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

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4
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0answers
18 views

Tangent of Circles

$k_1$ is a circle with center $O_1$ and radius $r_1$. Similar for $k_2(O_2;r_2)$. $r_1 < r_2$. $AB$ and $CD$ are tangent lines to $k_1$ and $k_2$. Prove that $AP=DQ$.
0
votes
1answer
13 views

Quadratic equations

The width of a rectangular TV screen is 22.9 in longer then the height. Of the diagonal is 60 in find dimensions of the screen. 1. Using Pythagorean theorem express the given information in the ...
0
votes
1answer
8 views

How can one prove that (AD) and (EB) are orthogonal?

ABC is a triangle , we make outside two squares CBGD and ACEH I have to show that (AD) and (EB) are orthogonal . So im sure that there is many ways to solve this exercise I did it using the scalar ...
0
votes
0answers
5 views

Check if ray intersects internals of $D$-facet

Given a ray $\overrightarrow{r_0} + \overrightarrow{v} \cdot t, t \in [0;+\infty)$ and a $(D - 1)$-simplex, defined by $D$-tuple of its vertices $p_i = (p_i^1, p_i^2, \dots, p_i^D), i \in \{1, 2, ...
0
votes
3answers
17 views

Greatest area using a string with the length of $l$

Suppose we have a string with length of $l$ what is the shape that has highest area? In other words,with a constant perimeter of $l$ what is the shape with the highest area? P.S:My own speculation ...
0
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0answers
9 views

How do I find the rate of change in area of rotating loop?

Say we have a rectangle of side lengths $a$ and and $b$ that is rotating with one of its sides $a$ about a fixed axis with angular speed $v$. Consider a line $l$ a distance $x$ from the axis of the ...
0
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0answers
5 views

Given the maximum side of an integer scalene triangle, is it possible to determine how many triangles will have an integer median?

This paper finds a formula to calculate the amount of integral isosceles and integral Pythagorean triples with an integral median: http://arxiv.org/vc/arxiv/papers/0901/0901.1857v1.pdf However, is ...
2
votes
0answers
39 views

reference required for a well-known result

Consider the following classic problem: Given a 2-dimensional cube (a square) $[0,1]^2$, one of the minimum (area) simplex covering the 2-cube is bounded by $x_1 =0 , x_2=0, x_1+x_2 =2$. For ...
0
votes
0answers
11 views

Drawing an arc within two defined points in C graphics

I would like to know whether there is any mathematical equation to draw an arc in c within the defined points using mathematical equations. Right know I'm doing an trial and error method to fit an ...
-2
votes
0answers
20 views

Triangle: Given one point, one angle and 2 lengths find point [on hold]

Given point (h, k), two sides of a triangle and a constant angle of 120 degrees, what formula can i use to find (ax, ay)? I'll be using the formula to solve isometric projections.
0
votes
1answer
35 views

Calculate coordinates of a point on a circular arc

I have following dilemma I need to solve for my software: I have a circular arc, and I do know these: x,y coordinates of startpoint of the arc x,y coordinates of endpoint of the arc x,y coordinates ...
2
votes
1answer
13 views

Check if convex polygon is completely contained completely within another convex polygon.

How can I determine if a convex polygon is completely contained within another convex polygon where speed is critical? I've thought about doing this, which will only use inequalities: pcp = ...
3
votes
2answers
36 views

Calculating the area of an ellipse

I need to calculate the area of an ellipse described in polar coordinates by the following equation $$r=\frac{p}{1+\epsilon \cos{\theta}},\qquad |\epsilon| < 1$$ I need to so it by solving the ...
-2
votes
0answers
18 views

Need help identifying a classification of tetrahedra. [on hold]

Does anyone know what type of tetrahedra the below would be classified under?
2
votes
1answer
49 views

Some relation between parallel vector field and Jacobi field along a geodesic

Cross posted from my question: http://mathoverflow.net/questions/204097/parallel-transport-along-a-geodesic-and-the-related-jacobi-field This is a formula/theorem (written below) that I found ...
3
votes
1answer
27 views

How to find the largest disk in a square when there are points we must avoid?

We have $n$ points $X =\{x_1, x_2, \dots, x_n\}$ inside (let's say) the unit square $Q$. We must find a disk $D\subset Q$ such that none of the points of $X$ are inside the disk. (The points can be on ...
9
votes
0answers
73 views

What Rubik's Twist configuration has the lowest visible surface area?

The Rubik's Twist has been a fun time sink. From the wiki page, [It] is a toy with twenty-four wedges that are right isosceles triangular prisms. The wedges are connected by spring bolts, so that ...
2
votes
1answer
34 views

Does a simplex with equal altitudes have to be equilateral?

