Questions on coordinate systems, a geometric method where a point in n-dimensions is assigned a corresponding n-tuple of numbers.

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Alternatives to polar coordinates for mapping point onto one dimensional coordinate

I can map a point (x,y) to polar coordinates (angle,length). However, let's say in this (angle, length) pair, "length" doesn't actually interest me, so I can map (x,y) to a one dimensional ...
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0answers
24 views

Example of a Problem Made Easier with Skew Coordinates

I'm looking for an example of a problem which would be hard (or significantly harder) to solve in orthogonal coordinate systems, or at least the Cartesian coordinate system, but is reduced to an ...
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1answer
71 views

Convert $r^2\cos(2\theta)=9$ to Cartesian

I need to convert $r^2\cos(2\theta)=9$ to Cartesian coordinates. How should I do it? What I did: $$r^{2}\cos2\theta=r^{2}2\cos^{2}\theta-1=9\Rightarrow r^{2}\cos^{2}\theta=5\Rightarrow x^{2}=5$$ Did ...
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1answer
51 views

From any arbitrary point $P$ on $y =\cos x$ tangents $PA$ and $PB$ are drawn to a circle which passes through

From any arbitrary point $P$ on $y =\cos x$ tangents $PA$ and $PB$ are drawn to a circle which passes through the points $(1,0)$ and $(3,0)$ and touches the circle $x^2+y^2-2x-8=0$ and have its ...
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1answer
36 views

Consider a series of n concentric circles $c_1,c_2 \cdots c_n$ with radii $r_1,r_2.\cdots r_n$ satisfying $r_1>r.$.

Consider a series of n concentric circles $c_1,c_2 \cdots c_n$ with radii $r_1,r_2.\cdots r_n$ satisfying $r_1>r_2>r_3 \cdots r_n$ and $r_1=10$ The circles are such that the chord of contact of ...
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1answer
19 views

Longitude and Coordinates

Let $X=(x_1,x_2,x_3)$ and $Y=(y_1,y_2,y_3)$ be two points on the unit sphere $S^2=\{(x_1,x_2,x_3)\,|\,x_1^2+x_2^2+x_3^2=1\}$. Is there a "nice" necessary and sufficient condition on the coordinates ...
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2answers
81 views

Collision detection between two accelerating spheres with no initial velocity?

We have two non-touching spheres of radii r1 & r2 are lying in space at rest. Both of them are then given accelerations a1 & a2 respectively at time t=0. Find whether they will ever come in ...
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1answer
160 views

Using paraboloidal coordinates

I have the 3-dimensional paraboloidal coordinates $$s_{\pm}=\sqrt{x^2+y^2+z^2}\pm z$$ $$\phi=ArcTan(y/x)$$ with the inverse transformation $$x=\sqrt{s_+ \cdot s_-}\cdot cos(\phi)$$ $$y=\sqrt{s_+ ...
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0answers
45 views

Locus of point moving with circle

Consider the circle of radius $1$ unit with its centre at the point $(0,1)$. From the initial position, the circle is rolled along the positive $x$- axis without slipping. Find the locus of the point ...
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1answer
75 views

Pi for non mathematician

I've been long gone from math (shamefully) and have trouble using some quite familiar concepts... Consider the following picture in which I render two circles with radius 32 (...
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1answer
20 views

2-dim. pendulum: Which coordinates?

I have a rather elementary question: I have a 2-dim pendulum and I do not know how I can descrive the coordinates. In the 1-dim case one coordinates is enough_ the angle. But I do not know how it is ...
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2answers
45 views

how to calculate the coordinates center of a squar [closed]

I need to calculate the center of square cells each cell has 4 (x,y) coordinates. Can one help me to Know how can I calculate the coordinates of the center of each cell?
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2answers
172 views

Global and local coordinates on a manifold, and their relations to curvature

I would be pleased to have some information about coordinates in differential geometry. A) First I would like to check whether or not the definitions I use are correct. (Mainly for the sake of ...
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0answers
34 views

Mapping between two unknown 3D coordinate systems from common motion

Coordinate systems A and B are rigidly linked in an unknown way. The platform then moves and the motion vectors [RA|TA] and [RB|TB] are calculated in each coordinate system. They are parallel but not ...
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1answer
60 views

Dot product in Curvilinear Coordinate Systems

I came across the dot product in polar, cylindrical, and spherical coordinates, today. After checking they were equivalent to the Cartesian versions, I started wondering how one would figure them out ...
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1answer
23 views

