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
36 views

3D rotation of an object with respect to another object's rotation

I am writing a python code to translate and rotate an object with respect to another object. Please take a look at the picture bellow: The smiley face and the arrow have initial poses (position ...
0
votes
2answers
27 views

Reflection of a point about a straight line in 3-D space [closed]

Let there be an arbitrary point $P(-2, 5, 7)$ in 3-D space & a straight line having the equation $$\frac{x-2}{5}=\frac{y-1}{4}=\frac{5-z}{3}$$ What will be the point of reflection about the above ...
1
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2answers
27 views

Finding the points of a line with a known direction and distance joining 2 ellipses

I have 2 ellipses, say $e_1$ and $e_2$. I want to draw a line $l$ connecting $e_1$ and $e_2$ in a known direction $(u,v)$, with a known distance $d$. Is there a way to solve for the points of ...
1
vote
1answer
26 views

converting a n-gon with side length s into a 2n-gon with side length t

So I have to prove that $$ t= \sqrt{2-\sqrt{4-s^2}} $$ If I have a n-gon with side length s inscribed in a unit circle then bisect it to create a 2n-gon with side length t, there should be some ...
1
vote
1answer
46 views

What is the name of this (circumscribed) triangle?

I am meeting the following triangle more and more in my investigations of ideal triangles in the Beltrami Klein model of hyperbolic geometry. That made me wonder: is there a name for it? (And does it ...
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0answers
7 views

Approximating a grid-valued signed distance function with a continuous function

I want to solve a continous optimization problem using IPOPT. My optimization involves a signed distance function whose values are defined on a 2D grid. Since IPOPT can't handle piecewise functions, I ...
1
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1answer
33 views

Recursive Hexagon Problem to find number of hexagons at each stage

The source of this problem is this SPOJ question. Let me simplify it: A valid beehive is recursively defined as follows: 1. A single regular hexagon is a valid beehive. 2. To all the external cells of ...
3
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1answer
44 views

Triangle Center Midpoint

Consider the following construction of a triangle center: (The method could also be easily generalized to any shape with finite perimeter) For each point $X$ on the triangle, find point $X'$ such ...
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2answers
38 views

Is there a measure for how thin or squat a triangle is?

Is there a measure for how thin or squat a triangle is? Similar to eccentricity for ellipses.
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0answers
23 views

how to construct a regular pentagon in only 11 steps??? [duplicate]

how to construct a regular pentagon in only 11 steps??? Using straightedge and compass. Only 11 steps. Considering a step drawing a straight line or a circle
0
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3answers
39 views

Why is the velocity and accleration vector not necessarily perpendicular

I have read somewhere that the velocity vector and the acceleration vector are not necessarily perpendicular. I don't really understand why, since velocity and acceleration are represented by: $$ v ...
0
votes
1answer
19 views

Distance between the centers of two adjacent hexagons in a hexagonal tessellation

Given a hexagonal tessellation where each hexagon has a inradius r, could we say that the distance between two adiacent hexagons is 2r, and in general the distance between any two hexagons is k2r ...
2
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2answers
108 views

A question about $ (2 \times 3) $-rectangles.

The following is a problem from TopCoder: Problem. Given the width and the height of a rectangular grid, return the total number of non-square rectangles that can be found on the grid. For ...
2
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2answers
22 views

What is the relation between inradius and circumradius of a hexagon

Let R and r be respectively circumradius and inradius of a hexagon, I would like to know the math relation between R and r. Thanks,
5
votes
2answers
67 views

An interesting point of a triangle. (Help needed to prove a statement.)

Consider a triangle whose sides are segments of $\color{red}{\text{line}}$, $\color{blue}{\text{line}}$, $\color{green}{\text{line}}$ falling in the circum-circle $c$. Let ...
2
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0answers
30 views

Is there an equidissection of a unit square involving irrational coordinates?

An equidissection of a square is a dissection into non-overlapping triangles of equal area. Monsky's theorem from 1970 states that if a square is equidissected into $n$ triangles, then $n$ is even. ...
2
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1answer
29 views

Showing that an equation of a curve in the plane defines a surface in $R^3$.

