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
3answers
121 views

Explain branches of geometry for non-mathematician

Some background - I'm an advanced physics undergrad and lately was motivated to self study basic contemporary geometry to get a better grip on general relativity (maybe there is a more appropriate ...
0
votes
1answer
55 views

Area of the figure within the circle and outside a polygon

For which values of the parameter $c \in \mathbb{R}$, the area $S$ of the figure $F$, consisting of the points $(x,y)$ such that $$\begin{gathered} \max \{ \left| x \right|,y\} \geqslant 2c \hfill ...
2
votes
1answer
45 views

Conversion between coordinate systems

I am trying to convert between two coordinate systems and think I've come up with the answer but would like to make sure my assumptions are correct and to help with some of the math. The problem is ...
3
votes
1answer
70 views

Why can't the nth triangular number be expressed as the area of an equilateral triangle?

It should be self-intuitive that the $nth$ triangular number is an equilateral triangle with base $n$, and thus its area should equal the value of the triangular number. So, I was wondering: why ...
1
vote
1answer
54 views

How to know which side of the right angled triangle is the base?

If we are given a right angled triangle without any angle or length of any side. How we will find that which side is the base, which side is the perpendicular.
1
vote
2answers
80 views

Extension of Descartes' “Kissing Circles” Theorem

Descartes' "Kissing Circle" Theorem relates the radii, $r_1$, $r_2$, $r_3$, $r_4$, of four mutually-tangent circles thusly: $$( k_1 + k_2 + k_3 + k_4 )^2 = 2 ( k_1^2 + k_2^2 + k_3^2 + k_4^2 ) ...
0
votes
0answers
15 views

Subset of Jordan set of positive lebesgue measure

let $T \subset \mathbb{R}^d$. Given on $T$, a Jordan set of positive Lebesgue measure, $l(T)>0$ . Let a set $M \subset T$; with $l(M)=0$. Please explain what is special about the set M. Has it got ...
0
votes
2answers
35 views

Triangle and Ratio : Find the length of a side.

Let $\theta = \angle CAD, \phi = \angle CDB, \varphi=\angle DBC, \alpha = \angle BCD$ and $\beta=\angle ACD$. Then we have the following system of equations $\theta + \varphi = 90^{\circ},$ ...
1
vote
2answers
37 views

Why does the equation of a circle have to have the same $x^2,y^2$ coefficients?

In one of my geometry texts, it tells me they should be the same but not why. I am unsatisfied with this. Suppose that: $$ax^2+by^2 + cx + dy + f = 0 \text{ such that } a \neq b$$ is the equation ...
-3
votes
1answer
44 views

How to prove for any point $P$ inside an equilateral triangle $ABC$, $PA+PB > PC$ [closed]

Prove that, for any point $P$ inside an equilateral triangle $ABC$ , $PA+PB \gt PC$.
2
votes
2answers
58 views

Trying to understand the limit of regular polygons: circle vs apeirogon (vs infinigon?)

In the definition of regular polygon at the Wikipedia, there is this statement about the limit of a n-gon: "In the limit, a sequence of regular polygons with an increasing number of sides becomes ...
0
votes
0answers
22 views

Suppose from the point P (m,n) two tangents PQ & PR are drawn to the points Q & R on the circle [x^2+y^2=a^2].Then find area of triangle PQR .

Suppose from the point $P = (m,n)$ two tangents $PQ$ and $PR$ are drawn to the points $Q$ and $R$ on the circle $x^2+y^2=a^2$. Find area of $\triangle PQR$. The information related to this ...
2
votes
0answers
21 views

can't figure out multilateration with xyz positions of each post and difference in time

I'm having some real issues figuring out multilateration. I'll start by saying I'm not a math whiz, but I am usually able to figure most things out, but this one has been throwing me through a loop ...
1
vote
1answer
70 views

One Square and one straight line(pipe) [closed]

Edited: A farmer has a farm.The farm is a square whose sides have length 1. A single straight water pipe passes somewhere under the farm with depth one meter. He wants to dig furrows to find the ...
1
vote
0answers
27 views

A question about possible differences between plane and spherical geometry

Are the theorems about Brocard points and the Brocard angle of plane triangles also true for spherical triangles?
0
votes
0answers
23 views

How many grams of coating is being yield per volume width?

The cylinder is 8.00 inches in diameter and 4.940 inches in width. 1.500 inches in width has a volume of 15. 3.440 inches in width has a volume of 12. The total grams of coating yield from the both ...
1
vote
0answers
36 views

How much heigth can a roll of pipe insulation cover?

