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

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-6
votes
2answers
50 views

Ayn Rand and mathematics

Am an honors undergraduate in mathematics . I take intrest in objectivism. I came across a discovery of Ms.Ayn Rands in mathematics, "In a triangle the inscribed circle touches the circle that passes ...
0
votes
0answers
8 views

Finding grid nodes a line passes through

For 2D grid pathfinding, I want to do a quick broadphase to check if there is a direct path from the start to the target by conceptually checking all nodes touching the line segment formed by ...
12
votes
0answers
60 views

Is Tolkien's Middle Earth flat?

In the first introductory chapter of his book Gravitation and cosmology: principles and applications of the general theory of relativity Steven Weinberg discusses the origin of non-euclidean ...
11
votes
3answers
109 views

Product of Cosines: $ \prod_{r=1}^{7} \cos \frac{r\pi}{15} $

Evaluate $$ \prod_{r=1}^{7} \cos {\dfrac{r\pi}{15}} $$ I tried trigonometric identities of product of cosines, i.e, $$\cos\text{A}\cdot\cos\text{B} = \dfrac{1}{2}[ \cos(A+B)+\cos(A-B)] ...
2
votes
1answer
11 views

Local existence of parallel vector field

Let $M$ be a Riemannian manifold, $p\in M$ be a point in the manifold, and $\xi\in T_p M$ be a vector in its tangent space. I am wondering whether, for some small neighborhood $U\subset M$, it is ...
0
votes
0answers
12 views

How to trace the path of a moving point in geogebra

I created a simple animation in geogebra, two intersecting lines rotating around fixed points. I want to trace the paths of the vertex points of these lines. I mean is there a way when the animation ...
0
votes
2answers
18 views

Algorithm for intersection of n circles with approximate values

I'm trying to come up with a sort of trilateration algorithm that, given n >= 3 circles, finds the point of intersection. The radii come from samplings of electromagnetic magnitudes, therefore there ...
5
votes
3answers
68 views

Circles revolving around each other and infinities

I just watched this video, and I'm a bit perplexed. Problem: ...
-1
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1answer
15 views

Area of a quarter circle C1 equals the area of an inner circle C2 where C2.diameter = C1.radius

Say we have a circle C1 with radius 2. Inside of that we draw circle C2 going from the centre point of C1 to the perimeter of C1 (making it diameter = 2) ...
0
votes
1answer
33 views

compact image of a continuous function from compact set to C

Suppose that we have a continuous function $h:[0,1] \times [a,b] \to G$, where $G$ is an open subset of $\mathbb C$. Prove that we can partition $[0,1]$ and $[a,b]$ to $\{x_0, x_1, \ldots, x_n\}$ ...
2
votes
1answer
33 views

Diameter of a 10-ball in a 10-box is larger than the side length of box?

I came across this idea in a lecture on elementary topology. While it makes sense algebraically, I'm hoping someone could shed some light on the way this is possible. So you begin with a square of ...
1
vote
1answer
18 views

What's the name given to the ratio $P^2/A$ for a closed figure in the Euclidean plane?

Let $\mathscr{F}$ be the set of all plane, closed Euclidean figures having positive perimeter, and let $\sim$ be the similarity relation on $\mathscr{F}$. Then, for any equivalence class ...
3
votes
1answer
51 views

Area of the shaded part in rectangle

The question asks you to determine the shaded part of the rectangle in terms of x. please will someone help with this problem, i have spent a while on it with not much progress.
1
vote
1answer
23 views

Get the Equation of a Plane from a Vertex and 2 Angles?

What is the simplest way to algebraically get the equation of a Plane (ax + by + cz = d), if you only have 1 point on the plane, and 2 angles (horizontal and vertical) which define the direction the ...
2
votes
5answers
122 views

Looking for elementary proof of “for a circle, $C^2/A = 4 \pi$”

If $C$ and $A$ are the circumference and area of a circle, then $$ \frac{C^2}{A}=4 \pi\; . $$ I'm looking for a reference to an elementary but rigorous proof of it. I'm particularly interested in ...
4
votes
2answers
81 views

Show that in any triangle, we have $\frac{a\sin A+b\sin B+c\sin C}{a\cos A+b\cos B+c\cos C}=R\left(\frac{a^2+b^2+c^2}{abc}\right),$

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. Here is my work: ...
0
votes
1answer
26 views

Transformation of axes by rotation

How can I intutively understand the formula for getting new coordinate of point P after rotation of axes which was P(x,y) with respect to the old axes?
1
vote
1answer
19 views

Arcs and surfaces. Why are there finitely many arcs on the surface up to the action of MCG?

