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

learn more… | top users | synonyms

1
vote
1answer
28 views

Showing that $\alpha$ satisfies the equation $\sin 2x=x$

This is an A level question. For better understanding, I will attach a screenshot of the question and the mark scheme. Question: Here's what I have done: $$A(OBA) = \frac 12r^2α$$ [basic ...
2
votes
1answer
31 views

Quarter Circle packing

Just today, I was making tortilla chips, and I began to wonder, what is the most efficient way to pack circular quarters onto the plane? This sort of circle packing is most efficient for circles, ...
-6
votes
2answers
41 views

The area of square [on hold]

What is the area of the square versus a,b and c ? Thanks
0
votes
1answer
20 views

How do you calculate the change in thickness of a cylinder, if you shave off a flat section?

I have a piece of steel, cylindrical (hollow), 200mm outside diameter with 160mm inside diameter (...
-3
votes
2answers
29 views

How to determine that the 3 points given in homogeneous coordinates are collinear? [on hold]

How do I prove that the 3 points given in homogeneous coordinates are collinear? $$A=(1,3,2)^T, B=(0,6,8)^T, C=(3,3,-2)^T$$
0
votes
1answer
20 views

length of radius of circles between their tangents

In this question, we have five circle that touch each other. we draw their tangents. If we know that smallest circle radius is 8 and biggest circle radius is 18, then what is the length of PF? Note: ...
0
votes
1answer
14 views

Translate a Rectangle Position from 1 Image to another [on hold]

I have a Large Size Image.Since its too large for processing within a small time, i need to resize it.I have the coordinates of a rectangle in the resized image.Is there a way i can translate this ...
0
votes
3answers
18 views

Area of rectangle and triangle derivation

I was wondering about the derivation for the area of a triangle and the area of a rectangle. Of course, we all know them to be $\dfrac{1}{2}bh$ and $bh$ respectively, but where is the derivation of ...
0
votes
0answers
16 views

locus of a variable straight line [on hold]

Geometry: A variable straight line always intersects the lines x=c,y=0; y=c,z=0; z=c,x=0. find the equation to its locus. taking the equation of a line in parametric form and substitute the given ...
0
votes
1answer
18 views

Deriving formula for externally tangent circle to internally tangent circle

($x^2+(y+1)^2=R^2$ should say $x^2+(y-1)^2=R^2$) I am trying to derive a formula for the radius of the circle that is externally tangent to the internally tangent circles of the quarter-circle, and ...
1
vote
0answers
41 views

Why are carrom boards square? [on hold]

This question may seem a little off-topic for this site.... We have all seen carrom boards.Now,why are carrom boards always square and not rectangular?Is it only because distance to the pockets will ...
0
votes
1answer
27 views

How many non-congruent triangles with perimeter 11 have integer side lengths? [on hold]

How many non-congruent triangles with perimeter 11 have integer side lengths? I failed to solve it. Can anyone help?
-1
votes
2answers
32 views

Triangle with a square in it, with the side of $2\sqrt{3}$, what's the altitude of the triangle? [on hold]

We have a triangle and within is a square with the side of $2\sqrt{3}$. What's the altitude of the triangle ABC? All 3 angles in the triangle are same (60). Pic: http://imgur.com/gallery/SAmhU7z/new ...
2
votes
1answer
40 views

Does a convex hull solution in 3 dimensions result in a minimum-area or maximum-volume solution?

The wikipedia entry for convex hull shows a 2-d example of a random set of points on x-y plane, and the "elastic band" solution that bounds the points with the convex hull solution. The definition of ...
0
votes
1answer
18 views

Prove that the sum of the vectors from the centre to the vertices of a regular hexagon is 0

Prove that the sum of the vectors from the centre to the vertices of a regular hexagon is 0 Let's call the centre $O$ and the vertices are $A, B, C, D, E$ and $F$. Therefore, the sum in the ...
0
votes
1answer
17 views

Finding $y_{A,i}$ and $y_{B,i}$ in this geometric relationship problem.

