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

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-5
votes
1answer
63 views

Can anyone tell me how to factor this expression? [on hold]

...$\dfrac{2x^2-4x}{x+10}$ this is in response to a side splitting theorem question where these values are part of the proportions. Here is the complete question: We have 2 similar right triangles. ...
-2
votes
1answer
28 views

Proof involving circumradius of triangle and Law of Sines

Show that in any triangle, we have $ \frac{a\sin A+b\sin B+c\sin C}{a\cos A+b\cos B+c\cos C}=R\left(\frac{a^2+b^2+c^2}{abc}\right), $ where $R$ is the circumradius of the triangle. I'm not quite ...
1
vote
0answers
11 views

What is the solid angle of the intersection loop between a cone and an off-axis sphere?

An upright (green) cone with opening angle $2a < \pi/10$ has its vertex at point O with cartesian xyz coordinates $(0,0,0)$. The cone axis (dotted line) lies in the plane $y=0$ and is parallel to ...
0
votes
0answers
18 views

Show that the midpoint of $AB$, $AC$, and $DE$ are aligned.

Let $ABC$ be a rod, $D$ and $E$ two points such as: $\vec{EC} = k \cdot \vec{EA} / \vec{DA} = k \cdot\vec{DB}$. How can I show that the midpoint of $AB$, $AC$, and $DE$ are aligned?
0
votes
1answer
14 views

isoperimetric inequalities in permutohedron

Consider the graph whose vertices are all n! permutations of numbers 1..n and there is an edge between two vertices iff we can get from one to another by an adjacent transposition. We call this graph ...
3
votes
1answer
36 views

Rectangle circumscribed to an ellipse of max area/perimeter

I could solve the classical problem of maximizing the area (fixing the perimeter) or maximizing the perimeter (fixing the area) of an inscribed rectangle, but I don't know how to solve ...
2
votes
0answers
22 views

Jacobi Elliptic Functions Special Case

I have spent some time analysing the pendulum problem, and hence the Jacobi elliptic functions recently, and have come across what seems to me to be a slight inconsitency. I define my $am(t|k)$ as the ...
-2
votes
0answers
20 views

hollow sphere problem [on hold]

A hollow space on earth surface is to be filled. Total cost of filling is 20000 Rupees. The cost of filling per mt3 is 225 Ruppes. How many times a size of 3 mt3 soil is required to fill the hollow ...
0
votes
1answer
27 views

Fattest scalene quadrilateral

What angles of a plane scalene quadrilateral maximize its area? By 'scalene' I mean the four lengths are unequal. It is known that if a quadrilateral has opposite sides equal and parallel as a ...
0
votes
0answers
24 views

Geometrical interpretation of an overidentified linear system

In my econometrics class we talked about Instrumental Variables. Suppose one has a $n\times k$ matrix $X$ of regressors and a $n\times m$ matrix $Z$ of instrumental variables. Given the matrices are ...
1
vote
1answer
32 views

Find part of segment between two circle centers

I drew the following image to help me explaining the question: Having two circles Source and Target, I want to build an arrow like in the image. The Source has coordinates $Source(sx, sy)$ and ...
-6
votes
0answers
41 views

An Interesting Areas Question [on hold]

Let the area of the triangle $ABC$ be $x$. The points $A_1$, $B_1$ and $C_1$ are the mid points of the sides $BC$, $CA$, and $AB$ respectively. The point $A_2$ is the mid point of $CA_1$. Lines ...
2
votes
1answer
55 views

Surface normal to point on displaced sphere

I want to calculate the surface normal to a point on a deformed sphere. The surface of the sphere is displaced along its (original) normals by a function $f(\vec x)$. In mathematical terms: Let ...
0
votes
1answer
32 views

Ratio of squares touching edge of circle?

Consider an infinite amount of squares stacked on top of each other where the top left corners are touching the edge of a circle: Call the largest blue square x. How would I find the ratio of ...
1
vote
2answers
28 views

Construct a midpoint of two parallel lines with only straightedge

Say I have a large plank of wood that I'm trying to cut in half the long way, but I only have a straightedge (no compass). How can I mark the midpoint between the long edges? (As a note, this isn't a ...
2
votes
1answer
43 views

Finding the radius of a third tangent circle

Sorry if this is a foolish question, but I'm having difficulty understanding how to solve for $r_3$ in the following diagram... According to WolframAlpha's page on tangent circles, the radius of ...
3
votes
1answer
42 views

Inequality between area and boundary length, $4\pi A \leq L^2 $

Suppose we have a simply connected region $R$ in $\mathbb{R}^2$ with area $A$ and the boundary of $R$ is a curve sufficiently well behaved (say piecewise $C^1$) that we can say it has length $L$. Then ...
0
votes
1answer
20 views

The vertical projection of a chord of a circle?

