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
votes
0answers
224 views

What is a bi-rhombus? [closed]

Can anyone tell me what a bi-rhombus is? I need it for my school project.
3
votes
2answers
27 views

What is the ratio of the side length of a regular hepatgon to the side length of the internal heptagon?

Given a regular heptagon with side length 1, create a star heptagon by connecting every vertice. Note that removing the "points" of the star yields a similar heptagon. I want to know the side ...
5
votes
1answer
47 views

Circle with perpendicular chords

A blue circle is divided into $100$ arcs by $100$ red points such that the lengths of the arcs are the positive integers from $1$ to $100$ in an arbitrary order. Prove that there exists two ...
3
votes
3answers
143 views
+50

An equilateral triangle formed using points of tangency

P.S:I am looking for a hint and not the whole solution. BdMO 2012 nationals secondary: The vertices of a right triangle $ABC$ inscribed in a circle divide the circumference into three arcs. The ...
0
votes
4answers
89 views

Calculate angle between two lines

We have four points: a, b, c and d. We only know length ...
0
votes
0answers
30 views

Geoemetry [circle] [closed]

AC and BC are two chord of a circle BA is produced to any pointP and CP , when joined cut circle at T then which of the following statement is true 1.CT:TP =AB:CA 2.CT:TP =CA:AB 3.CT:CB=CA:CP ...
5
votes
1answer
37 views

Abstract question about the rotation in 3D [on hold]

I've made the following observersations: Zero-dimmensional entities, points, don't really rotate. One-dimmensional entities, lines, rotate about a stationary point. Two-dimmensional entities, ...
6
votes
0answers
62 views

I would like to show that all reflections in a finite reflection group $W :=\langle t_1, \ldots , t_n\rangle$ are of the form $wt_iw^{-1}.$

I would like to show that all reflections in a finite reflection group $W := \langle t_1, \ldots , t_n\rangle$ are of the form $wt_iw^{-1}$ for some $i$ and some $w \in W$ Clearly all such elements ...
0
votes
1answer
24 views

What is $s$ in s-energy (eg. Riesz s-energy)

I'm trying to understand fekete problems. There is a variable $s$ and a related concept of 's-energy' [1] [2] [3] [4] that comes up repeatedly when borrowing the concept of potential energy to find ...
1
vote
1answer
25 views

N points and N perpendiculars

This is actually a set of two problems: (in one question, I believe it is useful and convenient to analyse them together) Problem A $N$ arbitrary points are given in a plane (all different). ...
1
vote
1answer
88 views

Minimum Value of $x_1+x_2+x_3$

For an Acute Triangle $\Delta ABC$ $$\begin{align}x_n=2^{n-3}\left(\cos^nA+\cos^nB+\cos^nC\right)+\cos A\,\cos B\,\cos C\end{align}$$ Then find the least value of $$x_1+x_2+x_3$$ My Approach: I have ...
0
votes
1answer
16 views

Semicircumference, and tangent circumference satisfying certain conditions.

Please suppose you have a semicircumference of diameter AB, and radius r. Please help me to determine the radius of a tangent circumference in the point D of the diameter AB, and tangent in the point ...
3
votes
3answers
83 views

How can I find the volume of prism: $V = \frac{(a + b + c)Q}{3} $

In the book Handbook of Mathematics (I. N. Bronshtein, pg 194), we have without proof. If the bases of a triangular prism are not parallel (see figure) to each other we can calculate its volume by ...
-2
votes
0answers
38 views

Trigonometry-how to do? [closed]

AB (3m) is an advertisement board perched on pole BC. CD is a horizontal ground level. AD=12m and BD=10m. Find the length of elevation of A from D and B from D. Find the length of BC.
2
votes
1answer
35 views

What does taking the $n^{\text{th}}$ root of a complex number geometrically mean?

What are the geometrical implications of taking the $n^{\text{th}}$ root of a complex number, say $3+4i$. What is the geometrical implication of $\sqrt[n] {3+4i}$ in the complex plane?
1
vote
1answer
17 views

intersection of cone axis with plane

So when the plane intersect the cone, the intersection is a conic. Is (or when is) the axis (of the cone) intersection with the plane the focus of the conic?
0
votes
0answers
20 views

Finsler Metric from page 2 of the book by Chern and Shen.