A generalized cylinder is a ruled surface for which teh rulings are all Euclidean parallel. Thus there is always a parametrization of the form $$\mathbf{x}(u,v)=\beta (u)+v\mathbf{q} \; ...
2
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2answers
43 views

Finding angles of hyperbolic triangles

I am trying to learn about how to find the angles of hyperbolic triangles. Now below is a problem: It has all the steps but I am not understanding the concept (the ones that are underlined in green ...
4
votes
1answer
60 views

Sketching a Cyclic Quadrilateral

In cyclic quadrilateral $ABCD$ consider $DD_1 ⊥ DC$ with $D_1$ on line $AB$, $BB_1 ⊥ AB$ with $B_1$ on line $DC$. Prove that $AC ∥ B_1D_1$. I'm having trouble drawing this cyclic quadrilateral. At ...
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0answers
18 views

Diagonal of triangular bipyramid with 3 edges next to a point length 1 and orthogonal, and the lengths of three known.

I am working on a lighting system for a voxel game. It requires recursive euclidean distance calculation for successively further blocks, and the distance of each block from the light source needs to ...
2
votes
1answer
33 views

Operator that mantains unit vector

Let $\hat u\in\mathbb R^m$ and $\hat v\in\mathbb R^n$ (with $m \neq n$) represent unit vectors in different vector spaces, and let $B$ be a matrix such that: $$ B\cdot\hat u=\hat v $$ What kind of ...
3
votes
1answer
105 views

Largest of the smallest angles of incidence from arbitrary point to tetrahedron vertex/centroid line

Picture a regular tetrahedron where each vertex has a line through the centroid and a plane normal to it. I need to show that the range of the smallest angles of incidence from an arbitrary point to ...
3
votes
3answers
40 views

What is the area leftover from an inscribed circle called

What are the little triangle things called (displayed as red in the picture)? If the ones on the corners and the ones on the sides are different, then I would like to know those names too.
5
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3answers
452 views

Tricky Rectangle Problem [closed]

How many rectangles are there which do not include any yellow squares?
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0answers
30 views

geometric description of equivalence classes [closed]

For each of the following relations on $\mathbb{R}^{2}$, give a geometric description of the relation classes $[(0,0)]$ and $[(3,4)]$ 1) Let $S$ be the relation defined by $(x,y)S(z,w)$ iff ...
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0answers
14 views

Hyperplane Equation

Would it be correct to say that the function $$ A\cdot T_1+B\cdot T_2+C\cdot T_3=D\cdot x_1+E\cdot x_2+F\cdot x_3+G $$ Generates a hyperplane in 6D? (A through G are constant parameters) Thank you.
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1answer
17 views

Find $y$-coordinate of point on three-dimensional rectangle.

Given a quadrilateral in $3$-dimensional space and the coordinates of each of its vertices, can I find the $y$ of any point on this quadrilateral given this point's $x$ and $z$?
1
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1answer
85 views

The minimum perimeter and maximum height of a triangle under constraints

I'm developing a web application that consists of a calculator triangles. Although I am not a mathematician, with paper, derive and Geogebra I managed to get a lot of formulas to calculate a triangle ...
9
votes
1answer
116 views
+100

$p \in C - D$, inflection point for $C$ iff inflection point for $C \cup D$.

Show that if $C$ and $D$ are projective curves in $\mathbb{P}_2$ and $p \in C - D$ then $p$ is a point of inflection for the curve $C$ if and only if $p$ is a point of inflection for the curve $C \cup ...
0
votes
2answers
38 views

How to determine the location of a mark on an object that has changed size?

I apologize up front for the horrible title, I do not have the mathematics vocabulary to eloquently summarize this in a title. This first picture and question is a lead-up to the actual question. In ...
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0answers
22 views

Realistic Bounce (Using Trig?)

background: I am making a graphics program where the major purpose of it is to have a ball (traveling on an arbitrary slope) to bounce realistically off of a line (which is also at a arbitrary slope). ...
2
votes
4answers
82 views

How to calculate the probability of a point being inside a polygon [closed]

Given that a point is in a polygon, I am assuming that this point is more likely to be on (or near) the Centroid of the polygon than it is likely to be on (or near) the edges of the polygon. Is that a ...
1
vote
1answer
27 views

Krein-Rutman for cones with empty interior

My question concerns the following theorem (a finite-dimensional version of Krein-Rutman): Let $V$ be a finite dimensional real normed space and $C \subseteq V$ a closed cone (i.e. a convex subset ...
2
votes
1answer
85 views

How to find expected angle between two randomly generated vectors?

