# Tagged Questions

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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### How to convert 2D coordinates to 3D coordinates?

I am writing some software for image processing where a user can just draw something (e.g. a cube) in paint and the software will give you the 3d coordinates of the corners on that drawing. What would ...
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### How do I convert an index for a one-dimensional array into x and y?

Given a flat array of values as such, representing a Sudoku board: ...
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### Christoffel symbol in 2D Euclidean-Space

In 2D Euclidean space straight line in $(x,y)$ coordinate $x=x(s)$ and $y=y(s)$ satisfy $$\frac{d^2x}{ds^2}=\frac{d^2y}{ds^2}=0$$ is the Christoffel symbol $\Gamma^a_{bc}=0$ in $(x,y)$ coordinate? ...
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### Coordinates on a Riemannian manifold given by a distance function

I am currently studying the book "Riemannian Geometry" by Petersen. Defintion: Let $(M, g)$ be Riemannian manifold and let $U \subset M$ be an open set. A function $r : U \to \mathbb{R}$ is said ...
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### Collision point of trajectory

I'm wondering how you could determine which object a trajectory hits first. This is quite hard to explain, but I'll try. I only want to consider the initial velocity, initial angles and gravity. I ...
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### Distance between two Polar-Coordinates

I choose two Points in Berlin with the coordinates: 1: lat: 52.511206 long: 13.546486 2: lat: 52.527501 long: 13.319206 With an online tool I got the ...
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### Transforming points between two polar coordinate systems

I have 2 dimensional points (r, theta) defined in a polar coordinate system A, and a second polar coordinate system B with a known homogeneous transform T transforming between A and B in a Cartesian ...
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### Why is it bad to pick basis for a vector space?

Reading `This Week's Finds', http://math.ucr.edu/home/baez/week247.html, I'm informed that one should avoid picking coordinate systems and I'm unsure why that is the case. Any help on the matter is ...
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### eccentricity of the conic

I'm given this question to find the eccentricity of this conic : $x^2 + ky = 0, k>0$ The given equation can be written as $x^2 = -ky$ now we can say compare this with the equation of parabola. But ...
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### d3x - Cartesian to Cylindrical Coordinates

Given is $d^3x = dxdydz$ and I need to convert it to cylindrical coordinates (given through: $x = r\cos\varphi$ and $y = r\sin\varphi$). The expected result is: $(dz)(dr)(r)(d\varphi)$ and I cannot ...
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### Devide line to 3 points

I have two point in a coordinates system, let's say $(x_1,y_1)$ and $(x_2,y_2)$, and I want to find the coordinates of the point that separates the line into 3 parts Like this I want to know the ...
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### Vector Calculus in Curvilinear Coordinates and Index Notation

I am trying to understand how would I use the index notation in curvilinear coordinates. Checking out this reference, I got until this point $$\vec{\nabla} = \sum_a \vec{e}_ah_a^{-1}\partial_a$$ ...
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### Are Cartesian coordinates considered to be curvilinear coordinates?

In the wikipedia page on curvilinear coordinates it is said: "Well-known examples of curvilinear coordinate systems in three-dimensional Euclidean space (R^3) are Cartesian, cylindrical and spherical ...
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### What is the locus of the points of intersection of the lines as shown in the figure?

I don't know if it should matter but the sum of the intercepts the lines make with x and y axis is constant I think. It looks like a hyperbola to me.
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### Loci of intersection of lines with positive intercepts?? [closed]

How does one go about proving the equation of the curve that is formed by tracing the intersection of the lines with each other?
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### How to draw a curve through every point. [closed]

I have x,y coordinates. They are arranged at fixed intervals of 1 unit along the x axis. The Y values are arbitrary. I want to draw smooth curvy line that passes through all of them. Or rather, I want ...
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### Using the Dirac delta function to find the density of point masses/charges

Here is an example from a textbook: Suppose there is a unit charge or unit mass at the point $(x,y,z)=(-1,\sqrt{3},-2)$; then in rectangular coordinates, the ...
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### Get two specific coordinates on a linear function.

I've been trying to build an algorithm for my Unity3D project to get some specific coordinates, but I got stuck with some math problem. I have two coordinates of ...
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### Angle of rotation based on direction cosines

I have a question which is bothering me for days! Suppose that we have a fixed frame $XYZ$ and a moving frame $xyz$ in 3D. The moving frame is orthonormal and is defined based on the fixed one using 9 ...
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### Relative Motion between two rotating frames

I am looking for mathematical relations between equations of motion between two rotating frames. Relating the said motion by first going to a globally fixed frame is not an issue but how to approach ...
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### The existence of a specific kind of coordinate system

Suppose a massive, perfectly spherical ball is fixed on a point in space, and that there is a second free particle of negligible mass. I have noticed that the magnitude of the force exerted on this ...
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### Matrix to represent transformation $T(a_0+a_1t+a_2t^2) = a_1+2a_{2}t$ with respect to a certain basis

I'm having so much trouble understanding this very concept.. This is a problem from the book. The Mapping $T:P_2\to P_2$ is defined by $T(a_0+a_1t+a_2t^2)=a_1+2a_2t$ is a linear transformation. ...
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### formula to locate x and y coordinates from two point with x and y known and distance to third point known as well

updated pictureI am trying to find the formula or at least the name of this operation to locate x and y coordinates for a point from two other reference points with x and y known and distance to third ...
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### Pullback metric, coordinate vector fields..

I'm doing this computation on $\mathbb{R}^3$ with cylindrical coordinates $(r, \theta, z)$, (which aren't defined on the whole of $\mathbb{R}^3$, but I don't care about that) and I seem to get a ...
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### Limiting points

For a system of coaxial circles why are there only 2 limiting points? Shouldn't there be infinite limiting points? After all system of coaxial circles are pairs of circles which have same radical axis,...
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### Calculation of $\min$ distance between $x^2+y^2=9$ and $2x^2+10y^2+6xy=1$
Calculation of $\min$ distance between $x^2+y^2=9$ and $2x^2+10y^2+6xy=1$ $\bf{My\; Try::}$ Using the fact that the distance between two curve is independent of shifting. So put $x=u+v$ and $y=u-v$ ...