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

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8 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 moves along the path AB with ...
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1answer
35 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 ...
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0answers
18 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
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1answer
15 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} ...
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1answer
20 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.
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0answers
136 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 ...
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0answers
34 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 ...
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0answers
11 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 ...
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1answer
21 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 ...
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0answers
18 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
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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 ...
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2answers
38 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 ...
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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 ...
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1answer
27 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
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2answers
38 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
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0answers
16 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 ...
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1answer
21 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 $b \geq \dfrac{a}{\sqrt{2}}$?
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2answers
39 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 ...
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1answer
43 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 ...
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1answer
31 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 ...
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1answer
40 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 ...
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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
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1answer
51 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 ...
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2answers
36 views

Using an ellipse, do all inscribed angles have to be congruent?

For circles, it is well known that all inscribed angles are congruent. With the definition of inscribed angles maintained to ellipses, are all inscribed angles of an ellipse congruent?
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1answer
28 views

Surface area of platonic solids inscribed in unit sphere.

If one inscribed each of the platonic solids in the unit sphere, what can be said about the surface areas? Is it a monotonic sequence? Does any "meaningful" (see paragraph below) continuous (or ...
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3answers
44 views

$N$ circles on a circle

Perhaps a rather elementary question, but I simply couldn't figure out the calculations on this one. Say one takes a circle centered at the origin with radius $R$. He or she then proceeds to place $N$ ...
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1answer
15 views

atanh2 / “ polar argument”

In many application you get a function of the form: $$\tan(x) = \frac{f(A)}{g(B)}$$ Where you then have to use the "polar argument" (to account for all 4 quadrants): $$\arg \left( f(A), g(B) ...
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1answer
17 views

The projective space of all lines through the origin

I have a question to the following example: Assume that $\mathbb{A}_2$ is an affine plane over a field $\mathbb{K}$, and we have fixed affine coordinates $x, y$ on $\mathbb{A}_2$. Let $\mathbb{P}$ be ...
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0answers
40 views

Geometry problem – triangle [on hold]

Stiind ca $A(-4;0)$ si $B(0;-4)$ sunt doua puncte dintr un sistem de axe cu originea $O$, sa se precizeze natura triunghiului $AOB$ si sa se calculeze aria acestui triunghi. Knowing that ...
2
votes
1answer
31 views

How to calculate the surface of overlapping ellipsoids

I want to calculate the surface of a body made of at least 3 overlapping ellipsoids. Below there is a picture of the cross section of the body. I already know how to calculate the surface of single ...
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1answer
13 views

Jacobian of the Kelvin transform

The Kelvin transform of the circle in $\mathbb{R}^n$ with centre $\textbf{u}$ and radius $r$ is defined by $$\textbf{y} \mapsto \textbf{u} + r^2|\textbf{y} - \textbf{u}|^{-2}(\textbf{y}-\textbf{u}).$$ ...
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0answers
31 views

How to find shaded area of square? [on hold]

How to find shaded area of square if it has four circles in it each having 2 meter square area?
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2answers
57 views

All right angles are equal to each other

Why is it that All right angles are equal to each other -a postulate in Euclid's Elements (Wikipedia). Shouldn't it be a congruence rather than an equivalence? Isn't this just a special case of ...
2
votes
3answers
72 views

Intersection of two moving objects

There are two objects. The first object moves with speed $U_1$ from known point $A$ to known point $B$. The second object has speed $U_2$ and starts from known point $C$. What is the direction the ...
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0answers
27 views

Prove an upper bound [on hold]

Let $O$ be the origin, and $K$ be a convex polygon in $\mathbb{R}^2$ with edges $K_1, \dots K_n$. Let $\nu_i$ be the unit outer normal of each $K_i$. Suppose $O \notin K$. Prove that there exists a ...
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0answers
34 views

Determine the minimum and maximum angles, to the nearest tenth of a degree, that a pipe can make with the horizontal.

