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

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Projection of n-Simplex into k-Simplex

I try to find properties of orthogonal projections such that a standard n-Simplex $S_n$ is projected into a k-Simplex $S_k (k\leq n)$. Literature provides work on "smallest projections" in this ...
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0answers
17 views

Inequalities in a quadrilateral

In a quadrilateral ABCD, it is given that AB is parallel to CD and the diagonals AC and BD are perpendicular to each other. Show that ...
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26 views

Convolution of convex polygons and a Gaussian

I need to find the closest solutions for convolution of convex polygons/circles with a Gaussian function for computer graphics purposes. I was only able to find solutions for rectangles, like this ...
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1answer
28 views

Rectangular piece of paper

From a rectangular piece of paper, a triangular corner is cut off resulting in a pentagon.If the sides of the pentagon have lengths 10,17,18,24 and 39 in some order.Find the sides of the rectangle and ...
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0answers
20 views

Unique representation of each point in 3d space by Linear combination of 3 mutually perpendicular vectors.

I intuitively accepted that there is an unique representation of any point in a 3d space by linear combination of 3 mutually perp. vectors. But now I'm wondering is this an axiom or a theorem? If ...
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0answers
20 views

Getting a peak value from a sequence of information

I would like to do a software program which looks into some data I collected from a test I did and figure out the best (highest) value out of these data. The data include two values the azimuth ...
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1answer
33 views

Finding the argument of a complex number,

I'm trying to locate my four zeroes of a complex-valued function, in order to apply the Residue Theorem. After using the quadratic formula, I am left with $$z^2 = [-3 \pm i\sqrt7] / 2$$ writing the ...
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0answers
5 views

Inertia tensor of a triangle in 3d

I am computing inertia tensor of a triangle given by its 3 vertices. The tensor should be computed at some local origin. I used covariance as explained in this Wikipedia article, but I am not sure ...
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1answer
36 views

Surfaces on which not every pair of points is connected by a geodesic

Let $S$ be a surface in $\mathbb{R}^3$. I believe that, if $S$ is smooth, bounded, and closed, then, for every pair of points $x,y \in S$, there is at least one geodesic $\gamma$ connecting $x$ to ...
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1answer
20 views

Given the following image, find the measures of angles 1, 2, 3, 4 in terms of $\theta$

It is given that AB=AC and CD is a diameter. I can find m$\angle$1 and m$\angle$2 using the isosceles triangle theorem, the euclidean angle sum, and the inscribed angle theorems. I find that these ...
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0answers
7 views

Distance to a rotating sloped cylinder

I am having trouble to derive the distance $x(\beta)$ of the sloped pink cylinder, when it rotates ($\beta$ is rotation angle). The slope angle is $\alpha$ ($\alpha=0$ if the cylinder is straight). It ...
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2answers
53 views

What is the fourth dimension of a Tesseract?

Is the fourth dimension of the Tesseract time? That is why it is represented as a moving 3D structure on Wikipedia? I am asking because I have trouble understanding what it is.
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1answer
43 views

Geometric Interpretation of the Cross-Ratio

The cross ratio of 4 points $A,B,C,D$ in the plane is defined by $$(A,B,C,D) = \frac{AC}{AD} \frac{BD}{BC}$$ And it's a ratio which is preserved under projections, inversions and in general, by ...
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1answer
23 views

Plane-geometry problem with circles and tangents

I have a problem that even my smartest colleagues were able to solve. This is to get the radius of the smallest circle in the drawing below. Using a computer program, I managed to get that lightning ...
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1answer
31 views

Triangles, flagpoles and heights, oh my!

Here is a math question i got from school: On a horizontal plane, there are two flagpoles. One is 20m, and the other is 10m. There is a wire connected from the top of each flagpole, to the bottom of ...
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3answers
38 views

What's the technical term for “ternary interpolation”?

While researching how to render 2D bezier curves given the control points, I found a simple formula and the resource where I found this marked this iterative process as a ternary interpolation and ...
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1answer
28 views

How to get the equation of a circle tangent to two other circumferences and one axis at the same time?

