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
43 views

How to calculate distance from the International Space Station given coordinates?

How would one calculate how far away a point is (latitude/longitude) from the international space station given its latitude/longitude/altitude? The distance would be direct as if drawing a straight ...
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0answers
30 views

Proof of Simple Properties of Volume

Let $e_{1},\ldots,e_{n}$ be vectors in $\mathbb{R}^{n}$. Define a parallelepiped $P$ to be a translate of the set $$\left\{x\in\mathbb{R}^{n} : x=t^{1}e_{1}+\cdots+t^{n}e_{n}, 0\leq t^{i}\leq ...
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0answers
14 views

Getting the angle that is needed for covering a given distance on an ellipse's cirumference

In a small programming exercise I asked myself, I want to calculate various things about ellipses. The part I'm stuck with is the following: I want to calculate the angle that is needed cor covering a ...
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1answer
29 views

Show that a point lies on the diagonal of quadrilateral

In a quadrilateral ABCD we choose a point E on the side AD and a point F on the side CD. Then we choose a point G on the line EF. Let H be the second point of the intersection between the circles that ...
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1answer
18 views

geometrical problem on triangle [on hold]

Given a triangle ABC, if $$a = \dfrac{2(b^2 - c^2)}{-b + \sqrt{b^2 + 4c^2}}$$, prove that $3m(C) = 2m(B)$.
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1answer
17 views

Write $CX,AY,BZ$ in terms of $CA,CB$ and the ratios $\alpha, \beta, \gamma$?

The point $X$ divides $AB$ in the ratio $\alpha$, $Y$ divides $BC$ in the ratio $\beta$ and $Z$ divides $CA$ in the ratio $\gamma$. Write $CX,AY,BZ$ in terms of $CA,CB,\alpha, \beta, \gamma$. I ...
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1answer
33 views

Combinatorial problem of choosing points inside an equilateral triangle without them being too close.

Determine the smallest integer $m_n$ which satisfies the following property: If $m_n$ points are chosen inside an equilateral triangle of sides 1, then at least two of them are at distance ...
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1answer
16 views

What's the necessary condition for that any three vectors are parallel to the edges of a triangle in the plane?

What's the necessary condition for that any three vectors are parallel to the edges of a triangle in the plane? I answered the following: The necessary condition is that the vectors are ...
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1answer
14 views

How do I find a Bézier curve that fulfills a given width and height?

I am building a software application that works with vector graphics and I need to use Bézier curves to draw a heart shape, like this one here which I created in MS Paint: The only information ...
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0answers
13 views

Geometric proof of circular mil formula $A=d^2$

The circular mil "is a unit of area, equal to the area of a circle with a diameter of one mil." "The area in circular mils, A, of a circle with a diameter of d mils, is given by the formula:" ...
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1answer
27 views

Width of trapezoid at any height?

Assuming I have a trapezoid where I know the height, bases, and legs, I would like to obtain the width of this trapezoid at any height y. What I want is very similar to the median formula for a ...
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1answer
35 views

Metric tensor for n-sphere in ambient coordinates

Let $S^n$ be the unit n-sphere embedded in $\mathbb{R}^{n+1}$: $$ S^n = \{ a \in \mathbb{R}^{n+1} \mid a \cdot a = 1 \} $$ What is the induced metric tensor for the sphere, in $\mathbb{R}^{n+1}$ ...
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0answers
16 views

$n$-tuples of points of $\mathbb{C}$, identification.

Fix $n \in \mathbb{N}$. Forgive me if this is a very silly question, but how can I see that the set of unordered $n$-tuples of points of $\mathbb{C}$ can be naturally identified with $\mathbb{C}^n$?
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2answers
29 views

Need help proving this geometry problem.

My friend asked me one question yesterday.It is as follows. Let there be two triangles ABD and ACD.D is a point on base BC such that BD=CD(given).Also,clearly side AD is common.Now we know median ...
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1answer
14 views

Project point on plane - Unique identfier?

I have a number of planes (in $\mathbb{R}^3$), each represented by a point $\vec{P_i}$ which lies within each plane and the normal vector $\vec{n_i}$. If I project a point $\vec{Q}$ (which does not ...
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0answers
21 views

Prove that $\sin\theta_1.\sin\theta_2.\sin\theta_3=\frac{r^2_1}{16R^2}$

If $2\theta_1,2\theta_2,2\theta_3$ are the angles subtended by the circle escribed to the side $a$(opposite to vertex $A$) of a triangle at the centers of the inscribed triangle and the other two ...
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0answers
7 views

Kiselev's Book I Plainimetry Question 242 - Question in the Description

Two lines passing through a point Μ are tangent to a circle at the points A and B. Through a point С taken on the smaller of the arcs AB, a third tangent is drawn up to its intersection points ...
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0answers
26 views

If line has no width, we couldn't understand difference of a curved line and straight line if we could see from its perspective, right?