Given a bordered surface $S$ (I imagine this is true for non-orientable surfaces too, but you may restrict to the case of orientable surfaces) with finitely many marked points on each boundary ...
-1
votes
1answer
29 views

Parabola problem [on hold]

Water squirting out of a horizontal nozzle held $4$ ft above the ground describes a parabolic curve with the vertex at the nozzle. If the stream of water drops $1$ ft in the first $10$ ft of ...
1
vote
0answers
20 views

About Homothetic transformation

I have one question regarding the way which a homothetic transformatior is written. Why is it written in the following way: $$\vec{OH^{k}_{O}(P)}=k\vec{OP}+(1-k)\vec{OO}?$$ From where ...
1
vote
1answer
22 views

logarithmic spiral around cone stump

Based on the answer on my previous question I managed to come up with the following equations: $$\begin{eqnarray} k &=& 1 \\ r_\Delta &=& r_b - r_t \\ r(\theta) &=& r_t * ...
0
votes
0answers
16 views

How does the steepness of lines through a hyperboloid change the further away they are from the apex?

I'm a geoscientist and am trying to figure out how the steepness of the flanks of a hyperboloid change for straight lines that cross them. The line of reference is through the apex. Basically any ...
-5
votes
0answers
44 views

If I invent(in maths) something , Then I want to give it to world, what is process? [on hold]

If I invent(in maths) something , Then I want to give it to world, what is process?
0
votes
0answers
11 views

Determine when an object moving along a line crosses a constantly rotating ray

I'm trying to make a visual experiment akin to a radar, where there are 'ships' moving across lines in a $2$-dimensional space and in the center of that space is a ray extending outward, which ...
1
vote
1answer
29 views

How high above sea level do your eyes have to be to see a point that is 4.1 miles away “as the crow flies”?

There's a fireworks show going on tonight at a little town that's 4.1 miles away from my house, and I want to watch it from a hill near my house. So I thought I'd set up a simple geometry problem to ...
6
votes
1answer
50 views

$\frac{MA}{BC}+\frac{MB}{CA}+\frac{MC}{AB}\geq \sqrt{3}$

Given ∆$ABC$ and $M$ is an interior point.Prove that: $\dfrac{MA}{BC}+\dfrac{MB}{CA}+\dfrac{MC}{AB}\geq \sqrt{3}$ When does equality holds?
2
votes
1answer
39 views

Collision between moving circular discs

I am trying to figure out how to detect collision between two moving circular discs that move along a pretedermined path with a known speed. Example: Circular disk $A$ with radius $r1$ moves along ...
-1
votes
2answers
63 views

Six variables. System of equations.

$$ \begin{align} x & =\frac{R+\frac{G+B}{-2}}{R+G+B} \\[10pt] y & =\frac{\frac{(G-B) \sqrt{3}}{2}}{R+G+B} \\[10pt] z & =R+G+B \end{align} $$ How do I get the formula for ...
2
votes
1answer
54 views

inscribed circle in $n$-gon

If I'm given a circle with radius $r$ and I want to create a polygon with side $n$ (say $n=5$) which can cover the circle fully, then how to prove that a regular polygon is the solution with minimum ...
0
votes
0answers
27 views

Relation between farthest pair of points and closest pair of points in plane

I am writing program for obtaining distance between shortest and farthest pair of points among the given points in plane .I am able to calculate them both the shortest one using divide and conquer ...
2
votes
1answer
17 views

Find intersection of non-parallell planes without further assumption on their normals

Finding the intersection line between two planes is basic linear algebra but is it possible to find one formula, without having to dealing with different cases? Example: $$ \left\{ \begin{aligned} ...
1
vote
1answer
22 views

Checking whether points form a polygon in complex plane

If z^8=(z-1)^8 then the roots are 1) concyclic 2) form a polygonal 3)none I found the roots to be 1+cot(k.pi/8) for k is a natural number and less than 8. Then couldn't figure it out.
1
vote
0answers
214 views

Find radius of Circle

There is a circle C1 of Radius R1 and another circle C2 of radius R2 (R2 ≤ R1) such that it touches circle C1 internally There is another circle C3 with radius R3 such that it touches the circle C1 ...
1
vote
1answer
49 views

Area of overlapping squares

I'm working on a programming project and got to the point where I need to find how much is the blue square overlapping each of the other 9 squares. The squares' sides(including the blue one's) are ...
0
votes
0answers
13 views

Find intersection between conotur point list and a line

Given: List of points representing a closed contour Task: Choose a random point on the contour and shoot a ray inside the contour and determine where the ray intersects the contour. This needs to be ...
0
votes
1answer
23 views

What is the angle of b?