I was wondering if anyone could help me with the problem below (finding x): So we are given t_i (the initial tangent angle to the circle), t_o (the exiting angle of the tangent of the circle), the ...
2
votes
0answers
30 views

Creating an ellipsoidal 3D surface

I am trying to find the equation of a 3D ellipsoidal surface. I have thought of two approaches which are schematically shown below: By revolving an elliptical arc over a 3D elliptical path: Or by ...
0
votes
0answers
19 views

Projection of a Triangle into a Tetrahedron

I was referring to a paper to implement an algorithm in which one of the step was to project the triangle into the ...
2
votes
1answer
65 views

Compute the area of a parallelogram defined by a particular construction

I got stuck with this mathematical task. Can someone help me how to solve this problem? I need to find the F(area) value. It is kind of a thinking task Context The problem is extracted from a ...
1
vote
1answer
26 views

Geometrical calculation to determine size difference between two rectangles when rotating one

I've asked a programming question on StackOverflow here which should give you a good understanding why I'm trying to do this. I'm asking it here because it's now down entirely to the mathematics of ...
2
votes
1answer
42 views

Requiring a Geometrical proof

In the figure, ABCD is a square circumscribing a circle ($\pi_1$) whose center is E, the point of intersection of the diagonals AC and BD. With A as center, AB as radius, sector ABD is drawn cutting ...
3
votes
1answer
36 views

Triangulation of hypercubes into simplices

A square can be divided into two triangles. A 3-dimensional cube can be divided into 6 tetrahedrons. Into what number of simplices an n-dimensional hypercube can be divided? (For example, a ...
0
votes
1answer
42 views

Do two altitudes uniquely determine the third

BdMO 2014 Nationals If the lengths of two altitudes drawn from two vertices of a triangle on their opposite sides are $2014$ and $1$ unit, then what will be the length of the altitude drawn from ...
0
votes
1answer
27 views

Find other coordinates on a rectangle given 1 side length and 2 opposite points

I have two problems I'm hoping to solve with one equation for a game. This game uses a square for its key (rotates) but I'd prefer to treat it as a rectangle instead. I want to find the coordinates so ...
0
votes
0answers
11 views

Is the dual curve ofa dual curve guaranteed to be of the same degree as the original curve?

I understand that I can take a curve, and I can draw tangents to every point, and somehow (I don't understand how) I can pick another plane and where all those tangents hit that plane (see below for ...
0
votes
1answer
19 views

rotate a time series with constraints for start and end

I have a time ordered series of data that I can represent in R like: ...
0
votes
2answers
49 views

Self-Learning Geometry

I'm an undergraduate senior wondering where he should start in learning geometry. My university unfortunately offers no such course. Should i begin with riemann geometry or differential geometry and ...
0
votes
3answers
60 views

Problem of axiomatic euclidean geometry

Let the usual five postulates of Euclid been given. Let's take also this postulate: "If two points lies on the same plane, the whole straight line joining the two points lies on that plane". Is it ...
0
votes
2answers
27 views

Describe geometrically the set of solutions to the following equations in 3-space

Given $a, b \in \mathbb{R}^3$ and $\lambda \in \mathbb{R}$ I'm looking to describe, geometrically, the set of all $x \in \mathbb{R}^3$ satisfying both equations $a\cdot x = \lambda$ $a \times x = b$ ...
2
votes
1answer
52 views

What do you call 'perpendicular but skew' lines?