Finding $y_{A,i}$ and $y_{B,i}$ in this geometric relationship problem. I'm an high-speed aerodynamics student. I am studying a sweptback wing like in the figure below (in green). Notice that I ...
0
votes
1answer
33 views

Find $|CM|$, if $|CA|=a$ and $|CB|=b$. [on hold]

Let $O$ be a center of a circle, circumscribed over $\triangle ABC$. Perpendicular, drown from the point $A$ on the line $CO$, cross the line $CB$ in the point $M$. Find $|CM|$, if $|CA|=a$ and ...
1
vote
1answer
33 views

Prove that $MN = \dfrac{|b − c|}{2}$

In triangle $ABC$, point $M$ is the midpoint of $BC$ and $N$ is on the angle bisector of $\angle A$ such that $MN \parallel AB$. Prove that $MN = \dfrac{|b − c|}{2}$. Attempt: I drew it out and ...
1
vote
2answers
34 views

Expand polygon to grid in $x-y$ plane

Given a polygon in the $x-y$ plane, what is the simplest formula for expanding the polygon so that all sides lie on a grid? The image below demonstrates the problem I am trying to solve. The filled ...
0
votes
0answers
13 views

Conformal curvature line parametrization

While reading a paper I found a definition which is confusing me. Def: A conformal curvature line parametrization $(x,y) \to F(x,y)$ is called isothermic. I know what a conformal ...
0
votes
0answers
19 views

Distance function for N-prism

Im looking for distance function that describes N prism. Im looking for pentagon prism, heptagon prism and octagon prism functions. Function accepts vec3 position, which is observer position. ...
0
votes
0answers
12 views

How to compute homography matrix H from four corresponding points [duplicate]

I am using 4 point correspondence to compute elements in Homography matrix $H$. \begin{align*} [x']={}& [h_1 h_2 h_3] [x] \\ [y']={}& [h_4 h_5 h_6] [y] \\ [(1)]={}&[h_7 h_8 h_9] [(1)] ...
2
votes
2answers
27 views

Find Length of line which has rotating object.

I have 3 Images. A, B and C. if I place it on graph, its look something like this. Now main image is A and I place B and C on that image's (A) center point. For easy understanding, let's consider ...
0
votes
1answer
24 views

Four Spheres Intersect Along Circles: Prove That Circles' Planes Are Either $\parallel$ to The Same Line, Or Have a Common Point

Problem: Let $\,A,\,B,\,C,\,D\,$ be four distinct spheres in a space. Suppose the spheres $A$ and $B$ intersect along a circle which belongs to some plane $P$, the spheres $B$ and $C$ intersect ...
0
votes
1answer
33 views

How many triangles ABC with 𝐴𝐴 angle ABC= 90° and AB= 20 exist such that all sides have integer lengths? [on hold]

How many triangles ABC with angle ABC= 90° and AB= 20 exist such that all sides have integer lengths?Is it somehow related to the Phythagorean Theorem?Here is my attemp to solve it: 400+BC^2 = AC^2 ...
3
votes
1answer
73 views

How to determine the reflection point on an ellipse

Here is my problem. There are two points P and Q outside an ellipse, where the coordinates of the P and Q are known. The shape of the ellipse is also known. A ray comming from point A is reflected by ...
5
votes
0answers
38 views

Interesting cube subdivisions: what is going on here, and what are these polytopes?

I was messing around recently with a unit cube. If you draw vertices on the midpoint of each edge of the cube, then connect those points by new edges, you will form the wireframe of what I figured ...
3
votes
4answers
50 views

Prove that the altitudes of an acute triangle intersect inside the triangle.

Prove that the altitudes of an acute triangle intersect inside the triangle. I can pretty easily see that this is true by a pythagorean theorem argument. Given any two sides, the smaller length ...
1
vote
1answer
17 views

Rotation matrix between two similar cuboids using their upper sides ( and the planes defined by these sides)

I have two different images and with them an estimation of two planes ( defined in the same system). I would like to get the rotation matrix, quaternion or euler angles of a surface within this ...
0
votes
1answer
37 views

Center point of 2 tangent circles along 2 tangent lines

Given points P1, P2, and P3, I need to calculate the center point of 2 tangent circles, C1 and C2, with radius R. Line P1P2 is tangent to circle C1 at P2, line P2P3 is tangent to C2, and C1 and C2 are ...
0
votes
0answers
34 views

Geometry perpendicular proof

How would I prove that there is a line perpendicular to any given line through a given point not on the line?
3
votes
2answers
34 views

Is it possible to define the position of a gunshot using and array of microphones?