So first off, I know how to find the missing length of the leg of the triangle using the pythagorean theorem. $6^2 + b^2 = c^2$ $36 + b^2 = 100$ $100 - 36 = 64$ $\sqrt{64} = 8$. So angle angle ...
0
votes
0answers
21 views

Calculating the Major Axis of an Ellipse using its Circumference and Minor Axis

I am trying to calculate the value of the radius of the major axis of an ellipse, but am having a bit of trouble coming across the proper equation based on the data I have. I have values for the ...
2
votes
1answer
17 views

“Square,” line-preserving models of the hyperbolic plane

The Klein model of the hyperbolic plane is a line-preserving map from $H^2$ to the disk. Is there a model of the hyperbolic plane which is a line-preserving map from $H^2$ to $[0,1]^2$? By ...
1
vote
3answers
49 views

Length of a belt?

I know this is vague, but I am studying for a test. I remember the shape of the object, but not much else. Basically I have to find the length of a belt, when given the radius of a circle. The belt ...
0
votes
0answers
14 views

Outlining floorplan of a room given it's distance and image

Is it possible to draw an accurate room floor plan given: A camera on a tripod that is in the approximate center of a room. The camera takes 8 images for a 360 degree panoramic shot, each at shot is ...
0
votes
1answer
30 views

Why are compact complex manifolds Liouville?

I know this is true but strangely can't find references. Also, consider the trivial $n$-bundle over any connected compact manifold, does Liouville imply that all holomorphic sections are constant? ...
2
votes
2answers
40 views

Find the Ratio $BM \colon ME$

In Triangle $\Delta ABC$, the Point $D$ is on $BC$ such that $D$ divides $B$ and $C$ in the Ratio $1 \colon 3$ and there is a point $E$ on $CA$ such that $E$ divides $C$ and $A$ in ratio $1 \colon 3$. ...
2
votes
0answers
17 views

Question about the radius of the smallest enclosing disk containing $k$ points of a point-set

I am reading a book where in the middle of a lemma's proof the author assumes something without explaining the step. I am struggling to show why that is true. Consider a finite point set $P$ with ...
0
votes
1answer
24 views

Equation of the locus

Find the equation of the locus of a point $P = (x, y)$ when the sum of the squares of the distances from $P$ to the points $(a, 0)$ and $(-a, 0)$ is $4b^2$, where $b \geq \dfrac{a}{\sqrt{2}}$?
0
votes
2answers
40 views

Question about the existence of points and lines.

Say we draw a point on a graph. If the point should not take up any area than how come we could see it. Say we graph $y=x^2$, we obviously could see it. However, because $y=x^2$ is a function made up ...
-3
votes
1answer
45 views

Proving Ordering of Angles

I'm trying to prove $$\text {If}\ \angle P \lt \angle Q, \text & \ \angle Q \cong \angle R, \text{Then}\ \angle P \lt \angle R$$Which seems super basic and makes sense, but I got told that I'm ...
0
votes
1answer
32 views

alternative approach than center of mass?

For my bachelor thesis i am modelling the electric output of wind-power plants with the help of a multi agent based simulation. I have the information of all wind-power plants in my country (about ...
1
vote
1answer
41 views

Fitting n number of squares into n area

I am a mobile developer and I have a problem and need to find a formula to get the dimensions of squares to fit inside a space. My problem is that I have a rectangle of dimensions lxw and need to fit ...
1
vote
1answer
34 views

What is the correct way to denote a coordinate system in writing?

I want a systematic way that is readable but also mathematically rigorous for defining a coordinate system in writing. For example for a cartesian coordinate system centered on the fixed or moving ...
2
votes
1answer
52 views

Looking for various proofs there is no faithful representation $\rho:S_4\rightarrow GL(\mathbb{R}^2)$

I stumbled on the question when thinking about a representation $\rho:D_4\rightarrow GL(\mathbb{R}^2)$ as symmetries of the four points $\{(\pm 1, \pm 1)\}$. There didn't seem to be a good geometric ...