I am thinking about points and lines, how they form etc and i just thought this logic. if my intuition is correct, it is absurd to talk about curve of a line in 1 dimension. I wonder if that is ...
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1answer
39 views

Elementary geometry question involving quadrilateral and bisector given with picture.

$ABCD$ is a quadrilateral. $m(\widehat{BAC})=48^\circ$. $m(\widehat{CAD})=66^\circ$. $m(\widehat{CBD})=m(\widehat{DBA})$. What is $\color{magenta}{m(\widehat{BDC})=x}$? Tried lots ...
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0answers
12 views

Geometrical interpretation of the condition number as measure of matrix dissimilarity

Consider two $p$ by $p$ symmetric positive definite matrices $\pmb F$ and $\pmb G$ and denote $$\pmb D=\pmb G^{-1/2}\pmb F \pmb G^{-1/2}.$$ Sometimes, the condition number of $\pmb D$ will be used ...
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1answer
21 views

Calculate scaled coordinate

I got 2 Squares with the following corner coordinates. Square 1: (-128,-128) (128,128) Square 2: (0,0) (512,512) How can I calculate a coordinate inside Square 2 and translate it to the scaled ...
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1answer
41 views

The Rhombohedron

I am trying to model a rhombohedron (using Blender) as a first pass to building Dürer's solid so I am trying to calculate the (x,y,z) values for a given side length 'a' and angle 'theta' (starting ...
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0answers
18 views

What is number of faces in a k-ary n-dim cube?

What is the number of $(n-r)$ dim faces for a $k$-ary $n$-dim cube ? Definition of k-ary cube: In a $k$- ary $n$- cube , each node is identified by an $n$-bit base-$k$ address $b_{n − ...
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0answers
12 views

Stellating the Octahedron

I am trying to create a very primitive animation/demonstration that shows the stellation of an octahedron to yield the stella octangula. Unfortunately, it seems that the mental image I have for ...
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1answer
32 views

An inequality about the areas of two triangles

There is point $P$ in a triangle $ABC$. $Q,R,S$ are the symmetric of $P$ with respect to the sides $AB,BC,CA$ respectively. I have to prove that the area of $ABC$ is $\geq$ than the area of $QRS$. ...
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0answers
9 views

What is the perspective projection of a 3d point relative to a quarternion encoded camera?

I'm representing a camera on the cartesian space as a tuple of a 3d point (position) and a quarternion (rotation). I get the front, right and up vectors of the camera by applying the quaternion to the ...
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1answer
32 views

Distance from point to sides of a quadrangle [on hold]

$A(a_1,a_2)$ , $B(b_1,b_2)$ , $C(c_1,c_2)$ and $D(d_1,d_2)$ form a quadrangle. What is the sum of (perpendicular) distances from point $P(p_1,p_2)$ (inside the quadrangle) to all the four sides? I ...
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1answer
16 views

About the stable/invariant point sets in a plane with respect to shift/linear transformation

I'm reading Vlademir A. Zorich's Mathmatical Analysis I, meeting exercise question as following: a) A set $S \subset X$ is stable with respect to a mapping $f:X \rightarrow X$ if $f(S) \subset ...
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2answers
37 views

Prove that $\Delta BPQ$ is an isosceles triangle

Given was the following figure: Also the following were given: $M_1$ and $M_2$ are the centres of the two circles The two circles have the same radius First, I added an other line through the ...
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1answer
11 views

Prove that all hyperbolic straight lines are congruent to $x$-axis

I have the notes on the proof but I cannot fully understand the proof. Let $C$ be a hyperbolic straight line through $z_o\in \mathbb{D}$ and $z^*_o$ the point symmetric to $z_o$ wrt the unit circle ...
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0answers
29 views

Triangular Identity. [on hold]

I have an equation $f(x)=5x+2$.I know the slope is 5 and I take the $5^2$ which is 25. I add $25+1=26$ and take the inverse of 26 which is$\frac{1}{26}$ and subtract it from 1, which is the ...
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1answer
41 views

Find cartesian coordinates of the incenter

$A(a_1,a_2)$, $B(b_1,b_2)$ and $C(c_1,c_2)$ form the triangle $ABC$. What are the cartesian coordinates of the incenter and why?
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0answers
24 views

How to calculate optimal sizes of rectangles for this type of array visualization?