For example, the seat tube and rear axle of a bicycle or motorcycle. That is, when viewed from above, the seat tube would appear 'perpendicular' to the rear axle. But in 3d reality, the lines are ...
-9
votes
0answers
52 views

Find equation for circle given center and radius [on hold]

whats the equation of a circle that's center is -3,1 and radius is 3
-4
votes
3answers
49 views

Find the equation of the circle passing through points - (5,7),(8,1) , and (1,3). [on hold]

Find the equation of the circle passing through points (5,7),(8,1), and (1,3). I need to use these general formula of circle. Please help me to solve this Now i got g=3/2 and f=-19/2
0
votes
1answer
20 views

Finding the minimum value of squares of sides of a quadrilateral

What is the minimum value of $\frac{a^2+b^2+c^2}{d^2}$ where $a,b,c,d$ are the sides of quadrilateral I assumed the diagonals to be $p$ and $q$. I got that for minimum angle $A$ and $C$ must be ...
0
votes
2answers
43 views

Finding whether the quadrilateral is cyclic or not

Is a quadrilateral with sides lengths $3$, $3$, $4$, and $4$ cyclic? Progress I found that sides joining 3 and 4 are of equal length. then I found that other diagonal should also have same length ...
1
vote
2answers
32 views

Length of a right triangle created by skewing a rectangle's edge by a fixed amount

I have the above problem for a grid-based graphics system I'm working on, and I'm not sure if the math is solvable or not. I'm trying to determine the value of $A$. I've attempted to use ...
2
votes
1answer
34 views

Number of samples needed to get a given expected distance

Suppose I have a surface in $\mathbb{R}^3$ with surface area $A$. How many points do I need to (uniformly at random) sample so that the expected distance from each point to its nearest neighbor is ...
1
vote
2answers
23 views

How does one measure angles in minutes and seconds?

I've searched for an answer on Google, and I really do not understand it at all. Can someone please explain it to me in the simplest terms possible?
3
votes
1answer
25 views

Splitting a vector into two axis aligned vectors

I'm not familiar with mathematical terms, so I'll try my best to explain this issue. Also, I don't know if this is a programming question or a mathematical one. I guess both... I'm making a 2D ...
1
vote
2answers
29 views

area under a curve and units

If we introduce a unit of length like meter for $x$ and integrate the function $f(x)=x^2$ from $0$ to $2m$ we get $\dfrac{8}{3} m^3$. How can this be interpreted geometrically? My initial thought was ...
0
votes
0answers
27 views

For which values of $n$ does $x^n+y^n=i$ has a zeros in $\mathbb{R}$? [on hold]

$ x $ and $y$ are real numbers and $i$ : is unit imaginary part . 1-for which values of $n$ does $x^n+y^n=i$ has a zeros in $\mathbb{R}$ ? 2-what are the possible geometrics forms of $x^n+y^n=i$ ...
0
votes
2answers
38 views

Sine on a Circle

I'm walking a quarter mile circular walking track. The width of the track is 8 feet across. If I walk from one side of the track to the other, walking a sine wave that has a 20 foot period, how much ...
2
votes
2answers
33 views

Solids of revolution, how come we use the inverse function when we use method of cylindrical shells?

Doing my second course in college calculus, and we are doing integrals and volumes by slicing/solids of revolution. The question I had trouble with was: "Find the volume of a solid $S$, using the ...
2
votes
1answer
34 views

Find a 12-gon and 33-gon that tessellate the plane

Not sure how to approach this. I think both figures have to be non convex in order for this to occur. I created a 12-gon using four house pentagons and it tessellates but I'm lost with the 33-gon. ...
1
vote
0answers
43 views

Pentagon Forms a 10-sided Polygon Ratio Problem

Let $A_1A_2A_3A_4A_5$ be a regular pentagon with side length $1$. The sides of the pentagon are extended to form the $10$-sided polygon shown in bold in the picture that I have attached. Find the ...
2
votes
1answer
20 views

Point in a rectangle

$ABCD$ is a rectangle and $P$ is a point in the same plane. If the perpendicular through $C$ to $AP$ and the perpendicular through $B$ to $DP$ intersect at $Q$, prove that $PQ \parallel AD$. ...
0
votes
1answer
64 views

Finding the value of k

If $x,y,z$ are perpendicular distances from circumcenter on the sides $BC,AC$ and $AB$ respectively. In need find $k$ such that $$\frac ax+\frac by+\frac cz=\frac{abc}{kxyz}$$ (Lowercase letters ...
2
votes
1answer
36 views

Finding the third side of a triangle, given ratio of two sides and difference of two angles [on hold]

Given $a=2b$ and $|\angle A-\angle B|=60$ degrees. Find the third side, where lowercase letters denote opposite sides and uppercase letter angles. Progress I could find the $\cos C$ but then ...
2
votes
1answer
32 views

Properties of the simplest object in n-dimension

In my boredom, I was thinking about why the simplest 3d object (i.e. the one with the least faces, sides, vertices) was the tetrahedron. After it made sense to me, I realized some cool stuff which was ...