Physicist here not a mathematician. I am trying to understand the notation for the Finsler metric in Chern and Shen's book. The equation is $$\textbf{g}_y(u,v):=\frac{1}{2} ...
6
votes
1answer
69 views

Probability that two circles in space are linked

Let $C_0$ be a circle centered on the origin, and $C_1$ a circle centered on $(1,0,0)$, center distance of $1$. Q1. If both $C_0$ and $C_1$ are randomly oriented and have the same radius $r ...
2
votes
1answer
42 views

When does intersection of measure 0 implies interior-disjointness?

If there are two "nice" shapes in $R^2$, such as circles or polygons, whose intersection has area 0, then they must be interior-disjoint, as their intersection can only contain pieces of their ...
-1
votes
4answers
32 views

Finding the condition for similar Triangle [closed]

Is there any way to prove the two triangles are similar?
7
votes
2answers
72 views

Evenly space holes in circle

A picture is worth a thousand words: This gear is part of an interactive SVG Spirograph I'm creating. I'm dynamically generating the gear based on a number of parameters (gear radius, number of ...
0
votes
0answers
416 views

Fitting Expanding Spheres in the Irregular Surface

This is a kind of a puzzle: I have a convex hull filled with $N$ small spheres(with radius $r$). Now, the balls grow in size till it hit any side of the Cavity (Convex hull) or any other ball. ...
3
votes
2answers
58 views

How to find the area of the shaded region? [on hold]

How do i find the area of the following shaded region? The figure consists of two circles, one of radius $2r$ and the other of radius $r$. The distance of the center of the circle of radius $r$ from ...
0
votes
1answer
32 views

Rotation matrix of triangle in 3D

How can I find out the rotation matrix of a right angle triangle defined by 3 points in 3D space (assuming the un-rotated triangle faces the x axis)
1
vote
1answer
19 views

Reduce distance computation overhead between a point and several rectangles

We are given several rectangles in the plane, without loss of generality, assume there are three of them, namely $R_1$, $R_2$ and $R_3$. For a point $P$, we can compute three distances $d_1$, $d_2$ ...
1
vote
2answers
31 views

Thinking of sohcahtoa with 90 in a triangle.

I know the answers from a unit circle. But when looking at a triangle how do you interpret Angle C sin C = cos C = tan C = I know the cos 90 = 0 and ...
2
votes
1answer
75 views

Area of the quadrilateral within a triangle

Given the area of tringles $BEF=X,BFC=Y$ and $FDC=Z$, Can we find the area of the quadrilateral $AEFD$ in terms of $X,Y,Z$?
2
votes
1answer
55 views

Ratio between surface area on either side of a line's own supercover

Let's say we have a line on a raster that goes from any position on any edge to any other edge: And take its supercover: We now have a polygon that is cut in 2 by a line, intuitively it seems that ...
0
votes
2answers
16 views

Problem about moving sides of triangle

Imagine a triangle XOY which sides lie on x-axis and y-axis with hypotenuse XY of length 5 m. Suppose the point X moves away from the (0,0) along x-axis with speed = 1 m per second. What speed the ...
0
votes
1answer
20 views

recutting a polygon to obtain its flip

I am curious if it is possible to cut the triangle with vertices (0,0), (0,1), (1,0) into many polygonal pieces and only translate each piece appropriately to construct the triangle with vertices ...
-1
votes
0answers
38 views

Incenter Geometry Proof [closed]

A circle is drawn that intersects all three sides of triangle $PQR$ as shown below. Prove that if $AB=CD=EF$, then the center $U$ of the circle is the incenter of triangle $PQR$.
0
votes
1answer
45 views

How to solve geometric question like this?

Rectangle ABCD has length 10 breadth 20. P and Q trisect AB. CD is bisected at R. The diagonal AC intersects PR and QR at E and F. Find the area of the quadrilateral PEFQ. This was asked in this ...
2
votes
1answer
43 views

Maximum number of pairwise externally tangent congruent cylinders in space

What is the maximum number of congruent cylinders (radius $r$, height $h$, for your choice of $r,h$) that can be arranged in space so that each cylinder touches every other cylinder? I'm aware of an ...
-1
votes
1answer
59 views

How to find the volume of a solid [closed]

Suppose the solid $E$ is given by $$E=\{(x,y,z): (x^2+y^2+z^2+8)^2 \leq 36(x^2+y^2)\}.$$ Find the exact volume of $E$.
0
votes
1answer
18 views

Symmetrization Methods

I was wondering if I could get a list of the symmetrization methods out there i.e. methods that rigidly transform a set A into it's equimeasure ball $A^{*}$. Here are some: a) Steiner Symmetrization ...
1
vote
0answers
11 views

Finding triangulations on 2D space by projecting lower hull of 3D

So we know that we can get the Delauney triangulation of a polygon if we map all points to the 3D space such that $p'=(p.x,p.y,p.x^2+p.y^2)$, compute the lower hull of that polyhedron, and then ...
1
vote
2answers
51 views

Math and equations for external tangent lines between two dissimilar circles?