If I had four microphones, located on poles that were at corners of a square that's 300 feet on a side (or some other specific configuration that would make the math easier), would I be able to use ...
0
votes
1answer
27 views

Computing the approximate or exact area of an isosurface

The isosurfaces I'm reading about are defined by a constant value v in a scalar field. The scalar field is defined by placing n vectors in k-space such that ...
0
votes
0answers
54 views

Perimeter of a teardrop (made by two adjacent circles)

I'm trying to determine the perimeter of a teardrop shape formed by two adjacent circles (non-intersecting) with mutually tangent lines drawn on both sides of the circles. I've attached a sample ...
-6
votes
0answers
54 views

Find $a$, $b$ and $c$. [on hold]

As title said, How to find angles $a$, $b$ and $c$? Thanks in advance!
4
votes
1answer
53 views

Number of ways to separate $n$ points in the plane

Say you are given $n$ points such that no three are colinear. Show the number of ways to separate them into two subsets by drawing a straight line depends on $n$ but not the position of the points.
0
votes
1answer
29 views

Partitioning a convex object without cutting existing convex subsets

$C$ is a convex object in the plane. $D_1,\dots,D_n$ are pairwise-disjoint convex subsets of $C$ such that $D_1\cup\dots\cup D_n \subsetneq C$, like this: Is it always possible to partition $C$ to ...
0
votes
0answers
13 views

Geometry trapezoid angle bisectors

Let $ABCD$ be a trapezoid with $AB||CD, AB=11, BC=5, CD=19,$ and $DA=7$. Bisectors of $\angle A$ and $\angle D$ meet at $P$, and bisectors of $\angle B$ and $\angle C$ meet at $Q$. What is the area ...
1
vote
2answers
39 views

What is the length of the 4th side? [on hold]

Given the figure in this image (I don't know the correct name in English. I wish to know the length of the 4th side. How to calculate it and what's the length of the 4th side?
1
vote
3answers
44 views

Area stacked between common tangent and circles [on hold]

Is there any way to find area of shaded region? The radii of circles are $4$ and $12$ units.
0
votes
0answers
19 views

A vector which is perpendicular to two vectors not in the same plane

Assume that I have two vectors $v_1, v_2$ which are not parallel and they don't lie the same plane. How to find a third vector $n$ perpendicular to $v_1$ and $v_2$? You could take the cross prosuct, ...
0
votes
2answers
39 views

Geometry/ Triangles problem

I have been struggling with this problem, and I think it should be possible to solve but right now I cannot find how. Given two coordinates/points (x1,y1) and (x2,y2) The angle d1 with the ...
1
vote
0answers
35 views

Distance between point and ellipse - explanation of a paper

EDIT: I notice that the link is hidden, but this post is made with reference to THIS PAPER I'm trying to solve quite an old problem (once again) - to find the distance between a point (in 3d space) ...
-2
votes
1answer
17 views

If we rotate the rectangle about centre how to check angle amount in Geometry. [on hold]

If we rotate the rectangle about centre how to check angle amount in Geometry. Mean how much angle rotated, which line segments form angle.
0
votes
0answers
12 views

General dependencies among Invariants

I've found the following dependency in an article: We have 3D points $X_i , i = 1; ... ; 5$ in 3D space, of which at least the first four are not coplanar. We can express fifth point as a linear ...
-1
votes
0answers
12 views

Normal bundle and global function [on hold]

Suppose $M \subseteq \Bbb R^m$ is a closed embedded submanifold. If $M$ admits a global defining function, show that its normal bundle is trivial. Conversely, if $M$ has trivial normal bundle, show ...
3
votes
1answer
31 views

Expressing a point in $\mathbb{R}^n$ as a sum of unit vectors

I'm pretty sure that any point in $\mathbb{R}^n$ can be written as a sum of finitely many unit vectors (in $\mathbb{R}^n$, of course). However, I have no idea how to go about proving this. Any ideas? ...
0
votes
0answers
9 views

How to extract custom tool in “Active Geometry” [on hold]

I'm using a Win10 APP, the name is "Active Geometry". I want to extract some custom tools , but I don't know how to do. Who can help me?
2
votes
3answers
52 views

Basic question about angles and measurement in degrees

I have a doubt related to angles which I am a bit embarrassaed to ask since I know is something of basic geometry, but nevertheless my question is the following: As I understand it, an angle between ...
2
votes
0answers
19 views

Hexagons share interior points

Can we draw infinitely many hexagons, not necessarily convex, on the plane so that any three of them share a common interior point, but no four of them does? For four hexagons this is possible, using ...