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
9 views

Locus of equidustant points

I have problem which involves finding the vornoi diagram of n points in the $\mathrm{R}^2$ plane with distance metric as1.) the $L_1$ i.e is distace between two points is $d(A,B)=|A_x-B_x|+|A_y-B_y|$ ...
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0answers
8 views

Volumes and Areas - optimisation

I have enough silver to coat one metre squared of surface area - I plan to coat a sphere and a cube - find dimensions of solids if total volume is to be a maximum? A minimum? One of the solids may ...
1
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0answers
8 views

Simplicial maps between simplicial 2-manifolds

Suppose I have two simplicial two-manifolds ("triangle meshes") $M_1$ and $M_2$. I want to compute a surjective simplicial map between $M_1$ and $M_2$, i.e. a surjective function $\phi$ between the ...
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0answers
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2
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1answer
15 views

Find the “surface vertices” of a collection of points.

I am currently doing some experiments in order to simulate liquids. I have a collection of 3D points that interact with each other to form a body of water. I would like to form a mesh from these ...
2
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0answers
23 views

Roll one ellipse on another: Locus of center ever a circle?

Let $E_1$ be an ellipse fixed in the plane. Let $E_2$ be a second, possibly different ellipse, which rolls around without slippage outside $E_1$, touching perimeter-to-perimeter. Let $c_2(t)$ be the ...
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1answer
13 views

Cylinder with an volume of 400 [on hold]

What radius and height do I need to make a cylinder with a volume of 400 cm cubed?
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1answer
16 views

difference between normal and diameter in circle.

A line through the centre of the circle meet the circle at two points is called a)normal b)tangent c)secant d)diameter I am pretty sure that the answer is diameter but my notes say the answer is ...
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6answers
46 views

Is it possible to draw trapezoid by compass and straightedge if 4 sides given?

I tried to construct trapezoid with lengths of 4 sides given. Without success. Then searched in internet. I believe it is not possible, but I am not sure. The only way is to calculate the high of the ...
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0answers
31 views

How long does one remain in the square

This is a slightly known question: There is a square of unit side. Its centre is $O$. Two movable points $X$ and $Y$ are placed randomly in the square. Let $A$ be the midpoint of $OX$ and $B$ ...
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1answer
17 views

Possibility of a Figure with infinite area or perimeter [duplicate]

Is there any figure possible with infinite area but finite perimeter or finite area but infinite perimeter? If yes, then what's the proof of its existence.
1
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1answer
21 views

Definition of angle between non-differentiable curves

(Background: I am trying to understand the definition of angle-preserving function..I posted a question earlier but I still have doubts) My question is:how is the angle between two curves defined if ...
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0answers
25 views

Possible areas within an integer grid

Given a 1x1 grid with 4 lattice points $[(0,0),(0,1),(1,0),(1,1)]$ (equivalent to a $2 \times 2$ grid of vertices), there are 2 shapes and areas that can be formed: a triangle and a square. There are ...
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3answers
43 views

Rectangular paper fold

Given: A rectangular piece of paper $ABCD$ with $AB = 8$ and $AD = 12$. Fold the paper such that $B$ coincides with $D$. Find the length of the fold. (AoPS) My work: I first made a parallelogram ...
4
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1answer
34 views

Which ellipses settle to 1-point contacts within a snow-globe circle?

Suppose you have a solid ellipse with axes $a$ and $b$, $(x/a)^2 + (y/b)^2 = 1$, confined inside a unit-radius circle. You shake the circle like a snow globe, and the ellipse settles to the bottom ...
1
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1answer
30 views

Working with mathematical models, HELP.

I'm currently doing a lot of self study with mathematics. I live in The Netherlands and hope to be admitted to Leiden University somewhere in 2016. Now, I have encountered a problem in my workbook ...
2
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1answer
30 views

Finding vertices of regular polygon

I am trying to find the vertices of a regular polygon using just the number of sides and 2 vertices. After the second vertex, I will make left turns to find each subsequent vertex that follows. For ...
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2answers
27 views

Move a point with known angle on a circle

Having a circle of radius $R$ with the center in $O(0, 0)$, a starting point on the circle (e.g. $(0, R)$) and an angle $\alpha$, how can I move the point on the circle with $\alpha$ degrees? I need ...
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1answer
33 views

how to find area of segment of only given the radius? [on hold]

I have a thought question it will be tough to explain but here we go. My teacher gave us three circles which each have a radius of 5in. Inside the circle there's a triangle with no angles? Inside the ...
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0answers
15 views

Invariant point (flex) invariant under projective transformations.

