For questions about geometric shapes, congruences, similarities, transformations, as well as the properties of classes of figures, points, lines, angles.

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1answer
45 views

Is it true there exists $f:S^{2n}\longrightarrow S^{2n}$ making the diagram commutative?

Let $g:\mathbb R\mathbb P^{2n}\longrightarrow \mathbb R\mathbb P^{2n}$ be a continuous map where $\mathbb R\mathbb P^{2n}=\mathbb S^{2n}/\{\pm x\}$. Is it true there exists $f:\mathbb ...
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0answers
8 views

equal-variance whitening transform

Out of all the whitening transformations, PCA gives us the one that maximizes the discrepancy in variances, i.e. the components in the PCA basis have the biggest and the smallest variances. How does ...
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2answers
33 views

Maximize the distance between a point and a bounding rectangle

There are $n$ random points in the $x-y$ plane, whose coordinates are known beforehand. We can use a minimum bounding rectangle (MBR) to bound these points. In this scenario, the MBR can be rotated, ...
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1answer
31 views

The simplest way to calculate area of a pentagon

I have a pentagon, whose all sides and angles I know. What would be the simplest way, i.e requires least calculations, to calculate its area? If possible, can I generalize your way to higher ...
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1answer
27 views

$C^{-1} (1+|x|^{2})^{\frac{s}{2}} \leq (1+|x|)^{\frac{s}{2}} \leq C (1+|x|^{2})^{\frac{s}{2}}$?

Let $s\in \mathbb R,$ and define $f: \mathbb R^{n}\to [0, \infty)$ such that $f(x)= (1+|x|^{2})^{\frac{s}{2}}, (x\in \mathbb R^{n})$ and $g:\mathbb R^{n}\to [0, \infty)$ such that $g(x)= ...
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0answers
20 views

How to prove a parallel $(u=u_0) $it self curvature?

My name is Gita, and I had aproblem with my math. and need help, I know that a parallel $C$ in a surface of revolution in $M$ be a geodesic if and only if $f'(u_0)=0$. and $C$ is non arc lenght ...
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1answer
35 views

Tangent of a curve

Consider the curve $x=1$ in $xy$ plane. I want to know whether tangent at any point on this curve exist which is $x=1$, or tangent does not exist.
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0answers
25 views

To construct a right triangle given the hypotenuse and sum of two legs [duplicate]

NOTE: I want a hint only. A compass and a straightedge construction:Given a hypotenuse and the sum of lengths of the legs,we need to construct a right triangle. MY TRY: From any ray $BE$, ,let ...
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0answers
10 views

How to properly clamp Beckmann Distribution

I am trying to implement the Cook-Torrance Microfacet BRDF shading model and I am having some trouble with the Beckmann Distribution: Beckmann Distribution with width parameter ...
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0answers
26 views

How to find the minimal path between points in a planar set with holes in it?

When I was a commuter student, I would park in a very large parking that that had a set of stairs in a corner that I had to climb. In general, I had to park far away from this corner in an almost full ...
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1answer
98 views

Algebra, Geometry and Algebraic Geometry

I want to know, what is the difference between Algebra, Geometry and Algebraic Geometry ? Your reply is highly appreciated.
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3answers
56 views

How many square based pyramids are in a bigger pyramids?

The biggest challenge to solve the problem is that I can't really picture a pyramid. And it is hard to make a model. The pyramids I am trying to find include those on all tiers.
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1answer
60 views

How to find the equation of a line which intersects these lines at 90 degrees?

How to find the equation of a line which intersects these lines at 90 degrees? $p\equiv \dfrac{x}{2}=\dfrac{y+1}{0}=\dfrac{z-2}{1}$ $q\equiv \dfrac{x-1}{1}=\dfrac{y-2}{1}=\dfrac{z+5}{0}$ Since the ...
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1answer
37 views

Finding distance of point from 4D ray

I'm working on a programming project. In this project, a ray is fired from a point in 4-space. I need to find the distance from this ray to a number of other points in 4-space. I attempted to solve ...
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1answer
28 views

How to find how many rectangular prisms ( including cubes) are in a n by n by n cube?