Let us say two random points have been generated in a d-dimensional space by uniformly sampling from a unit cube centered at origin. How to calculate the expected angle between them?
1
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2answers
21 views

How to detect all points of rectangle by given one point A, height, width, and angle between AC and X axis? [closed]

How to detect points B, C, D of rectangle with given point A, height, width and angle L between AC and X axis.
0
votes
3answers
53 views

How to check if two rectangles intersect? Rectangles can be rotated

How to check if two rectangles intersect? Each rectangle is defined by three points in 2d space. The rectangles can be rotated around any point as on the image below.
1
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0answers
30 views

Imagening the Thurston geometries

I can (more of less) imagine how it would look if space was Euclidean, spherical of hyperbolic. But there are 8 Thurston geometries see https://en.wikipedia.org/wiki/Geometrization_conjecture how ...
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0answers
22 views

Ideal Triangles and Klein Beltrami Disc

I'm trying to prove something with the ideal triangle in hyperbolic geometry and someone told me that the ideal triangle looks like a euclidean triangle inscribed in a circle in the Klein Beltrami ...
0
votes
1answer
76 views

Pointy triangles exists

In Yahoo Answers, here, Rita the dog defined a pointy triangle, (more or less) as having three properties. The lengths of two sides are rational and greater than 1. The length of the third side is ...
1
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2answers
41 views

Finding the missing length

How do i find the ST?? What more information do I need? I used Pythagorean theorem, but I still can't find the answer.
1
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3answers
26 views

Find two points on two lines in the plane where the line between the two points go through a third point and are equidistant from that point

I have the following situation (see pic below). I have two lines $B$, $C$, in the plane, the intersection point $a$, and a point $p$. I need to find the points $b$ and $c$ along $B$ and $C$ such that ...
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votes
1answer
28 views

Geometry: Perimeter of triangle formed by intersections of tangents

I'm a bit stuck on the question below, and I wondered if anyone out here might be able to help: Construct a circle with a centre in O(0,0) and a radius of 5. Two tangents of the circle intersect in ...
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1answer
25 views

Given two points on a plane, and an area find all possible lines connecting the points.

Say I have a $10\times10$ plane and I am given two points on the plane, suppose $(0,0)$ and $(10,10)$. What formula or algorithm could be used to trace all the possible paths between these two points? ...
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votes
1answer
81 views

Is there a closed form expression for the infinity symbol?

I was looking for a closed form expression which plots the infinity symbol.
0
votes
2answers
70 views

Hyperbolic Ideal Triangle

I have everything pretty much figured out everything but I need help proving the unique point formed by the three perpendiculars in the picture
0
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1answer
32 views

Is there an algorithm to determine if an arc through 3 points is concave up or concave down?

Armed with only the three points in 2-dimensional space, $X = \{x_1, x_2, x_3\}$, is there a simple inequality or algorithm that can return whether or not an arc $A$ through these three points is ...
3
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0answers
29 views

Curios relation between parabola, circumcircle and circumellipse

When playing around with conics in GeoGebra, I have found out that the following relation seems to hold: Let parabola $p$ be tangent to sides/extensions of sides $BC,CA,AB$ of triangle $ABC$ at ...
5
votes
1answer
85 views

Three planes in general position, one point in each, construct sections

I have three planes in general position, and in each plane an arbitrary point is selected : this gives us three points $R,S,T$. Is it possible to construct the intersection lines of the $(RST)$ plane ...
6
votes
1answer
79 views

How to divide a pizza between friends equally without using centre

Here's a really fun question a friend told me abut. He claims to know the correct answer, and told me the answer, but left proving the answer as an exercise to me. Now, It's been ages since he asked ...
0
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0answers
29 views

Finding equation of line at a given angle from point to ellipse

Given a point $p_0$ and the parametric equation of an ellipse. I want to find the vector $v$ from $p_0$ such that when it intersects with the ellipse, it forms an angle $\theta$ with the ellipse's ...