Find the nature of the curve

Given: $x=t^2+t+1, y=t^2-t+1$ Find the nature of the curve. My approach: I was trying to relate $x$ and $y$. However I haven't been able to. Please suggest some methods to solve such kind of ...
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1answer
38 views

Coordinates of specific points on a triangle, given the triangles coordinates

I'm working on a programing project. For that project I have a triangle with points $A,B,C$, where $A(a_1,a_2,a_3);B(b_1,b_2,b_3);C(c_1,c_2,c_3)$. Given the coordinates of the points $A,B$ and $C$, I ...
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2answers
66 views

Better way to denote position on a sphere's surface

TL;DR: Read the bold text. If you have a rectangular plane, you can use two coordinates (X, Y) to define any position on the plane. If you have a sphere, you can still use polar coordinates to denote ...
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2answers
86 views

What is a coordinate system?

What's a coordinate system? I was watching a Khan video about coordinates with respect to orthonormal bases. It is mentioned that orthonormal bases make for "good coordinate systems". I didn't ...
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0answers
29 views

Ellipsoidal Coordinates Geometrically

Is there a quick, geometric, way of writing down (the square root of?) the Cartesian coordinates $$\begin{align} x^2 &= (a^2+\xi)(a^2+\eta)(a^2+\zeta)/(b^2-a^2)(c^2-a^2)\\ y^2 &= ...
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2answers
159 views

converting kph and heading to xyz velocity vector

I am writing software (in C++) that is required to send out messages from our simulation system to another simulation system. Problem is we track the simulation object's current speed (kph) and ...
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1answer
20 views

How to find the $ x,y$ coordinates of a point in between $2$ points in $3$ dimension

Point $1 = (0,0,0)$ Point $2 = (5,6,7)$ Given that point $3$ have a $z$-coordinate of $3$, how can I find the $x,y$ coordinates of point $3$?
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1answer
58 views

How many different ways are there to go from $(0,0,0)$ to $(3,3,3)$?

There is a cube that is on the $(x, y, z)$ coordinates. How do I construct a systematic way to go from $(0,0,0)$ to $(3,3,3)$? Which subject should I study for this question? Please help me! I'm ...
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1answer
104 views

Equation of tangent on Cartesian plane given center and radius of a circle

If I have a generic circle with radius $r$ and center $(h, k)$, and a tangent line with point of tangency $(x, y)$, can you give me the equation of the tangent line? Thanks!
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1answer
69 views

Point transformation of ODEs

I am trying to understand a passage in the introduction to this book, which deals with algorithmical procedures to analytically solve ODEs. Specifically, I do not understand how the ODE $$ y''(y+x) + ...
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1answer
75 views

maximum radius of a circle inscribed in an ellipse

Consider an ellipse with major and minor axes of length 10 and 8 resp. The radius of the largest circle that can be inscribed in this ellipse, given that the centre of this circle is one of the focus ...
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1answer
52 views

N points in a circle around a point on a sphere.

Consider a 3D sphere: $(x_{c}, y_{c}, z_{c})$ : cartesian coordinates of the center $r$ : the radius Consider a random point on the surface of this sphere of coordinates : $(x_{0}, y_{0}, ...
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0answers
21 views

Separation of the centre of mass coordinates for an N-electron atom

Can anyone tell me how to derive [A8.5] and [A8.6] in Appendice 8 of "Bransden: Physics of solid state matter", in this screenshot: http://i.imgur.com/zSCkVnI.jpg ? It should be easy, but damn me I ...
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0answers
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What does the phrase “uncoupled across coordinate directions” mean in this text?

The following paragraph is from a paper about comparison of maneuvering target tracking models.In the paragraph it talks about constant acceleration models. The above models are simple but crude. ...
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16 views

create local coordinate system with one axis aligned with a line

I have a line from p1=(x1,y1,z1) to p2=(x2,y2,z2) in global coordinate system. I am trying to create a local coordinate system with origin at p1, whose local z axis i.e. z' is aligned with (parallel ...
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0answers
24 views

Integration over length

Trying to integrate over length with natural coordinates I stumbled upon the following equation. Where can I find the explanation of it? Thanks. $$ \int_H L_1^\alpha L_2^\beta \,dH = ...
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0answers
11 views

New Axis calculation

I have a task whereby I use an accelerometer to calculate acceleration for a vehicle. The problem I am attempting to solve is to allow the accelerometer to be in any oriertaion. Basically I have a ...
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0answers
35 views

Differential Operators in different coordinates

How does one show this identity? $$\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}=\frac{\partial^2}{\partial r^2}+{1\over r}\frac{\partial}{\partial r}+{1\over ...
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3answers
156 views

Alternative form of equation of circle?

