# 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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### Quaternion to Euler angles conversion

I have written the following MATLAB code for transforming Quaternion to Euler angles based on the mathematical formula from wikipedia: ...
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### complex number multiplication by a real number [closed]

I'd like to multiply a complex value by a real integer. I know that multiplication of complex numbers is similar in the polar form, but the way I know and have been taught is to multiply the two real ...
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### Cartesian to spherical coordinate :MATLAB program

I am a beginner to MATLAB. I have written this function, but don't understand what is wrong. I have used a if statement to correct the phi. Say if i use (x,y,z) = (0,-4,3) i should get (5,270,53.13) ...
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### Recognising patterns and turning it into a formula

On a coordinate plane lets name a move dot A. The dot A moves each day. On day 1, it moves 1 in the x- axis direction. On day 2 it moves $2^2$ in the y- axis direction. On day 3 it moves -$3^2$ in the ...
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### Coordinates and formulas

Say there is a moving dot on the coordinate plane. It starts on the coordinates of (0,0). On the 1st day it moves to (1,0) the next, (1,4) then (-8,4) then, (-8,-12), then, (17,-12) and so on. Now I ...
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### Explicit non-singular coordinate system for $S^3$

Define a "non-singular" coordinate system on a manifold as a continuous, everywhere differentiable set of coordinates such that the determinant of the metric tensor $g_{\mu\nu}$ is everywhere ...
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### How to calculate coordinates $(x,y)$ of rotated polygon?

I have coordinates $x,y$ of a point (red point on the image). If I rotate the image with a specific angle (for example 30 degrees) how can I get the coordinates $x,y$ in the new polygon (which is ...
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### Interesting Locus problem

A variable line passes through $P(2,-1)$ and cuts the co-ordinate axes at $A$ and $B$ respectively. $Q$ lies on line AB such that $$\frac{2}{PQ} = \frac{1}{PA} + \frac{1}{PB}$$ Find the locus of ...
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### Diffeomorphism group of product manifold

For a given differentiable manifold $M$, the diffeomorphism group $\mathrm{Diff}\left( M \right)$ of $M$ is the group of all $C^\infty$ diffeomorphisms of $M$ to itself. Consider a product manifold of ...
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### Is there a solution to the equation $tan({\phi})=\frac{0}{0}$

I've been reading about conversion from Cartesian ($x,y,z$) to Spherical (r, $\theta$, $\phi$) coordinates. The formula to find the value of ${\phi}$ is given as: $\tan({\phi})=\frac{y}{x}$ My ...
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### Position of point between 2 points in 3D space

I need to find the position v3 between the given points v1, and v2 and a given distance d in 3D space. I came across this post: Position of point between 2 points which is basically what I need but ...
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### Informations about the cut-locus of a closed geodesic

Let be $(M^2,g)$ a closed riemannian manifold and $c:[0,L]\to M$ a simple closed geodesic on $M$. For each $s\in [0,L]$, let be $n(s)$ a unit normal vector field along to $c(s)$ and $\beta(s)$ the cut ...
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### Is it possible to calculate a surface integral of a vector field when the vector field is described in non-cartesian coordinates?

Every note and book I read about surface integrals of vector fields only show how to solve these integrals when the vector field is in Cartesian coordinates. I'm curious about what would be the right ...
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### A parallelogram between two points on a hexagonal lattice containing all the shortest paths

For any two points on a hexagonal grid with integer coordinates there is a unique parallelogram which contains all of the shortest paths (in terms of taxicab norm) between these points. See the ...
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### Understanding Coordinate transformation under tensor calculus

I am reading the book "Tensor Calculus" by Schaums Outlines and I came across this paragraph. Suppose that in some region of $\mathbb{R^n}$ two coordinate systems are defined and these two systems ...
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### Differential forms should be invariant under coordinate transformations

I am wondering why, if we transform the following differential form, it does not seem to be invariant under the coordinate transformation. The $1$-form on $\mathbb R^2$ is  \omega = \sqrt{x^2 + y^2}...
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### 2D coordinates of rotating a “bent line”?

I have this problem, when I am given a point A an an XY plane, and I need to find the coordinates of a point B that is of a constant distance of my point A, and my OAB angle is fixed (O being the ...
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### I'm looking for a rotation matrix for following transformation

I'm working with a 3D camera and I found out the formula to transform the camera measurements to real world coordinate system when you have a rotation around x and y (no z rotation). http://i.imgur....
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### Prove that an Equilateral cannot have natural number points

Let $OAB$ be an equilateral triangle with $O(0, 0),\ A(m, n),\ B(x, y)$, where $m, n \in \mathbb{N}^{\ast}$ and $x, y \in \mathbb{R}_{+}$. Prove that $B$'s coordinates can't be both natural numbers....
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### find the coordinates of the point that divides the join of A(-1,-7) & B(1,2) internally, in 2:1.

What I wanted to ask was that after finding the coordinates of the point my answer was (1/3, -1) now since the ordinate is -ve doesn't that make this an external division? How can it divide the line ...