I somehow got the answer to be [(n+1)!/2!(n+1-2)!]^2 *n Each part of the equation represents the height, length, and width of the possible rectangular prism in the big cube. You can multiply the ...
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1answer
30 views

Order of $A/2A$ for $A$ an Abelian variety

Let $A$ be an Abelian variety over $\mathbb R$ of dimension $g$. Then the size of $A(\mathbb R)/2A(\mathbb R)$ is $(\# A(\mathbb R)[2])/2^g$. I'm wondering how one might go about proving such a ...
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0answers
12 views

Question on Cobweb Diagram

Let f be a real map and assume that the points a and b form a limit cycle of order two of f. Derive a simple formula for the derivative of the second iterate of f at a.
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1answer
11 views

Finding angles in Barycentric system

How to find the angles of a triangle given the barycentric coordinates of its corners? Does it work if i take the first two components of every coordinate, and find the angles in the triangle (on the ...
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1answer
41 views

Volume of the pyramid…

I have such a problem from geometry: Five edges of a regular triangular pyramid have the length of $6$ $dm$, but the sixth- $4$ $dm$. Determine the volume of the pyramid. For me the problem is quiet ...
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1answer
53 views

How to find how many cubes are in a n by n by n cube?

I tried finding the answer using combinatoric by determining how many different length and width ans height are there for a cube, given the size of the bigger cube. But the formula I got turns out not ...
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1answer
33 views

Intersection of an $n-$sphere and a plane (when non-empty and not a point)

Let the n-sphere of radius $r$ centered at $(0,0,...,0,y)\in\mathbb{R}^{n+1}$ be defined by $$ \mathcal{S} \iff {x_1}^2 + {x_2}^2 + ... + {x_n}^2 + (x_{n+1}-y)^2 = r^2 $$ and consider the function $d$ ...
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2answers
36 views

A circle on the plane.

I have this problem: Let $C$ be a circle in the $xy$-plane with center on the $y$-axis and passing through $A=(0,a)$ and $B=(0,b)$ with $0<a<b$. Let $P$ be any other point on the circle, let ...
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3answers
90 views

What is the different between these two triangles? [duplicate]

What is the different between rigorous proof and proof based on intuition on this problem? It seems to me that these triangle are equivalent in area.
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1answer
26 views

Equation of hyperplane in Matlab

Given $n$ points in $n$-dimensions, using MatLab, how should we find the equation of the $(n-1)$-dimensional hyperplane passing through these $n$ points.
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0answers
59 views

What if segments are not infinitely divisible?

I almost got myself mixed up I a philosophical discussion again. Somebody was talking about the Planck time and length which are, according to him, the minimal possible time and distance, and how ...
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2answers
34 views

Explanation for the uniformity of the distance between a Gaussian variable to its nearest integer?

earlier I asked the question Expected distance for a gaussian variable to its nearest integer. and got a good answer. The expected distance is highly close to $1/4$, which is very similar to the ...
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1answer
14 views

Find a vector in cartesian coordinates given its relative location to another vector in spherical coordinates

Here is my problem: -I have an arbitrary normalized vector N in cartesian coordinates -I am trying to find normalized vector M, also in cartesian coordinates -I am given the azimuth and polar ...
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2answers
52 views

How many equilateral triangles can be inscribed in a triangle?

Given any triangle ABC find points D, E and F not A, B or C, where D is on segment AB, E on segment BC and F on segment CA, such that triangle DEF is equilateral. How many such triangles exist? I ...
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2answers
18 views

What is the result of these scalar products?

We know that : ABCD is a square. BGFE is a square. AEB and BCG are equilateral triangles. AB = 1. Here is the figure : I have already calculated the scalar products of BC.BE, DA.BE, EA.BE and ...
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1answer
27 views

Collinear points in 3dimension

Given three $3D$ points: $A,B$ and $C$, what is the procedure to check if they are collinear? In general, given $n$ points in $m$-dimension, how should one find out, if these $n$-points defines a ...
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2answers
54 views

How do I prove that this triangle is equilateral?

We know that : ABCD is a square. BGFE is a square. AEB is an equilateral triangle. AB = 1. Here is the figure : How can I prove that BCG is equilateral ?
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1answer
21 views

How do I find the dot product of these vectors?

We know that : ABCD is a square. BGFE is a square. AEB is an equilateral triangle. AB = 1. Here is the figure : How can I find the scalar products of : • BC.BE • DA.BE • EA.EB
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0answers
27 views

Why isn't my Pappus chain lining up?