Given array of positive numbers, I would like to draw this diagram and be able to put descriptions inside: There should be no empty space left, consider that these numbers represent % of total. Do ...
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1answer
28 views

Circle Packing, Estimate only of number of smaller circles in a circle.

Given x number of circles of radius r what is a good approximate size Radius for a bigger circle which they fit in. To explain in actual problem terms. I want to move units in a video games which ...
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0answers
25 views

determine point in triangle [duplicate]

How can I determine the point of X on the map, or the distance between X and either end point. The dashed line from X to point is perpendicular. The distance between each point is on the map, and the ...
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3answers
39 views

Intersections of Planes, Points…

I'm in sixth grade and learning geometry. Can someone tell me if I'm correct? The intersection of a point and a point is a point. The intersection of a point and a line is a point. The intersection ...
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0answers
17 views

Iterated circumcenters - proving collinearity and establishing distance ratios

Let $P_0, P_1, P_2$ be three points on the circumference of a circle with radius $1$, where $P_1P_2 = t < 2$. For each $i \ge 3$, define $P_i$ to be the centre of the circumcircle of $\triangle ...
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0answers
25 views

Distance between point and line with cartesian coordinates

$A(a_1,a_2)$, $B(b_1,b_2)$ and $C(c_1,c_2)$ are points. $A$ and $B$ form a line $AB$. What the distance between $C$ and $AB$ ?
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0answers
25 views

How to find location - multilateration

I have this data: $$ {x1} = 473463,100288[m]\\ {y1} = 5924242,046998[m]\\ {z1} = 0[m]\\ {t1} = 41919,84025[s]\\ {x2} = 473483,237020[m]\\ {y2} = 5924212,730018[m]\\ {z2} = 0[m]\\ {t2} = ...
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1answer
34 views

Number of polyhedron diagonals

Suppose that I have a polyhedron with given number of faces, edges and vertices are given. Is there a formula that gives me the number of polyhedron diagonals, ...
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0answers
21 views

Geometry midpoint [on hold]

John wants to center a canvas which is 8 ft wide on his living room wall which is 17 ft wide. Where on the wall should John mark the location of nails if the canvas requires nails every 1/5 of its ...
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2answers
61 views

Probability that distance of two random points within a sphere is less than a constant

Two points are chosen at random within a sphere of radius $r$. How to calculate the probability that the distance of these two points is $< d$? My first approach was to divide the volume of a ...
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1answer
45 views

Geometry question, prove that $\angle APB = \frac12 (\angle AMB + \angle CMD)$

I got the following question: Prove that $\angle APB = \frac12 (\angle AMB + \angle CMD)$, with the following figure given: Also, the following information is given: $M$ is the centre of the ...
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8answers
119 views

How can I parametrize $|x|+|y|=1$

I need parametrize $|x|+|y|=1$ but I don't know how to parametrize. I know that it is a rotated square, I would like understand so if you can explain to me like if I was still, thanks
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3answers
57 views

Geometric interpretation of inverse complex function?

Function $f\colon\mathbb{R}\to\mathbb{R}$ and its inverse $f^{-1}$ are symmetric over line $y=x$. It's easy to imagine inverse of real function, we just have to "flip" the plot over $y=x$. But what ...
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0answers
25 views

area of intersection between 2 circles [on hold]

could you please tell me how you solved 1/2(R)2 sin 120' Area of intersection between two circles Thanks.
2
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1answer
28 views

Multiplicative version of convex hull

The convex hull of a finite set of points, $(x_i,y_i) \in \mathbb{R_+}^2$ ($i=1,...,n$), is defined as: $$\left\{(\sum_{i=1}^{n} \alpha_i x_i,\sum_{i=1}^{n} \alpha_i y_i) \mathrel{\Bigg|} (\forall i: ...
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0answers
61 views

how many spheres can all touch a single one?

In Euclidian space, one sphere can be touched by how many equal-sized spheres simultaneously? Intuitively, the answer is 12. Is there a (geometrical) proof of this?
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1answer
435 views

Which Area of mathematics can explain this?

http://i.stack.imgur.com/rij3X.png As in the image we can see that ray of light is bouncing off objects. Black ones are opaque objects and white ones are transparent objects. I want to calculate how ...
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1answer
12 views

Show that a line is tangent to a circle in the extended complex plane.

The straight line $l$ in the extended-complex plane pasess through $2+i,2+2i$.The circle $C$ centered at $-1-2i$ with radius $3$. First, I find the parametrization of the straight line which is $$z = ...