Consider a simplex in $\mathbb{R}^d$. Assume that all its altitudes have the same length. Does it necessarily mean that the simplex is equilateral, i. e. all distances between its vertices are equal ...
4
votes
2answers
41 views

Four circles touching one another on a spherical surface

The diagram above shows four identical circles, each having a flat radius $r$ (i.e. flat area $\pi r^2$), touching one another at six different points (i.e. each of four identical circles touches ...
3
votes
2answers
26 views

Perimeter of the square

How to find the perimeter of the square? This is the question from a 14 years old textbook, I can solve this by using vector. But they are just 14 years old, they won't learn vector at the age. Is ...
1
vote
0answers
23 views

Bounding box of Ellipsoid

In page 15 of the document given in this link here the bounding box of a rotated ellipse is defined with simple formulas. Where can I find similar formulas for the bounding of an Ellipsoid?
0
votes
0answers
15 views

angle between tangent to the curve $\gamma(t)= t^3i+2tj+t^3k$ at $t=\pm 1 $

Find the angle between tangent to the curve $\gamma(t)= t^3i+2tj+t^3k$ at $t=\pm 1 $ Here $\gamma(t)= (t^3 ,2t ,t^3)$ $\gamma'(t)= (3t^2 ,2 ,3t^2)$ so, $\gamma'(\pm 1)= (3 ,2 ,3)$ now they give ...
1
vote
1answer
34 views

Hyperplanes divide space

Problem. What is maximal number of connected components on which $n$ hyperplanes divides $\mathbb{R}^m$ if they all have 1 common point. In fact this problem was firstly stated in $\mathbb{R}^3$ and ...
1
vote
1answer
32 views

Average distance between two random points in a square

A square with side $a$ is given. What is the average distance between two uniformly-distributed random points inside the square? For more general rectangle case, see here. The proof found there is ...
-1
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0answers
14 views

Construct a triangle when a, r, and ex radius opposite to A is given. [on hold]

I tried to solve this sum but I just could not solve it.
0
votes
1answer
23 views

Is it possible to create a parabola by intersecting a hyperboloid of one sheet and a plane?

By which I mean, is there anyway that the intersetion of a plane and a hyperboloid of one sheet will be a parabola? I know that intersecting a plane and a cone so that the plane is parallel to the ...
2
votes
1answer
25 views

How to calculate the volume of a skip bin container knowing the height of the material inside

I need to know hot to calculate the volume of a skip bin (also known as a skip container or dumpster in some areas) with varying length and width. It seems like a isosceles trapezoid when you look at ...
-1
votes
0answers
12 views

Geometery finding measures of inscribed angles [on hold]

I recently flunked a geo quiz and i need to make corrections and i cant figure out even after reviewing my notes for hours. Please help
1
vote
1answer
28 views

$K$ is a region in $\mathbb{R}^2$ where the area is $5$

Say that $K$ is a region in $\mathbb{R}^2$ where the area is $5$. Let B = \begin{pmatrix} 3 & 8 \\ 4 & 6 \end{pmatrix} Find the area of the region B$K$. Any starting hints? Is it possible ...
7
votes
0answers
19 views

Reference Request: Complete Proof of Braikenridge–Maclaurin Theorem

Where can I find a reference to a complete proof of the Braikenridge–Maclaurin theorem, which is stated as: If the three pairs of opposite sides of (an irregular) hexagon meet at three collinear ...
1
vote
1answer
22 views

How to parametrize circles on a sphere by the distortion of the equator?

I guess am having a very silly problem right now. Considering a unit sphere $S^2$ and, for example, a curve, in spherical coordinates, $c(t)=(1, \frac{\pi}{2},t)$ that goes around the equator how can ...
2
votes
1answer
37 views

Interpretation of median length for an invalid triangle

Background: My very first and naive take on the Project Euler problem 513 went wrong, as I counted also triples violating the triangle inequality. Many formulas return an invalid result for an ...
1
vote
1answer
31 views

Proof of Compound Angle from Ptolemy's Theorem

I have a query regarding a proof I'm reading on the additive Sine compound angle formula, which uses Ptolemy's theorem. http://www.cut-the-knot.org/proofs/sine_cosine.shtml I'm looking at the ...
3
votes
5answers
227 views

Technique for proving four points to be concyclic

While making my way through an exercise, I stalled on question 7: 7. Prove that the points $(9, 6)$, $(4, -4)$, $(1, -2)$, $(0, 0)$ are concyclic. The book does not provide any guidance on how ...
2
votes
3answers
28 views

Find all line equations that are tangent to $x^3 - x$ and pass through $(-2,2)$

So I have the equation: $f(x) = x^3 - x$ So we know that the slope of the curve for some $x$ is given by: $f'(x) = 3x^2 - 1$ And need to find equations of lines that are tangent to that curve, ...
17
votes
1answer
432 views

Can I represent groups geometrically?