TL;DR Why isn't my Pappus chain lining up? Visualisation: http://jan.jarfalk.se/pappus-chain/ Proof: http://jan.jarfalk.se/pappus-chain/debug.html Code: https://github.com/janjarfalk/pappus-chain ...
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2answers
24 views

Some help needed with a geometry question

What is a formula for all integers n for which a regular polygon with n sides can be constructed using a ruler and compass construction?
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1answer
57 views

Two touching circles inscribed in an angle

There are two touching circles inscribed in a $60^\circ$ angle. The distance between the vertex of angle and the center of smaller circle is $5j$. What is the ratio of the surfaces of two circles?
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0answers
29 views

Rectangle with side length of integer value. [duplicate]

There is a rectangle $D=[a,b]\times [c,d]$. This rectangle has finite partition with smaller rectangles with parallel sides $\{D_i\}_{i=1}^n$ $(n\in\mathbb{N})$. Let's put these rectangles as ...
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2answers
25 views

Find the value of EF and AC.

In the figure given below, BA, FE and CD are parallel lines. Given that AB = 15 cm, EG = 5 cm, GC = 10 cm and DC = 18 cm. Calculate EF and AC. I think the answer is EF= 8.66 and AC = 25.66 but I ...
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1answer
50 views

Classical geometry statement in modern terminology

Given two line segments $\overline{AB}$ and $\overline{CD}$, it's always possible to find a third line segment whose length divides evenly into the first two. In modern terminology, if we assign $x = ...
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2answers
37 views

Unusual 3D Packing Problem

I made up this interesting problem playing with wire sculptures: If I have a $10 \times 10 \times 10$ clear box and inside I can put wireframe unit cubes, what's the maximum number of unit edges (or ...
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1answer
25 views

Is there a smooth map from the square to the deltoid?

Is there a $C^\infty$ map between a unit square in $\mathbb R^2$ and a deltoid like this one The deltoid is obtained by varying the angles $\theta_1$, $\theta_2$ in the equations \begin{align} x_2 ...
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1answer
40 views

Calculate depth using triginometry

I was asked a question like this on an exam today and I'm wondering if I got it right or not. ...
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0answers
10 views

Generate X, Y, Z coordinates of 3D triangular prism with Edge Rounding

I'm trying to create an interactive 3D visualization with Python and Mayavi for inputs to an analysis program. The program accepts certain primitive shapes which it combines (constructive solid ...
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0answers
18 views

Solving for and x,y,z coordinate in a 3D plane

This is hard for me to explain, but basically I am making a game and I want a 3rd person like camera. I have a lot of information about how the camera should be but I can't seem to get the camera to ...
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1answer
13 views

Centroid of contiguous polygons

Say that I know which are the centroids of two polygons. These polygons share a number of edges (they belong to a planar subdivision). I want to compute the union of the two polygons and also to know ...
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2answers
35 views

Angle between two vectors, where am I wrong?

I am facing a problem, I want to find the angle between the vector u and the vector v, here is what I am doing to get this angle (I used this method) : So what I am finding is an angle that is about ...
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2answers
43 views

Geometric intuition: Seeing the regions in double integrals

Context: solving double integrals. I had the formula $$x^2+y^2=1-x-y$$ yet I could not see what shape it had. This is even more true with 3D pictures like $$2x^2+2y^2 \le 1+z^2.$$ Is there a summary ...
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1answer
28 views

Is there a way to find a point on a circle, given another point and an arc length without using trig functions?

Emphasis on not using the trig functions. For example, the problem would be something like find the point $\pi/3$ units counterclockwise from the point $(1,0)$ on the unit circle, without using trig ...
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1answer
50 views

Radius of the circle…

can you please give an idea of how can I solve the following problem. Given that $|AO|=\sqrt5$ and that $|OC|=\sqrt10$ find the length of the circle with the center in point $O$. Here's a picture ...
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4answers
38 views

How to determine the side on which a point lies?

Suppose we have a linear equation and a point in the plane, then how can one determine on which side of the line the point lies?
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0answers
14 views

action of symmetry group of cube on pairs of opposite faces.

I want to solve the following problem from Dummit & Foote's Abstract Algebra: Explain why the action of the group of rigid motions of a cube on the set of three pairs of opposite faces is not ...