Let $C$ be a projective curve in $\mathbb{P}_2$ defined by a homogeneous polynomial $P(x, y, z)$ and let $\alpha$ be a linear transformation of $\mathbb{C}^3$. Let $Q$ be the homogeneous polynomial $Q ...
4
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3answers
93 views

Is there any geometrical interpretation as to why matrix product is not commutative?

Is there any geometrical interpretation as to why matrix product is not commutative? Similarly, is there any geometrical interpretation of matrix product when you have matrices $A$, $B$ such that ...
1
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0answers
22 views

Distance from a point to the involute of a circle

I know that the involute of circle of radius $r$ centered at $(0,0)$ is given by the following parametric form: $$\begin{cases} x(\theta) = r \big(\cos(\theta) + \theta\ \sin(\theta) \big),\\ ...
3
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0answers
38 views

What does $x_e$ mean in $I(x_e,y_0)$?

A book I am using has a problem which includes two points on the graph of $y=\ln x$, $M_1(x_1, y_1)$ and $M_2(x_2, y_2)$ and identifies the middle of the chord $M_1 M_2$ between them as $I(x_e, y_0)$. ...
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0answers
29 views

Khayyam's method of solving a cubic equation

Can someone offer a worked example of how Omar Khayyam would have a solved a cubic equation with geometric solutions by means of intersecting conics?
0
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1answer
38 views

Constructibility of $\arctan\left(\frac{1}{2}\right)$

I would like to show that $\arctan\left(\frac{1}{2}\right)$ is not a constructible number. I would like to use the following lemma: Let $P(x)=x^3+ax^2+bx+c$ a polynomial with ...
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1answer
21 views

Geometry Transformation Problem [on hold]

Given two circles C1 and C2, line s, point D, and point E like the image below : Explain me the procedure to find point P on C1 and Q on C2 such that the length of PQ = the length of DE and line ...
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1answer
25 views

In Neutral Geometry, prove that the opposite sides of a rectangle are congruent.

I'm having some trouble proving a theorem of Neutral Geometry. First, allow me to clearly state what we are allowed to assume in Neutral Geometry: Hilbert's incidence axioms Hilbert's order axioms ...
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0answers
13 views

txml question help

In the coordinate plane, the vertices of a quadrilateral are (-4,-2), (8,5), (6,8), and (-1,6). What are the coordinates of the point in the plane for which the sum of the distances from this point to ...
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2answers
54 views

Easiest way to verify that $4x^2+y^2=1$ is an ellipse?

Normally I would just divide both sides by the number $4$ because it's not good in there, but I can't do it for $$4x^2+y^2=1$$ I must have $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$ So what's the ...
3
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1answer
33 views

Diameter of the Grassmannian

Just an interesting question that came to my mind while studying(!): Since the Grassmannian $G(k,\mathbb{C}^n)$ is a compact manifold, what do we know about its diameter? Do we know any estimate? ...
2
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1answer
25 views

Weighted mean of an object (Centers of mass)

I am having trouble understanding the concept. Usually when I calculate the center of mass of an object when given area and dimensions I'd multiply corresponding distances with areas etc then ...
2
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1answer
44 views

Some question about path connectedness

I think that's intuitively evident but I can't prove that the set $\mathbb{S}^n\setminus\{(0,\cdots, 1),(0,\cdots, -1)\}\; (n>1)$ is path connected. Does anyone have a formal argument to prove it? ...
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1answer
17 views

Length of curves with same images

From a geometrically intuitive point of view, it is obvious that if two injective $C^1$ curves $\gamma,\delta$ with values in $\mathbb R^n$ have the same images, then their lengths $\ell(\gamma)$ and ...
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0answers
25 views

find the corect angle to cut pipe

I have pipe penitrating a wall at an angle shooting up. I have to attach a 90 degree ellbow an drop from 90 plumb,so I will have to cut the unlevel pipe on an angle to achive a plumb drop from 90. How ...
0
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0answers
19 views

Using azimuthal and polar angles in ECEF coordinate system

I have a physical cone, which its vertex located in some point (x,y,z) in ECEF coordinates, and I want to check if another point is inside this cone. In order to do it, I have to take into ...
3
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1answer
45 views