I have just taken up abstract algebra for my college and my professor was giving me an introduction to groups, but since I like geometric definitions or ways of looking at stuff, I kept thinking, "How ...
0
votes
0answers
23 views

Geometric solution for $\frac{1-R}{| 1 - R e^{j\theta} |} = k$

Given: $\frac{1-R}{| 1 - R e^{j\theta} |} = k$ How to solve for R? (Suppose R is the only unknown quantity -- the task is to rearrange with R as subject). I encountered this problem in an academic ...
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votes
0answers
50 views

Mathematics doubt. [on hold]

What is mathematics. I need a proper definition mathematics.
0
votes
0answers
20 views

Specific polygons in \R^{3} [on hold]

Find all (convex) polyhedra P in $\mathbb{R}^{3}$ with following property: for every two vertices $v, u \in P$: $[u,v] \in \partial P$ . Here $[u, v] = \{w \; \vert \; w = tv + (1-t)u, \; t \in ...
3
votes
1answer
65 views

Projective line intersecting 3 projective subspaces

I am trying to solve the following problem: Let $\mathbb{P}(U),$ $\mathbb{P}(V)$ and $\mathbb{P}(W)$ be projective subspaces of dimension $k,$ $l$ and $m$ respectively in $\mathbb{P}_K^n$. Suppose ...
0
votes
2answers
30 views

AMC: Triangle area problem

In rectangle ABCD below, points F and G lie on segment AB such that AF = FG = GB and E is the midpoint of segment DC. Also, segment AC intersects segment EF at H and segment EG at J. The area of ...
-3
votes
2answers
28 views

How find the length of the third of the chord for of a circle of radius r? [on hold]

Three chord of a circle of radius $r$ are the sides of the triangle inscribed in the circle. Two of these chords have a length $\frac{r}{2}$ and $r\sqrt{3}$. How find the length of the third of the ...
2
votes
0answers
8 views

Identify the combination formed by first applying the glide reflection $γ_{A,B}$ and then applying $γ_{C,D}$

Question: Identify the combination formed by first applying the glide reflection $γ_{A,B}$ and then applying $γ_{C,D}$ where $A = (0, 0), B = (2, 0), C = (1, −2), D = (1, 0)$. Before, I jump in ...
1
vote
2answers
49 views

Surface area of a section of the unit sphere

Let $v$ be a vector on the unit sphere in $\mathbb{R}^n$ and let $S(\epsilon)$ be the set of vectors $s$ on the same sphere such that $$ |s \cdot v| \leq \epsilon.$$ What is the surface area of ...
14
votes
7answers
1k views

Can someone explain 4th dimensional objects?

I'm not sure if I should ask this in mathematics or in physics. From what I can tell, there are only 3 dimensions: X, Y, and Z. However, I have seen a lot of things about fourth and even fifth ...
3
votes
1answer
49 views

Tangent lines of a smooth curve $C \subseteq \mathbb{P}^2$

Let $C$ be a smooth curve, given as the zero locus of a homogeneous polynomial $f \in \mathbb{K}[x_0,x_1,x_2]$. Consider the morphism $\varphi_C:C\rightarrow\mathbb{P}^2$ such that ...
0
votes
0answers
9 views

Finding closest rectangle to another using concept of closest edge [on hold]

I know coordinates and size of rectangles. My goal is to find 'the closest' rectangle to one special rectangle using the concept of closest edge and also to find distance between them??
0
votes
1answer
10 views

A question on the requirement of a quadrilateral being an adventitious quadrangle

There is a special type of problem called Langley’s Adventitious Angles. See http://en.wikipedia.org/wiki/Langley%E2%80%99s_Adventitious_Angles The problem was solved and has the following ...
1
vote
3answers
32 views

Calculating last two angles of a quadrilateral when two angles and (relative) side lengths are known.

I've recently run into a problem that I can't seem to get. Given a quadrilateral, $ABCD$, with angle $D$ equaling 54 deg, and with the length of $BC$ equaling $CD$ while being double the length of ...
-3
votes
0answers
19 views

Find out the vertices of a regular polygon, given one side and number of sides [on hold]

We are given: 1)one side of the regular polygon , $ (x_1,y_1) $ and $ (x_2,y_2) $ 2)number of sides of the polygon 3)construct the polygon in counterclockwise direction And are asked to find all ...