I'm getting a bit confused on calculating how much insulation I need to buy. Here are the specs of the insulation: Dimensions: $1.5''\times 24''\times 25'$ Packaging: $50$ square feet per roll The ...
1
vote
0answers
53 views

Difference between exponential maps composed with parallel transport along two different geodesics?

Let $(M,g)$ be a Riemannian manifold, and let $\gamma_{p,v}, \gamma_{p,w}$ be two geodesics starting from $p$ with directions/initial vectors $v,w$ respectively. Consider the two operations (to be ...
1
vote
1answer
30 views

Help to Prove Convex Quadrilateral Problem

I'd appreciate help with solving this convex quadrilateral riddle. It appears to hold true in all of my test cases, but I'm not sure how I would go about writing a proof for it. Let $UVWX$ be a ...
0
votes
0answers
12 views

Using multilateration with weighted nodes in determining location

I'm using multilateration to determine the coordinates of a point, given distance estimates to $n$ fixed anchors (or nodes). Since distance values are only estimates, I'm actually calculating the best ...
0
votes
1answer
22 views

Calculate Volume m3?

I'm attempting to calculate the value that is m3 but i don't know how the person got these values. The first row first column is 22mm(width) x 100mm(height) .. then the bold in the second column is ...
3
votes
2answers
38 views

How is a vertex of a triangle moving while another vertex is moving on its angle bisector?

While trying to solve this problem the following conjecture came to my mind. Based on the statement conjectured I could solve the problem mentioned. I am unable to verify the statement that I found ...
7
votes
2answers
173 views

Mapping sphere surface to a vector space such that distances are preserved?

I have a unit radius sphere (say in 3D) centered on the origin. Thus the shortest distance between two points on the sphere is the geodesic. Is there a transformation (linear or non-linear) on the ...
0
votes
0answers
16 views

The congruence of Two Spherical Triangles

I found in Wikipedea following claim : Two Spherical triangles with corresponding angles equal are congruent (i.e., all similar triangles are congruent). I know that the Area of Two triangles are ...
3
votes
2answers
51 views

Point inside a triangle

Let $\triangle ABC$ be an acute triangle and let $P$ be a point inside of it. $PD$, $PE$ and $PF$ are respectively parallel to sides $AC$, $BC$ and $AB$. Prove that ...
1
vote
2answers
33 views

GPS-position in room

Given are GPS-positions (WGS84) "Point 1" and "Point 2". I need to find out wether a person (I know the GPS-position of the person) is standing outside of one of the virtual walls A, B and C and on ...
-1
votes
3answers
30 views

Obtaining the four corner coordinates of a square from the center point.

I'm trying to get the corner coordinates of a Square (NOTE, always a square) problematically. (EX: With a formula) and I'm having a hard time adding this into my computer application. Here's an ...
6
votes
1answer
50 views

How many triangles exist whose angles are rational and side lengths are roots to quadratic equations?

By "rational angles" I mean a rational degree measure (equivalently, angle a rational multiple of $\pi$). Obviously similar triangles should be counted once. Off the top of my head we have: 30-60-90, ...
2
votes
4answers
101 views

What is the direction along the edge of a circle called (in English and by chance German)?

Note: I am actually also searching for the term in German. That is why I posted this here (as opposed to the language SE's), besides me looking for this term in a mathematical/technical context. ...
-1
votes
0answers
26 views

Projected axes of an ellipsoid

Let's consider a 3D ellipsoid, with semi-axis a, b, c and let's project it along a random line of sight. Several papers in the literature (e.g. ...
1
vote
1answer
19 views

Fracturing of a 3D Object

Although this is a computer science applied subject, all the underlying logic is mathematical and geometric. I am trying to write code that will enable me to split an object into random fragments, ...
3
votes
5answers
51 views

If you know the slope of a line and the angle between them, can you find the slope of the second line?