In a problem set I was solving, one of the solutions used the equation of a circle in the form $$(x-h)^2 + (y-k)^2 + \lambda(ax + by +c) = 0$$ where, $(h,k)$ is any point on the circle $ax+by+c ...
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1answer
58 views

Find the maximum length of a line segment enclosed in a given area

$A = \{ (x, y) : x = u + v , y = v , (u^2) + (v^2) \le 1 \}$ . Then what is the maximum length of a line segment enclosed in this area? My friend suggested the answer $\sqrt{5}$, but I think it ...
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1answer
38 views

Change of Basis - Homework Question

Please help me understand what is being asked, I feel I am missing something. Compute the change of basis matrix for each of the bases, and use it to find the coordinate vector v with respect to B ...
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1answer
111 views

How to determine the direction of one point from another, given their coordinates?

If I have the coordinates of two points, how would I determine what direction the second point lies in, relative to the first point? Specifically, I'm writing an application that involves basically ...
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2answers
26 views

Region closer to one given point than to any other given point

(Q) *Consider 6 points located at P0=(0,0), P1=(0,4), P2=(4,0), P3=(-2,-2), P4=(3,3), P5=(5,5). Let R be the region consisting of all points in the plane whose distance from P0 is smaller than that ...
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1answer
85 views

Problem of a circle tangent to three other circles

Two circles with centres A and B and radii 14 and 7 units respectively touch each other externally. M is the mid point of segment DE and is the centre of the circle with radius 21 units. The two ...
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1answer
25 views

Finding conditions for a point residing in the interior of an ellipse

I have an ellipse with the equation $x^2+2y^2-2xy-1=0$. Suppose $(h,k)$ is a point residing in the interior region of the ellipse. Should this point satisfy any condition in terms of $h,k$?
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0answers
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homogenous coordinate system vs cartesian coordinate

“The homogeneous coordinate system is used in projective geometry as much of the math ends up simpler in homogeneous coordinate space than it does in a regular Cartesian space.” Excerpt From: Haemel, ...
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0answers
38 views

3D cartesian cordinates to 3D isometric cordinates

I am working on Isomer opensource project https://github.com/jdan/isomer and I need to convert 3D cartesian cordinates to 3D isometric cordinates. We already have 3D iso to 2D cartesian ...
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1answer
38 views

Straight Lines and Curves

If the line $y=x\sqrt3$, intersects the curve $x^3+y^3+3xy+5x^2+3y^2+4x+5y-1=0$, in three points $A,B,C$. If $O$ is the origin, then what's the product $OA\cdot OB\cdot OC$?
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1answer
35 views

Rotation of axes help?

This is not a duplicate of my other question in regard to this. I really am not understanding this rotation of axes stuff. If we want to graph a 45 degree shifted ellipse for example, we can think of ...
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1answer
22 views

Y-Coordinate of a Point - Notation

Given point $P$ on curve $\omega$, what expression is generally use to denote the $y$-coordinate of point $P$, also, the $x$-coordinate. Would it be $P_y$? Also, let $\omega$ be in $\mathbb{R}^2$, not ...
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1answer
119 views

Find a point using multilateration or triangulation

Suppose we have 3 points in a 3d coordinate system with the following locations. A=(100,0,0) B=(0,100,100) C=(0,0,100) If there is a 4th point D, where the distances from A, B, and C are known, can ...
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1answer
208 views

Finding the expected value of the length of a minimal spanning tree of n randomly generated nodes bound in a box with edge length a.

Say we specify a number (n) of random points (x,y), bound within the axes and x=a, y=a. Given the number of points and the constraints on the boundaries, how can you calculate the expected value of ...
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1answer
148 views

Finding the locus of a mid-point

Let $A$ be the fixed point $(0, 4)$ and $B$ be a moving point $(2t, 0)$. Let $M$ be the mid-point of $AB$ and let the perpendicular bisector of $AB$ meet the $y$-axis at $R$. Find the locus of the ...
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2answers
70 views

Calculating the expected value of n randomly generated numbers?

Say I have a random number generator that will generate x numbers - not necessarily integers - on the continuous range between a and b. How can I calculate the expected values for these numbers? My ...
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2answers
33 views

Rotation of axes give the same point in space?

I am playing around with rotation of axes formulas and not getting it. I don't understand how this rotates anything when it is just giving you different coordinates for the SAME point in space. How ...