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

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1
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0answers
12 views

Can ${n \choose 2}$ points be covered by lines determined by $n$ points?

Let $S=\{(a_1,b_1),\ldots,(a_{n \choose 2},b_{n \choose 2})\}$ be ${n \choose 2}$ points on the plane. Does there exist $n$ points, such that the lines determined by the $n$ points cover all the ...
1
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0answers
7 views

union of two Geodesics

Let $X$ be a metric space. $a,b,c \in X$ and $\sigma_1 , \sigma_2$ geodesics from $a$ to $b$. Let $\sigma$ geodesic from $b$ to $c$. Want to show : $\sigma_1 \cup \sigma $ geodesic $\Rightarrow ...
0
votes
1answer
15 views

Length of tendon in circle [on hold]

What is the length of chord that pass on two specific point. For example I have circle ( r=1) point1 :(x1,y1) point2(x2,y2); length of chord?
0
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0answers
15 views

a question about differential geometry, the relation between osculating plane and the points of $\alpha(s)$

question:please prove the limit position of the circle passing through $\alpha(s)$,$\alpha(s+h_{1})$,$\alpha(s+h_{2})$ when $h_{1}$ and $h_{2}$ approaches 0 is a circle in the osculating plane at s, ...
0
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0answers
13 views

Is kahler geometry related to finsler geometry? [on hold]

Is kahler geometry related to finsler geometry? Is the metric $\partial_a\phi\partial_b\phi$ always kahler?
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2answers
36 views

If a curve $\gamma$ through two points $P,Q$ satisfy $\|Q-P\| = \int^{t_1}_{t_0} \| \gamma^{'} \| \, \text {d}t$, then $\gamma$ is a straight line?

In a theorem called "A straight line is the shortest curve through two given points", I prove that for any two points $P,Q \in \mathbb R^2$ and any curve $\gamma : (a,b) \rightarrow \mathbb R^2$ with ...
3
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1answer
21 views

Average distance to a random point in a rectangle from an arbitrary point

I'm interested in the mean distance between an arbitrary 2D point, $(p, q)$, and a uniformly distributed point inside a rectangle defined by the lower left and upper right vertices $(x_0, y_0)$ and ...
0
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1answer
26 views

Trying to define a simple “warp” function

I'm trying to define a 2D "warp" function y=f(x,w). A picture is worth a thousand bytes: I am looking for a simple function f(x, w) that satisfies the ...
1
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2answers
14 views

Geometry: What is the height of a solid pyramid

So the question is OPQRS is a right pyramid whose base is a square of sides 12 cm each. Given that the the slant height of the pyramid is 15cm. And now I need to find the Height of the pyramid. I ...
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0answers
56 views

Prove that.. Please quick. [on hold]

If the length of perpendicular from the point $(1,1)$ to the line $ax-by+c=0$ be $1$, show that $1/c+1/a-1/b=c/2ab$. if $p$ and $p'$ be the length of the perpendiculars from the origin upon the ...
2
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0answers
18 views

Unique 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 is ...
0
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1answer
12 views

Inscribed Rhombus

Can a rhombus that is NOT a square be inscribed in a circle? A quadrilaterals opposite angles must add up to 180 in order to be inscribed in a circle, but a rhombuses opposite angles are equal and do ...
1
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1answer
18 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 ...
0
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0answers
5 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
17 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
votes
1answer
25 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 ...
2
votes
1answer
52 views

Calculationg the angle of a triangle

I am trying to find a specified angle of a triangle. In triangle $ABC$, $\angle A = 20^\circ$. $D$ and $E$ are points on $AB$ and $AC$, where $AB=AC$. $\angle EBC = 50^\circ$ and $\angle DCB = ...
0
votes
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 ...
1
vote
2answers
37 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 ...
6
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2answers
44 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 ...
0
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0answers
19 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
votes
0answers
32 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
votes
1answer
24 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 ...
0
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0answers
12 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?
0
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0answers
17 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 ...
1
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0answers
41 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 ...
0
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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
vote
1answer
27 views

Finding the length of $BC$ in a quadrilateral

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 ...
1
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0answers
18 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
16 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
votes
1answer
19 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 ...
-7
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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
votes
2answers
31 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 ...
1
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1answer
20 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 ...
0
votes
1answer
7 views

For which functions $r$ is the curve $r(t)(\cos t,\sin t)$ regular or unit speed?

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
votes
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 ...
0
votes
3answers
58 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
votes
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
32 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
votes
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
votes
1answer
28 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
votes
0answers
35 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
votes
0answers
21 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
votes
2answers
46 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
votes
1answer
21 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
votes
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
votes
0answers
28 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
vote
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 ...
0
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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 ...