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
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 ...
1
vote
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
104 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
votes
3answers
451 views

Tricky Rectangle Problem [closed]

How many rectangles are there which do not include any yellow squares?
-1
votes
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 ...
0
votes
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.
-1
votes
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
vote
1answer
76 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 ...
7
votes
0answers
90 views

$p \in C - D$, 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 ...
1
vote
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
vote
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
vote
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 ...
0
votes
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
vote
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
vote
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 ...
-1
votes
1answer
27 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 ...
0
votes
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? ...
-1
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
votes
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
votes
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
83 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
78 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
votes
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 ...
0
votes
1answer
20 views

Incommensurable units as ratios

I am having a bit of trouble understanding the concept of an incommensurable unit. From what I have gathered so far, it is simply a magnitude that cannot be expressed as the ratio of two natural ...
2
votes
2answers
50 views

Calculating the shortest route around cylinder

If I have the following situation, what would the path look like? Where would the path go and how would I calculate it? Cylinder with diameter $10\,\hbox{cm}$ and height $5\,\hbox{cm}$. Use the ...
1
vote
2answers
49 views

Calculating the coordinate of a point on a circular path

Say that I have a circular path like this: where I go from point $A(\alpha,\beta)$ where $\alpha,\beta\in\mathbb{R}$ are known values to point $B(x,y)$. My aim here is calculate the coordinates of ...
1
vote
1answer
37 views

Conjugate Hyperbolas.

What would be a good approach to tackle this problem. In a previous assignment I managed to show Pq=Pr. How do I show that this tangent intersects the conjugate hyperbola. Should I start by ...
0
votes
0answers
28 views

Calculate shifted unit circle values

I have the black unit circle and I need to shift it by x degrees getting the red unit circle. How do I shift it, because just subtracting x degrees from the original black circle doesn't work. ...
19
votes
9answers
5k views

Why are two planes parallel to the same line not necessarily parallel?

What is a case in which the statement, "Two planes parallel to the same line are parallel" be false?
1
vote
0answers
25 views

How can we formulate the art gallery problem as a mixed-integer linear program?

Specifically, how would one go about using 'intlinprog' in MATLAB to get a minimum value for the cameras required in a polygon-shaped art gallery? In other words, I think that what I am looking for is ...
0
votes
1answer
19 views

Midpoint of a line segment with a marked straight edge

Given a line segment $AB$ and a marked straight edge. How can I construct the midpoint of the line segment with the marked straight edge only (i.e., in particular without a compass)? I have no idea, ...
8
votes
2answers
59 views

Dividing an angle into $n$ equal parts

My question is simply: for which values of $n$ is it possible to divide any given angle into $n$ equal parts using only a compass and a straight edge? I know that it is possible for $2$ and not ...
1
vote
1answer
26 views

Question regarding an equation in a paper on parabolas

In this paper on parabolas by K. Kumar I was reading this morning I found an equation which I do not think I fully understand. On page 489, part 4 (Derivation), the author defines the distance ...
2
votes
1answer
54 views

Making the segment with given length $\sqrt[3]{2}$?

Using Pythagoras' Theorem we can make the segment with given length of Square root of natural numbers. For example the segment of given length The square root of 2 is equal to the length of the ...
1
vote
1answer
280 views

Points of symmetry of tessellation.

I was given this irregular hexagon: Then I was told to tessellate it: Now, I am being asked to find all the points on the hexagon (first picture) which are points of symmetry of my tessellation ...
0
votes
1answer
21 views

concurrency of angle bisectors, medians, perpendicular bisectors, altitudes

When you think of a triangle the basic constructions you think of are perpendicular bisectors of the sides, angle bisectors, altitudes, and medians. Now if you were someone who just started learning ...
0
votes
0answers
32 views

Asymptotic analysis of Integrals of powers of sine and their application to intersections of hyperspheres

I am trying to estimate the probability of an event in an algorithm. For simplicity, assume there are two hyperspheres of radius $r$, at a distance $r$ from each other. I am looking to see how the ...
0
votes
1answer
33 views

Square root of height of a paraboloid equal to radius?

I'm reading the book Mathematics: It's Content, Methods, and Meanings and I'm unsure as to how one of the variables in an example was derived. The question is about the volume of a paraboloid and here ...
1
vote
1answer
30 views

proving that the shortest line conntecting a point and a line will be perpendicular to that line

So I have a problem for my final math project that I've been fiddling with for hours without success. I have to use calculus to prove that the shortest line connecting a point to a line will always be ...
0
votes
1answer
27 views

How do I calculate center of mass of a grid-type object?

I am making a game with 2D objects that are grid based. These objects are made out of tiles that are actually the cells of the grid. Each tile has a "mass" that is more than 0 and no upper limit. I ...