I repeated this question in a better way: Plane-geometry problem with circles and tangents I ask the moderator to delete this post. I have a doubt in plane geometry. In the book of a problem there is ...
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0answers
45 views

Syzygies of $Gr_{2}(\mathbb{C}^4)$

I'm going to start the study the problem of syzygies. I read on web that it is possible to compute syzygies of an algebraic variety for example $Gr_2(\mathbb{C}^4)$, but I don't understand how can I ...
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0answers
36 views

Number of points required to define a paraboloid?

To better understand my question: $2$ points are required to define a straight line in $2$D $3$ non-collinear points are required to define a plane in $3$D So, how many non-collinear points are ...
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1answer
17 views

scaling/ word problem

clara wanted to enlarge a figure on the photocopy machine. she set the enlargement factor to 1.25 if the are of the figure was 10 square inches before it was enlarged, what will the area be after it ...
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1answer
76 views

Is it true that a arbitrary 3D rotation can be composed with two rotations constrained to have their axes in the same plane?

I am interested in decomposing an arbitrary rotation in 3D space into the product of two rotations which are constrained to have their axes in the same plane (for instance x-y plane). Statement of ...
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1answer
46 views

How to calculate the range of angles at which a line will intersect a growing circle? Arc length?

I am working on some simulation software in which I have an entity (e) that is spiralling around a particular point (p). As e continues to move around p, the radius of the circle that it is following ...
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0answers
12 views

What the Surface function will it be if a circle tilted with an angle and then rotating around z axis

My first idea is this will result in a elliptic torus. The horizontal semi-axis a=R and the vertical semi-axis b=R*cos(beta). assuming the titled or inclined angle is beta. The distance away from ...
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3answers
51 views

surface area of the solid (column side)

I made a problem But I'm stuck in solving .. :-( the problem is following. Find the surface area of the solid that lies under the paraboloid $z =x^2 + y^2$, above the $xy$-plane, ...
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1answer
47 views

Distribute small number of points on a disc

Firstly I strongly know how many similar questions there are here. It's about sets of evenly distributed points inside a circle. If we need a big set of such points, good solutions are: Isocell ...
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0answers
89 views

I can't learn math at all, I tried everything [closed]

When it comes to math I can't seem to understand anything about it. I tried asking my geometry teacher and my past teachers for help but they gave up on me saying I need someone else to help me, I ...
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4answers
87 views

Global Coordinates in Differential Geometry?

In trying to learn a bit about differential geometry I have hit a puzzler. Most texts emphasize that one coordinate system will not suffice in general, but the reasoning is never given. After all, if ...
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1answer
25 views

Tetrahedron- Inscribed Sphere

In tetrahedron $ABCD, AB=BC=CA$ and $DA=DB=DC$. Given that the altitude of $ABCD$ from point $D$ is $24$ and that the radius of the inscribed sphere of $ABCD$ is $11$, determine $AB$.
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1answer
25 views

Angle arising from circle rolling along an ellipse

In this problem the ellipse and circle are fixed. The ellipse has center $E$ on the origin, its semi-minor axis $r$ is on the $y$-axis, and its semi-major axis $R$ is on the $x$-axis. The circle has ...
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1answer
52 views

Is the group generated by two loxodromic isometries with a fixed point in common cocompact?

If you have two distinct loxodromic isometries of the hyperbolic plane $\gamma_1, \gamma_2$ such that they have a fixed point in common. For simplicity let's take the half plane model and let the ...
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1answer
36 views

minimum number of points on the surface of a 3D ellipsoid to define it uniquely

An ellipsoid in 3 D is described by 9 independent parameters: 3 for the coordinates of its centre + 6 independent components of a symmetric 3 x 3 matrix. What is the minimum number of points on the ...
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1answer
16 views

Geometry: perpendicular bisector and bisector unknown theorem

Inspired by one of the latest numberphile videos I started playing around with the specific configuration. I would like to prove the following: Given is a random $\triangle ABC$ with ...
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1answer
334 views

Minimal number of rectangles that cover a set of adjacent unit squares

Suppose I have an arbitrary number of adjacent 1x1 squares on a grid (Adjacent defined as "each square shares at least one side with another"). I'm looking for a good way to find the minimal number of ...
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2answers
31 views

CD is height of right-angled triangle ABC, M and N are midpoints of CD and BD: prove AM⊥CN

I was having some troubles proving this: CD is the height that corresponds to the hypotenuse of right-angled triangle ABC. If M and N are midpoints of CD and BD, prove that AM is perpendicular to CN. ...
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0answers
57 views

