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

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1answer
12 views

Prove that there is exactly one perpendicular line

Consider an absolute plane (i.e. it satisfies all axioms except the parallel axiom). Let $g$ be a straight line and $P$ a point not in $g$. Then there is a unique straight line going through $P$ which ...
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0answers
4 views

Calculating the position of the ascending and descending nodes in an orbit

I'm working on a space sim and I'm stuck getting the position of the Ascending and Descending orbital nodes. I know how to get the position at any angle of the orbit, but it's measured from the ...
2
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1answer
15 views

Proof: number of intersection points of borders of a convex polygon and its translate never greater than 2

How can I prove the observation that the borders of a convex polygon $P$ with no parallel sides in $\mathbb{R}^2$ and a translate of $P$ by any vector $t\neq 0 \in \mathbb{R}^2$ that is not parallel ...
2
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1answer
23 views

When the intersection between a sphere and a cylinder is planar?

We have a sphere and a circular cylinder. Let the sphere center be $O$ and radius $R$, and the cylinder axis $a$ and radius $r$. I solved the specific case intersection graphically on 2 planar ...
1
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0answers
29 views

Calculationg the angle of a triangle

I am trying to find a specified angle of a triangle. In triangle ABC, angle A = 20. D and E are points on AB and AC, where AB=AC. Angle EBC = 50 and DCB = 60. What is the angle of DEB? I can show ...
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1answer
13 views

Calculate perimeter of rhomboid

I am trying to solve the following problem but I got stuck In a rhomboid with an area of $48 \space cm^2$, the major diagonal is $4$ cm shorter than the double of the minor diagonal. Calculate the ...
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2answers
36 views

How do I solve the triangle?

Let $ABC$ be a given triangle, such that $AD=3$, $DE=5$, $EC=24$ and $∠ABE=90^\circ$, $∠DBC=90^\circ$, where $D$ and $E$ are points on $AC$ (and$ D$ is between $A$ and $E$). Then, find the length of ...
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1answer
31 views

Counter example to Mostow's rigidity theorem for 2-manifolds.

I am trying to understand a counter-example to Mostow's rigidity theorem. Here is the counter example I want to understand. Take two non-isometric octagons with the sum of interior angles equal to ...
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0answers
17 views

Get a function (equation) from data points?

Is there a way to get a function (equation) from data points? For example, we have this famous Google's 'Batman' function: ...
2
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0answers
22 views

Rational functions over curves define regular maps?

I've a rather simple question that is strucking me, perhaps because I'm a newbie in algebraic geometry. If we have a projective irreducible non-singular curve $C\subseteq \mathbf{P}^n_k$ where $k$ is ...
2
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1answer
23 views

Origin of period function model of primes

There is a web page attributed to Omar Pol, "Sobre el patrón de los números primos: Determinación geométrica de los números primos y perfectos." ("On the pattern of primes: Geometric Determination of ...
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0answers
11 views

What's another name for the non-negative quadrant, or any non-negative orthant?

Is there another canonical name for the non-negative quadrant, or for the generic non-negative orthant?
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0answers
13 views

Calculate change in distance to camera from scale

I have 2 pictues of an object. In one picture the object is close and in the other one it is far away. I have these values: $z$ = distance of object to camera in first picture $f$ = focal length ...
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0answers
35 views

one question about differential geometry,show the curvature k($\phi$)

One often gives a plane curve in polar coordinates by $p=p(\phi)$,$a\le\phi \le b$. (1)Show that the arc length is $$\int_{a}^{b}\sqrt{p^2+\dot p^2}$$,where $\dot p$ means the derivative of p with ...
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0answers
41 views

Find the angle in a triangle [duplicate]

Find the angle $a$: I came up with 20 degrees but not sure. Can somebody help here.
1
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1answer
19 views

Finding the length of $BC$ in a kite

Calculate the length of $BC$. I first started by letting $M$ the point of intersection of $AC$ and $DB$. Now $MB^2+MA^2 = 9$, $MD^2+MA^2 = 16$, $MD^2+MC^2 = 36$. Therefore, $BM^2+MC^2 = BC^2$ Can ...
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0answers
16 views

Mean width of an ellipsoid

Let $E$ be an ellipsoid in $\mathbb{R}^d$ defined by the equation $\sum \frac{x_i^2}{a_i^2}=1$. Is there a formula to express the mean width (or an approximation of the mean width) of $E$ in term of ...
1
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1answer
13 views

Perspective projection of a circle: what is the size of the semi-major axis?

It can be proven that the perspective projection (or camera projection) of a circle is an ellipse. But I also need to prove that the semi-major axis has the same size as the radius of the original ...
2
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1answer
16 views

How prove $\left(\frac{D}{\sqrt{3}}+\frac{d}{2}\right)^{2}\geq n\cdot\frac{d^{2}}{4}$ for $D=\max{A_iA_j}, d=\min{A_iA_j} (1\leq i<j\leq n)$?