Circle from three points on surface of sphere

I need to compute the circle on the surface of a sphere given three points on that very surface. It is very easy to do that in Euclidean geometry, but the sphere has no x and y, but just two angles ...
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0answers
16 views

Area of a bounded region $R$ of surface $z = f(x,y)$ is $A = \int\int_{Q} \sqrt{1 + (\partial_x f)^2 + (\partial_y f)^2}\; dxdy$

This is Exercise 5 from do Carmo section 2.5 (page 100). Area of a bounded region $R$ of surface $\left\{ z = f(x,y)\right\}$ is $A = \int\int_{Q} \sqrt{1 + (\partial_x f)^2 + (\partial_y f)^2}\; ...
2
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0answers
26 views

Repeatedly interpreting polar coordinates as Cartesian

Start with a Cartesian point $(x,y) \in \mathbb{R}^2$, convert it to polar coordinates $(r,\phi)$ ($\phi$ in radians), and then reinterpret $(r,\phi)$ as $(x,y)$, i.e., set $$(x,y) = (r,\phi) \;.$$ ...
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1answer
47 views

confused about how adding inches makes it square [on hold]

I have a fountain base that was 36 inches wide and 16 inches deep. I added 4 inches to both making it 40 inches wide and 20 inches deep. I am confused as to before at 36 and 16 it was not perfectly ...
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3answers
31 views

Volume of a Rectangular Prism when given only the Surface Area

So, in my equation, they ask you to find the volume of a rectangular prism when you only are given the surface area. As an example, one of the equations gave you a surface area of 240 yards squared, ...
2
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3answers
48 views

Can the formula for finding the slope of a line be reversed and still be right?

The formula for finding the slope of a line is $y_2-y_1\over x_2-x_1$, but can it be reversed into $y_1-y_2\over x_1-x_2$ and still be right?
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0answers
30 views

Complex singularity exponent

I am studying about complex singularity exponents of holomorphic functions. I need some help to clarify a few things: First, what a complex singularity exponent is, for the holomorphic function ...
1
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3answers
22 views

Calculate sides of right triangle with hypotenuse and area or perimeter

I'm trying to find if it is possible to find the lengths of the base and height of a right triangle with only the hypotenuse and the area (or the perimeter) of the triangle. I would have just figured ...
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2answers
41 views

Can some one explain why the answer to part a describes a circle, or part of it?

Problem Statement: The transformation $T$ from the complex $z$-plane to the complex $w$-plane is given by $w=\frac{z+1}{z+i}, z\neq i$. a) Show that $T$ maps points on the half-line $\arg ...
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1answer
23 views

Sketch $\text{Arg}( 1 - z ) = \pi/2$ and find the Cartesian equation

This is a question I was thinking about when doing Edexcel FP2, seen something like it before but not sure where. Tried to solve it but cannot.
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1answer
21 views

How do i scale 2D vector using matrix

I know that scale matrix is 2x2 { x, 0, 0, y } basis. My vector { 100, 2 } and i want to scale it using custom 2x2 matrix. I've read that if left operand is 2D row vector, then multiplying it on a ...
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3answers
61 views

Construct the great circle (geodesic) in spherical or Riemanian geometry

Given: a circle $C$ with centre $M$ two points $P_1$ and $P_2$ inside circle $C$, so that $M$ is not on the line $P_1P_2$. Cunstruct an other circle $O$ so that: $P_1$ and $P_2$ are on ...
4
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3answers
50 views

Orthogonal circles

What is the equation of the circle that is orthogonal to the circles $x^2 + y^2 - 8x +5 =0$ and $x^2 + y^2 +6x +5 = 0$ and passes through the point $(3,4)$? I've spent hours trying to figure this out ...
1
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1answer
39 views

Proof there exists a point $O$ such $|AO|\le p,|BO|\le q,|CO|\le r$

Give the postive numbers $p=\dfrac{y+z-x}{\sqrt{3}},q=\dfrac{z+x-y}{\sqrt{3}},r=\dfrac{x+y-z}{\sqrt{3}}$,in $\Delta ABC$, where $|AB|=z,|BC|=x,|AC|=y$,and $G$ is centroids, I have prove following ...
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0answers
20 views

The largest sphere trapped into a tetrahedral void

A tetrahedral void is formed by four identical spheres each having a radius $R$ (as shown in the diagram above). A largest sphere, centered at the point 'O' having a radius $r_{max}$, is completely ...