I am trying to determine the maths behind drawing a line from the top of one circle to the top of another (and bottom to bottom). I am doing this for a programmatically generated CAD file, I currently ...
1
vote
1answer
46 views

Merge two or more cubic Bézier curves for optimization

I am looking for an algorithm which can merge several cubic Bezier curves. For instance, I have a lot of cubic Bezier that are joined to form a poly-Bezier curve. The idea is to merge dynamically some ...
0
votes
1answer
35 views

Geometric Application of Cauchy-Schwarz Inequality Problem

I have been struggling with this problem, and would like to prove the inequality using the Cauchy-Schwarz Inequality: The vertices of a fixed triangle are $A$,$B$ and $C$, and $P$,$Q$ and $R$ lie on ...
0
votes
1answer
23 views

Isometries of the plane and fixed lines

I am given that for all reflections $g$ there are infinitely many lines $L$ satisfying $g(L) = L$ which makes perfect sense (just take lines perpendicular to the axis of reflection). I am asked to ...
3
votes
1answer
43 views

Do invariant lines of linear transformations contain a fixed point?

Suppose $A$ is a $2$-by-$2$ matrix, and $\mathcal{l}$ is an invariant line under $A$, so $(x,mx+c)$ is mapped to $(X,mX+c)$ for some variable $X$ linear in $x$. Then is there a point on the line ...
3
votes
2answers
42 views

Do the centroid of a unit n-hemisphere and that of the whole n-sphere coincide when $n \to \infty$?

It is known that the distance between the centroid and the center of a unit semicircle is $\displaystyle\frac{4}{3\pi}$, whereas that of a unit hemisphere is $\displaystyle\frac{3}{8}$. I am ...
21
votes
5answers
4k views

Why is $\sin(d\Phi) = d\Phi$ where $d\Phi$ is very small?

I haven't touched Physics and Math (especially continuous Math) for a long time, so please bear with me. In essence, I'm going over a few Physics lectures, one which tries to calculate the Force ...
0
votes
0answers
19 views

Detecting coplanarity by given pairwise distances

Given a 3D point set $P$, where $|P| \gg 4$ is there a way other than using Cayley-Menger determinant to detect if a group of points are coplanar or not? In other words, what are the methods to ...
3
votes
1answer
25 views

Find a maximum triangle that lies on a polyline (with constraints)

If there's a polyline (a GPS track, actually) with a lot of points (could be several thousand), that looks like this 1) How can I find such a triangle with the biggest possible perimeter, that its ...
1
vote
0answers
28 views

Given the circumcircle, the 9-point circle, and the angular measures for a triangle, construct the triangle?

This is similar to some questions that have been asked (e.g. construct-triangle-given-inradius-and-circumradius), but I don't see the exact same question. It arose out of an inversive geometry formula ...
1
vote
0answers
37 views

Numerical rounding errors in intersection code

I hope this question is in the right place, as it is as much about programming as it is about math. I'm trying to find the intersection between a circle and a line. My implementation of the algorithm ...
1
vote
1answer
29 views

How to find location of a source in TDOA Method

We have 3d system with a source is sending signal and four receivers and we know the coordinate location of these four receivers. We have four Time difference of arrival. How to calculate the ...
0
votes
0answers
37 views

Plane geometry in the complex plane

i am asked to find the area of a triangle that has vertices $0, w_{1}, w_{2}$ in $\mathbb{C}$ by applying the transformation $z \rightarrow \bar{w_2}z.$ My attempt: since we are multiplying by the ...
1
vote
2answers
18 views

Side length of a square in a squared rectangle

I have a squared rectangle where I want to find the side length of a sub-square (for the record, consult the omniscient Google). Here's what I've already done. $$14 + 4 + x = \mathrm{height}.$$ ...