# Tagged Questions

Questions on spherical coordinates, a three-dimensional coordinate system where a point is represented in terms of its distance from the origin, and its latitude and longitude angles (or complements thereof).

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### How can I pick a random point on the surface of a sphere with equal distribution?

I've got a random number generator that yields values between 0 and 1, and I'd like to use it to select a random point on the surface of a sphere where all points on the sphere are equally likely. ...
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### Surface Element in Spherical Coordinates

In spherical polars, $$x=r\cos(\phi)\sin(\theta)$$ $$y=r\sin(\phi)\sin(\theta)$$ $$z=r\cos(\theta)$$ I want to work out an integral over the surface of a sphere - ie $r$ constant. I'm able to derive ...
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### Can someone please explain the cube to sphere mapping formula to me?

I am wondering if anyone could explain how the following formula works, it is supposed to take the input as a point on a cube then map that to points on a sphere, please go gentle on me, I'm in 9th ...
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### How to perform a Fourier transform in spherical coordinates?

For a function $f(r, \vartheta, \varphi)$ given in spherical coordinates, how can the Fourier transform be calculated best? Possible ideas: express $(r,\vartheta,\varphi)$ in cartesian coordinates, ...
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### Rotating a point in spherical coordinates around Cartesian axis

If I have a point in spherical coordinates, and I rotate it around one of the Cartesian axes, what will be the new spherical coordinates for the point? Both spherical and Cartesian coordinate systems ...
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### Why is the differential solid angle have a $\sin\theta$ term in integration in spherical coordinates?

When you integrate in spherical coordinates, the differential element isn't just $d\theta d\phi$. No. It's $\sin\theta d\theta d\phi$, where $\theta$ is the inclination angle and $\phi$ is the ...
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### What is the general formula for calculating dot and cross products in spherical coordinates?

I was writing a C++ class for working with 3D vectors. I have written operations in the Cartesian coordinates easily, but I'm stuck and very confused at spherical coordinates. I googled my question ...
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### Transformations from n-sphere coordinates to cartesian coordinates.

I was wondering how one would proceed to convert between coordinate systems in $\mathbb R^n$. For $\mathbb R^2$ the conversion is easy and just basic trigonometry. Given $(r, \theta)$ we can ...
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### Surface area of the part of the sphere $x^2+y^2+z^2=a^2$ that is inside the cylinder $x^2+y^2=ax$

I've been solving some surface area problems lately, but I don't think that the same approach that I was using will work with this one (or at least will result in a lot work). So, I believe I should ...
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Given the integral $\int^{1}_{0}\int^{\sqrt{1-x^{2}}}_{0}\int^{\sqrt{1-x^{2}-y^{2}}}_{0} \dfrac{1}{x^{2}+y^{2}+z^{2}}dzdxdy$ I need to evaluate this using spherical coordinates. So far I have that $... 0answers 220 views ###$\operatorname{div}$and$\operatorname{grad}$in spherical coordinates. Formula from general relativity goes crazy I try to calculate the gradient of a function and the divergence of a vector field in spherical coordinates. Nothing special so far, but a formula that I learned in a general relativity lecture ... 0answers 116 views ### Probably Riemann surface integral Here is the integral: May you please suggest some beautiful idea on using Riemann surface, or some Gauss-Ostrogradsky at the beginning. Also, the initial integral looks really symmetric, so maybe ... 1answer 315 views ### why is the laplacian of 1/r equal zero outside the origin? In spherical coordinates, the laplacian can be written as:$\nabla^2 = \frac{1}{r}\frac{\partial^2}{\partial r^2}r + \frac{1}{r^2 \sin \theta}\frac{\partial}{\partial \theta}(\sin \theta \frac{\...
I have two orthogonal vectors $a$, $b$, which lie on a unit sphere (i.e. unit vectors). I want to apply one or more rotations to the sphere such that $a$ is transformed to $c$, and $b$ is transformed ...