Question:
I would like to prove $\angle B = \angle B'$, I try to prove that the corresponding angle $\angle C$ and $\angle B$ are equal, since $\angle C$ and $\angle B'$ are corresponding angles, I ...
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Find angle in Z figure [closed]
Given is the following figure:
Find the angle $\alpha$. I'll post a solution later, but I am curious what's the most elegant way to find the angle.
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Driving an inside box through rotation to fit inside an outside box
You're given a rectangular box centered at the origin, with its faces parallel to the coordinate planes. The box faces are at $x=-a$ and $x = a$, $y= -b$ and $y=b$ and $z = -c$ and $z = c $.
In ...
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Arbitrary-axis 3D rotation using only planar rotations [closed]
I’m studying whether 3D rotations around arbitrary axes can be achieved using only planar rotations in the XY, YZ, and XZ planes, instead of quaternions or rotation matrices.
I’ve encountered three ...
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An angle in a triangle satisfying $a^3 + b^3 = c^3$
$\triangle ABC$ is a triangle. Let $|BC|= a$ ; $|AC|= b$ ; $|AB|= c$.
We know that if: $a^2 + b^2 = c^2$, then angle $C$ is equal to $90$°. So, I asked myself the following question:
What happens when,...
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Calculating the area of a right triangle with hypotenuse $10$ and altitude $6$: Proof of impossibility in Euclidean and Spherical geometry? [closed]
There is a large right-angled triangle. The length of the hypotenuse (which serves as the base of the drawing) is explicitly labelled as $10$. An altitude is dropped from the right angle to the ...