Intersection Volume

Given that P is a square pyramid whose base consists of the four vertices $(0,0,0)$, $(3,0,0)$, $(3,3,0)$, and $(0,3,0)$, and whose apex is the point $(1,1,3)$. Then let Q be a square pyramid whose ...
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1answer
29 views

How to Derive Point on Plane from Normal Vector : geometric Margins

Consider the snippet below from Andrew Ng's lecture notes on Support Vector Machines. He goes on to state that $B = x^{(i)} - \gamma^{(i)} \frac{w}{\|w\|}$. I am having a hard time seeing why this ...
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1answer
46 views

Is there official name for “Manhattan visibility” measure?

I made up the measure (and its name) and I wonder if it is officially defined (and named!)? I need a name, because when I call it "Manhattan visibility" nobody will understand me unless I explain how ...
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2answers
52 views

Pythagorean triples in a triangle inside a rectangle

Suppose there's a right-angled triangle inside a rectangle in the following way: (just take any right-angled rectangle, "rotate" it and draw a rectangle around it) There are four right-angled ...
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1answer
36 views

A rectangle and non terminating decimals [closed]

If a=(428571)/(999999) and b=(571428)/(999999) are the two sides of a rectangle. Find the distance of each vertex from center (i.e the point of intersection of diagonals) of the rectangle.
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1answer
29 views

Rolling ellipse on line - tangent and normal of roulette

Suppose that an ellipse is rolling along a line. If we follow the path of one of the foci of the ellipse as it rolls, then this path formes a curve - namely an undulary. Now consider the following ...
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1answer
38 views

Smooth structure on $M\cup_f N$?

Let $M$ and $N$ be two smooth manifolds with $$\textrm{dim}(M)=\textrm{dim}(N)=n.$$ Let $U\subseteq M$ and $V\subseteq M$ be two open sets and $f:U\longrightarrow V$ a smooth diffeomorphism. Consider ...
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1answer
27 views

Convex hull of multiple circles

I am having difficulties figuring the convex hull of multiple circles. If I have 2 circles that are disjoint what is their convex hull and how to find it? Thank you
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1answer
51 views

Cops and robbers in a square

A problem from Moscow Mathematical Olympiad in 1973. goes like this: At the center of a square stands a cop and at one of the square’s vertices stands a robber. The Rule allows the cop to run ...
3
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1answer
60 views

What is the relationship between vector and its associated skew symmetric matrix?

This is my first post in this forum, so hello everyone! I am working with geometries (i.e. areas, volumes and inertias of polygons and polyhedrons in 3D space). For doing that, I to use both the ...
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2answers
36 views

Probability of two points being a certain distance apart on a circle

Is the probability of two points being a certain distance $k$ apart on a circle of length $m$, with $0\le k<\frac{1}{2}m $, always the same for any $k$?
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2answers
28 views

Calculate the origin of a sphere from a number of randomly placed points on the surface

My problem is to calculate the origin of a ball from some motion capture data which is random markers on the surface of the ball that may or may not be visible in any frame. I have from 0-5 markers ...
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0answers
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Crofton formula in higher dimension

In the plane, the Crofton formula states that for a rectifiable plane curve $\gamma$, we have $\int |line \cap \gamma| d\Omega_1=2\times length(\gamma)$ where $d\Omega_1$ is the ...
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0answers
16 views

Equal Angle Related To Midpoints In Quadrilateral

In convex $\square ABCD$, $\angle BAD=\angle CDA$ The midpoints of $AB$,$CD$,$DA$ are $L$,$M$,$N$ respectively. $AC$ meet $BD$ at $E$. Let a circle passing through $E$, (tangent to $AD$ at $A$) be ...
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0answers
31 views

Area covered by one disk more than by two disks

Given are three unit disks on the plane. Let $A$ be the area of the plane covered by exactly $1$ disk. Let $B$ be the area of the plane covered by exactly $2$ disks. Prove that $A\geq B$. ...
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0answers
92 views

Existence of a Pivot Point in Euclidean Geometry [duplicate]

In geometry there is a term called a pivot point. There exists a pivot point 'P' in the interior of a convex polyhedron in a euclidean space if and only if every single line through 'P' contains ...