Let be n points $A_1,A_2,A_3,...,A_n$ on plane $(n\geq 3$). Let $D=\max{A_iA_j}, d=\min{A_iA_j} (1\leq i<j\leq n)$. How prove $\left(\frac{D}{\sqrt{3}}+\frac{d}{2}\right)^{2}\geq ...
1
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1answer
22 views

Intersection of Two Planes

I keep hearing different answers for what the intersection of two planes is. I believe it is a line, but it can also be a plane IF the two planes are not distinct. However other sources are saying ...
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0answers
26 views

Pyramid inside a rectangular tank [on hold]

a rectangular tank has a base 60cm by 20cm. A solid metal pyramid with a square base of sides 10cm each and height 27cm is placed inside the tank. The tank is then filled with water until it just ...
2
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2answers
28 views

How to explain why a curve is on a cylindrical surface?

The question may be a bit general but I'm unsure about how to define it. I have a curve: $\vec r(t) = (2\cos(t),2\sin(t), 2t)$, for $0\le t \le 2\pi$, The problem I'm trying to pose : "Show that ...
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1answer
18 views

Getting the intersection of a line and a plain

My line (2,1,10) goes through the plain with the normal (-2,3,8). Now I would like to calculate the intersection with following ...
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0answers
5 views

Decide conditions on smooth function $r$ such that $\nu$ is a regular curve and decide functions $r$ for which $\nu$ has speed $1$

Decide conditions on smooth function $r$ such that $\nu$ is a regular curve and decide functions $r$ for which $\nu$ has speed $1$ Let $r: \mathbb R \rightarrow \mathbb R$ be a smooth function ...
5
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7answers
46 views

How does one prove that if $\cos(t) = \cos(t')$ and $\sin(t) = \sin(t')$ then $t = t' + 2k\pi$?

How does one prove that if $\cos(t) = \cos(t')$ and $\sin(t) = \sin(t')$ then $t = t' + 2k\pi$ ? I've tried proving the above statement, which I think is valid. I know $\sin(t)$ is injective on ...
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votes
3answers
56 views

Parametrization of the ellipse $\frac {x^2} {p^2} + \frac {y^2} {q^2} = 1$.

Consider the ellipse ($p > q > 0$) $$\frac {x^2} {p^2} + \frac {y^2} {q^2} = 1$$. I want to prove that $$\mu(t) = (p \cos(t), q \sin(t))$$ is a parametrization of the ellipse. I see that $(x/p, ...
0
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3answers
32 views

How to find the radius [on hold]

I have to find the radius of the circle. AB=1,5 AD=2 AD is a tangent Please help!
-2
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0answers
31 views

A 57“ arm has a vertical pin at one end, if the pin angle changes by .020” how much does the other end of the arm move? [on hold]

A 57" arm has a vertical pin at one end, if the pin angle changes by .020" how much does the other end of the arm move? ok, let me try this.
0
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1answer
31 views

Angle quadrisection in a triangle

In triangle ABC, AB=84, BC=112, and AC=98. Angle B is bisected by line segment BE, with point E on AC. Angles ABE and CBE are similarly bisected by line segments BD and BF, respectively. What is ...
2
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1answer
27 views

Homeomorphisms of different spheres

It is pretty straightforward to show that if $X$ is a Banach space under two equivalent norms, then the respective open unit balls $B_1$ and $B_2$ are homeomorphic only by showing that $B_i$ is ...
3
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0answers
33 views

Points Distributed evenly around a circle: how many points are in each region?

A circle of circumference $2$ is split into three arcs of length $\frac{2}{3}$ (so the regions are $[0,\frac{2}{3})$, $[ \frac{2}{3},\frac{4}{3})$, $[\frac{4}{3},2)$, $2$ identifies with $0$) and ...
0
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0answers
19 views

midpoint of the diagonal of the quadrilateral and rhombus

$EBA,FCB,GDC,HAD$ is a similar triangle which is drawn externally of quadrilateral $ABCD$, where the sides of quadrilateral $ABCD$ become the base of the similar triangle. Let $M,N,P,Q$ are midpoints ...
3
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0answers
23 views

Prove that the circle which contains ATB and incircle of ABC touch in one point(T).

