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

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2
votes
0answers
10 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 $\mathbb{C}^n$?
1
vote
2answers
24 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 ...
0
votes
0answers
9 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 ...
0
votes
0answers
15 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 ...
0
votes
0answers
6 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 ...
0
votes
0answers
25 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 ...
0
votes
1answer
29 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 ...
0
votes
0answers
11 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 ...
0
votes
1answer
20 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 ...
3
votes
1answer
37 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 ...
2
votes
0answers
17 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 − ...
0
votes
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 ...
3
votes
1answer
29 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 $QRS$. ...
0
votes
0answers
8 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 ...
0
votes
1answer
31 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 ...
1
vote
0answers
13 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 ...
2
votes
2answers
36 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 ...
0
votes
0answers
6 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 ...
-1
votes
0answers
28 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 ...
1
vote
1answer
33 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?
0
votes
0answers
21 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 ...
2
votes
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 ...
1
vote
0answers
22 views

determine point in triangle

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 ...
5
votes
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 ...
3
votes
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 ...
-1
votes
0answers
24 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 $AB$ ?
0
votes
0answers
23 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} = ...
0
votes
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, ...
-2
votes
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 ...
0
votes
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 ...
1
vote
1answer
41 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 ...
1
vote
8answers
118 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
3
votes
3answers
56 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 ...
-3
votes
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
votes
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: ...
3
votes
0answers
56 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?
1
vote
1answer
423 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 ...
0
votes
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 = ...
2
votes
1answer
65 views

Is angle an instance of something more abstract than angle? [on hold]

Is an angle (as generally understood) best described as a relation or a quantity?
1
vote
1answer
25 views

Half secant in Circle

OT and OQP are tangent and secant respectively drawn from external point $O$ of a circle centered at $C$. Mid-point M of the secant is joined to center $C$,an arc is drawn with center $O$ to be ...
0
votes
0answers
9 views

Minimum Curvature for Circular Trapezoids? [on hold]

I am thinking any shape that can be close to circular trapezoid having the surface curvature less than circular trapezoid. About the minimum curvature here. About the naming of circular trapezoids in ...
-4
votes
1answer
93 views

Whats the size of the X angle? [on hold]

In this question, we have no information about line. we just know that we have some angels and we need X. Please solve this question by geometry. http://borjianamin.persiangig.com/File1.jpg the ...
-2
votes
1answer
20 views

Relations involving the altitudes and orthocenter of a triangle [on hold]

For acute $\triangle ABC$ with altitudes $AD$, $BE$, $CF$, orthocenter $H$, and area $S$, I have to prove that: $$AB^2 + HC^2 = BC^2 + HA^2 = AC^2 + HB^2 \tag{a}$$ $$AB \cdot HC + BC \cdot HA + ...
-1
votes
1answer
27 views

$ DB\cdot DC = HA\cdot HB + KA\cdot KC.$ [on hold]

We have a point $D$ on the hypotenuse $BC$ of a right triangle $ABC$. $H$ and $K$ are the projections of $D$ on $AB$ and $AC$, respectively. I have to prove that: $$ DB\cdot DC = HA\cdot HB + ...
-1
votes
0answers
42 views

Geometry - points on a sphere [on hold]

Is there a way, or is it possible to describe a set of points on a sphere so that the they are distributed over the surface with maximal symmetry (or just evenly distributed)?
1
vote
1answer
36 views

Maximum number of equilateral triangles in a circle

I am stuck with a question. Given a circle with radius $x$ cm, what is the maximum number of equilateral triangles of side length 1 cm that can fit in the circle without overlapping or ...
0
votes
0answers
10 views

polar moment of area for nonplaner circle (cup)

Can somebody tell me the polar moment of area of chord for a sphere. for example when you cut a sphere at a point other than from center? Also polar moment of area for curved axis symmetry ?
10
votes
0answers
63 views
+100

Congruent quadrilaterals in a tri-colored $72$-gon

I recently watched a movie (A Brilliant Young Mind) in which this problem appeared: Let the vertices of a regular $72$-gon be colored red, blue, and green in equal parts. Show that there are $4$ ...
1
vote
1answer
23 views

Selecting a basis such that the orientation is preserved

I need to map a polygon from a 3D plane to a 2-dimensional basis, do some processing, and project the result back to 3D. The vertices in the polygon is always ordered counterclockwise and this ...
-4
votes
0answers
15 views

What are the possible applications of homothety? [on hold]

What are the possible applications of homothety? Give me some examples, please. I know it can be used to proof coincidence of lines but what else?