The two lines intersect at (1,4) and the slope of the first line is 3/5. The second line makes a 45 degree angle with the first clockwise so that the second lines slope must be less but I don't know ...
1
vote
1answer
51 views

Mapping the intersection of hyperplanes/simplex to lower-dimensional unit-simplex

Suppose I have an object in $\mathbb{R}^5$ described by: $$x_1+x_2+x_3+x_4+x_5=1$$ $$x_1+2x_2+3x_3+4x_4+5x_5=6$$ $$x_1+7x_2+8x_3+9x_4+10x_5=11$$ $$x_1,x_2,x_3,x_4,x_5 \geq 0$$ Is there a way that I ...
-1
votes
2answers
23 views

Length of any of the diagonals of a rhombus of given side and a given angle

Suppose, the values of any one of the angles and the side of a rhombus are given. How to find the length of any of the diagonals?
1
vote
1answer
29 views

Find the end points of a line segment in 3D space

I have a line segment in 3 dimensional space (x,y,z), and I want to find the 2 endpoints of this line segment. Is there a systematic way of doing this? To be specific, I have the line described by ...
1
vote
1answer
48 views

Constructible real numbers

I'm trying to understand constructible numbers. I know that a real number $r$ is constructible if it can be calculated from 0 and 1 by a finite number of additions, subtractions, multiplications, ...
5
votes
0answers
36 views

Proof of the Inscribed Angle Theorem

I want to give a proof of the Inscribed Angle Theorem by using the Laguerre formula. Let $C$ denote the circle. Take three different points $A,B$ and $P$ on $C$. Write $a := \overline{AP}$ and $b:= ...
-1
votes
0answers
18 views

Two variable quadtraic polynomials geometric representation?

We have learned about quadratic polynomials having two variables but I ran into the question of do all of these type of polynomials have empty sets? So... Given a quadratic polynomial in two ...
2
votes
0answers
26 views

The heat equation shrinking convex plane curves

In the article "The heat equation shrinking convex plane curves" by M. Gage and R. S. Hamilton, I didn't understand the following theorem: ...
1
vote
0answers
37 views

The curvature blows up

A curve evolves according to the evolution equation $\displaystyle\frac{\partial X}{\partial t}= k \times N$ where $k$ is the curvature of the curve and $N$ is the inward unit normal vector. Then ...
12
votes
1answer
80 views

Uniqueness of a configuration of $7$ points in $\Bbb R^2$ such that, given any $3$, $2$ of them are $1$ unit apart

This question from earlier today asks (paraphrasing here): Is there a configuration of $7$ points in the Euclidean plane such that, given any $3$ of the $7$ points, at least $2$ of them are $1$ ...
1
vote
1answer
32 views

Geometric Interpretation of a function

Look at the following functions: $$l(x)=x/\sqrt{1+x^2}$$ $$k(x)=x/\sqrt{1-x^2}$$ These functions give a homeomorphism between $\mathbb{R}$ and $(-1,1)$. Can someone give a geometric interpretation of ...
3
votes
2answers
81 views

Curvature flow for convex planes curves

Tentative translation of the original question. I've read several articles on the curvature flow for convex plane curves (the curve remains convex during evolution, and eventually shrinks to a point). ...
0
votes
2answers
52 views

Find the area of a triangle whose vertices cut the sides of $ABC$ in thirds [closed]

I have to find the area of $F$, given the following configuration: $\hspace1in$ What to do?
3
votes
2answers
89 views

Seven points in the plane such that, among any three, two are a distance $1$ apart

Is there a set of seven points in the plane such that, among any three of these points, there are two, $P, R$, which are distance $1$ apart?
1
vote
1answer
30 views

Given a circle, its diameter and an external point, use a straightedge to draw a line through the point and perpendicular to the diameter

Some time back I saw the following problem which originated in Russia: You are given a circle, its diameter and an external point not on the diameter (A, B and P in the diagram below). Using only ...
1
vote
2answers
34 views

Existence of Linear Transformation between 3D line and 2D line

I am wondering if there exists an invertible linear transformation between a line segment in 3D space and a line segment in 2D space. Basically, the red line above could be represented by the ...
2
votes
0answers
29 views

Calculating truncated cone taper angle from a projected image

I am imagining a truncated cone with taper angle $\phi$, shown in the left of the figure. I view the truncated cone inclined at some angle $\alpha$ from its axis. If $\alpha$ is large enough, I will ...
1
vote
3answers
46 views

How to find the side of this Parallelogram? [closed]

Here, AB=10 cm and altitudes corresponding to the sides AB and AD are 6cm and 8cm respectively. How can I find AD ? Or data is inadequate?
6
votes
2answers
56 views

Subsets of a set of points that can lie in the same sphere

Suppose I have a finite set $\mathcal{P} := \{x_1, x_2, \ldots , x_n\} \subset \mathbb{R}^d$. Is there any way to characterize the couples $(x_i, x_j)$ such that there exists a ball $B$ with $x_i, ...