Incircle of $ABC$ touches $AC$ in $D$, $BC$ in $E$ and $AB$ in $K$. $J$ is the center of the excircle which touches the side $AB$. The circumcircle of $ADJ$ and $BEJ$ intersect in point $J$ and $T$. ...
2
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1answer
20 views

Stereographic projection of a sphere

What should have been a simple exercise in geometry has morphed into a multi-day affair with me figuratively tearing my hair out. I have no clue what's wrong. This image accompanies the problem: ...
2
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1answer
21 views

Seperating points in the complex plane

Given a finite set of points say $p_1,p_2, \ldots, p_n$ in the complex plane, how do I find another point $q$ such that ray $R_i$ joining $q$ to $p_i$ are all distinct. I would be happy with any kind ...
0
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0answers
27 views

Linear transformation of vector

I have computer graphics class and i had something like that on lecture: $$ \begin{bmatrix} \overrightarrow{b1} & \overrightarrow{b2} & \overrightarrow{b3} \end{bmatrix} \begin{bmatrix} c1\\ ...
1
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1answer
45 views

Centre of symmetry of a triangle

Suppose we have a $\triangle ABC$ wherein points $D,E,F$ are confined to move along the edges of $BC, AC, AB$ respectively such that $\triangle DEF \sim \triangle CAB$. What would be the centre of ...
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0answers
9 views

Tangent cone to the graph and epigraph

Good morning! I am solving this example: Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a function given by $f(x) = \left\{ \begin{array}{rl} x \cdot sin(\frac{1}{x}) & \text{if } x > 0,\\ 0 ...
2
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1answer
19 views

How find $\min_{a\in\mathbb R}f\left(a \right)$ for $f(a )=\max_{1\le k\le n}\left|x_k+ay_k\right|$?

Let them be given points in the plane $P\left(x_k,y_k\right)$, where $k\in \{1,...,n\}$. Let $f(a )=\max_{1\le k\le n}\left|x_k+ay_k\right|$ , where $a\in\mathbb R$ . How find $\min_{a\in\mathbb ...
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0answers
20 views

What does 'forms a right-handed set' mean?

In a question I am reading, the following question appears. What if $\vec{A},\vec{B}$, and $\vec{C}$ are mutually perpendicular and form a right-handed set? What exactly does "form a ...
0
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1answer
19 views

Find the area of the convex quadrilateral

So i have $ABCD$ is a convex quadrlateral and $E$ is the intersection point of diagonals. Given that $AE=2,BE= 5, CE = 6, DE =10$ and side $BC = 5$. I know the formula $A=\frac{1}{2}d_1 d_2 \sin ...
3
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1answer
49 views

Volume of a sphere with two cylindrical holes.

Consider a sphere of radius $a$ with 2 cylindrical holes of radius $b<a$ drilled such that both pass through the center of the sphere and are orthogonal to one another. What is the volume of the ...
-6
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1answer
66 views

you know root square of -1, what is the larger of the square? [on hold]

there is a square ABDC, $BD = \sqrt{-1}$ what is the value of AB=BC=DC=AD?
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2answers
95 views

If the curvature of a curve in a plane is a constant, is the curve contained in a circle?

If the curvature of a curve in a plane is a constant, is the curve contained in a circle?(Suppose curvature is positive.) one of my homework problems needs to use this, but I am not sure whether this ...
0
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1answer
30 views

What is a transformation that can't have shearing called?

What is a transformation called when it can have separate scaling for x and y, rotation, and translation, but it cannot have shearing or scaling AFTER rotation? Basically if this transformation is ...
1
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2answers
71 views

The area visible from two lighthouses with angle of vision 30 degrees, built at distance 10km from each other

The distance between 2 lighthouses is 10 km. What is the maximum area of the ocean in which both can be simultaneously visible if the angle of vision for each lighthouse is 30 degrees?But the minimum? ...
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0answers
16 views

find a point $C \in r$ (line) such that $d(C,\pi)=d(A,r)$

I have a line $r:(x,y,z)=(2,1,0)+\lambda(0,4,-3)$, $A=(2,4,4)$, a plane $\pi:4y-3z-4=0$. I have to find a point $C$ such that $d(C,\pi)=d(A,r)$ where $d$ is the distance.
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1answer
11 views

Tetrahedron in vector space: Finding a vector connecting two points

Edited to add: The tetrahedron is not necessarily a regular one. First off, the point $M$ is the centre of gravity for this tetrahedron. I have a base $\{e_1,e_2,e_3\} = ...
0
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1answer
34 views

Distance between a point and a line! [duplicate]

I have a big problem with geometry. How I do calculate the distance between the vectorial line $r:(x,y,z)=(2,1,0)+\lambda(0,4,-3)$ and the point $A=(2,4,4)$? I tried to solve the problem but ...
2
votes
1answer
30 views

Rotating an inscribed square in Geogebra

I am trying to figure out how to rotate the inside square so that the sides lengthen based on the degree of rotation. For example, after rotating 90 degrees in either direction, it should precisely ...