For residential drains, a horizontal pipe needs to have a minimum slope of 1/4 inch per foot and a maximum slope of 1/2 inch per foot for waste to drain properly. This means that for every horizontal ...
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vote
1answer
25 views

Similar quadrilaterals in rectangle

While working on a problem on finding the shaded region in a rectangle, I realized that if a line cuts a rectangle into two quadrilaterals, then these two quadrilaterals are similar as the opposite ...
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0answers
22 views

Vector Geometry Proof with a Pentagon [on hold]

Pentagon $ABCDE$ is inscribed in a circle. For any edge of $ABCDE$, we can draw the line perpendicular through that edge that contains the centroid of the remaining three vertices. Show that these 5 ...
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1answer
40 views

Finding circumference of a circle with a hole in it [on hold]

The bigger circle has Radius R and smaller circle has radius r. I need to find circumference of circle with Radius R which has a hole cut in it of radius r(the smaller circle). I was thinking of ...
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0answers
20 views

Proof of the last part of the Reeb theorem

I'm trying to prove Reeb's theorem as stated in Milnor's Morse Theory. Suppose we have an $n$-manifold $M$ together with a smooth function $f$ with exactly two critical points (both ...
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0answers
37 views

Relation between polygons

I try to solve a system but I need another equation to make it solved... So I try to find a relation that give the $\beta''$ function of $\beta'$, $\alpha'$, $N$, $D$ et $L$ as described in the ...
3
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5answers
51 views

Showing that certain points lie on an ellipse

I have the equation $$r(\phi) = \frac{es}{1-e \cos{\phi}}$$ with $e,s>0$, $e<1$ and want to show that the points $$ \begin{pmatrix}x(\phi)\\y(\phi)\end{pmatrix} = ...
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votes
1answer
35 views

Orthogonal vectors and potential [on hold]

given the potential $ψ(x;y)$, such that $dψ=−u_2dx+u_1dy$, why are $∇ψ=(−u_2;u_1)$ and $ψ(x;y)=c$ orthogonal vectors ? $c \in \mathbb{R}$ is a constant, and $\mathbf{u}(x; y) = (u_1(x;y); u_2(x;y))$, ...
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1answer
21 views

What are the coordinates of a point given its distance from another point?

If the abscissa of a point is twice the value of the ordinate and has a distance of $2\sqrt{17}$ units from the point $(4,-5)$, what are the coordinates of the point?
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0answers
23 views

In a trapezium $PQRS$, $QP=a,RQ=b,RS=3a$ and the diagonals intersect at $X$. Express $RP$ and $QS$ in terms of a and show [on hold]

In a trapezium $PQRS$, $QP=a,RQ=b,RS=3a$ and the diagonals intersect at $X$. Express $RP$ and $QS$ in terms of $a$ and $b$. Show that $PX:PR=QX:QS=1:4$
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vote
3answers
73 views

Peripendicular distance from a line segment

I have a line given by $Ax + By + C= 0$, and a point $x0,y0$. From that point $x0,y0$ in the direction of the line up to distance $d$, I want to find the perpendicular distance of the points from this ...
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1answer
40 views

How to find m by given information.

If the chord $y=mx+1$ of the circle $x^2+y^2=1$ subtends an angle of measure $45^o$ at the major segment of the circle then m= . How to find m.
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3answers
36 views

Convert the equation to rectangular form $r = \frac {6}{1-\sinθ}$

Convert the equation to rectangular form $r = \frac {6}{1-\sinθ}$ The answer should be: $y = \frac{1}{12} x^2 -3$ But how to arrive at the answer? I tried replacing r with $\sqrt{x^2 + y^2}$, then ...
1
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1answer
41 views

What is the probability of two random line segments crossing in a unit square?

For the purposes of this question a random line segment is defined by connecting two random points inside the unit square, where a random point is found by generating two random numbers between 0 and ...
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0answers
43 views

How to give a rigorous proof of a fact about convex polygon?

I claim that there exists universal constants $0<\delta_1(m), \delta_2(m)<1$ such that for any convex polygon $P$ in $\mathbb{R}^n$ with $m$ faces, \begin{equation} \frac{\mathcal{H}^{n-1}(\{x ...