Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [spheres]

For geometrical problems involving spheres. Use the tag (geometry) as well. For intrinsic geometry of spheres, see (spherical-geometry).

An $n$-sphere is $$ S^n = \{\mathbf x \in \mathbb{R}^{n+1}\mid \lVert x \rVert_2 = 1\} $$ Its enclosed volume is the $(n+1)$-ball.

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About exterior(interior) sphere condition

We say that a domain $\Omega \subset \mathbb{R}^n$ satisfies the exterior (interior, resp.) sphere condition if for any $x\in \partial \Omega$, there exist a sphere $B_r(y) \subset \mathbb{R}^n \setminus \Omega$ ($B_r(y) \subset \Omega$, resp.) and…
MKim
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Immersion of sphere into $\mathbb{R}^2$

This is the first time I ask a question, and as a French I will probably make a few mistakes. Sorry for that. I want to show that there are no immersions between sphere and plane (in particular, I want to show that there is no immersion between $S^2…
jocelinbordet
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How to calculate dimensions of a pyramid consisting of spheres?

I have found an image that shows my problem pretty well. At the top, you can see a single phere stacked ontop of three other ones. Let's say the radius of all the spheres is a. I would like to calculate the height of a pyramid consisting of 4 such…
CodeSharpMarvin
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Collection of all smooth/continuous functions on n-Sphere in

Is there way to represent the collection of all smooth/continuous functions invariant under the antipodal map on the surface of the n-Sphere in the n+1 dimensional real space? In other words, is there a finite set of smooth continuous functions,…
student509
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Tangent to sphere in a given plane

I have a sphere centered on the origin $O$. I have a point in space $Cam$ and a vector $Dir$. How do I find a point $X$ and a Vector Hor where: The line starting at Cam and of direction Hor, passing through X, is tangent to the sphere in X Hor, Dir…
blackrack
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Why do we say that if two solid spheres intersect, circle will be a shape formed?

Why do we say that if two solid spheres intersect, the result will be as follows ? https://bit.ly/34NRMTF Empty ( Right, because everything is possible in reality plus virtuality) Point (Right, because they touch at one single point) Sphere…
Nikhil Sharma
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Two Sphere inside a cube

Find the radius of the largest possible sphere inside a cube when two sphere of equal radii are made to sit inside a cube of side $x$. My approach: since it is easier to start with single sphere, do that and find the distance between the sphere…
George carlin
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Sphere packing in spherical shell

What is the maximum number of spheres of radius $R$ that can be packed into a spherical annulus of inner radius $R_i$ and outer radius $R_o$? Is there an answer for this question? I am not a mathematician, and am overwhelmed by the language in some…
April
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Existence of a Binary Operation on the 3-sphere Derived from Compactification of 3-dimensional Real Topological Space

I realize this isn’t a well-put mathematical question, but it has been bugging me and so I ask it in hope of getting some feedback. The one point compactification of 3-dimensional Real space $\mathbb{R}^3$ is homeomorphic to the 3-sphere $ S^3$. I…
Wolf
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How far is it from the equator to the north pole if you keep going northeast?

You may simplify Earth as a sphere with 40 Mm circumference. I thought about it when I read the Mercator projection has straight lines for constant bearing courses. You'd spiral around the north pole infinite times, and the line on the Mercator…
darsie
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Moving a point on a sphere

I have a sphere and a point on it. Now I want to move this point in the direction of a randomly choosen angle "a" for for the arc length "l", over the surface of the sphere. What are the mathematical equations for that? I thought about maybe using…
jackjuni
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Finding Sphere radius given radius of intersecting circle and distance from the top of the sphere

How can I find the radius of a sphere if I am given the radius of an intersecting circle- 24cm. The only other unit I am given is the distance from the center of the circle to the top- most point of the sphere- 32cm. How would I go about solving…
Nandha
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dimension of a shape on sphere

I want to design soccer ball panels in solidworks software . I want to know dimension of a shape on sphere (like length and width) and i know sphere radius. For example i want to know dimesion of the surface in attachment picture.in this picture a…
k.h
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How to efficiently calculate point coordinates on a multi-dimensional sphere?

I have the radius of the multi-dimensional sphere plus angles for each dimension-1. I know I can use sin/cos functions to obtain coordinates, but is there a computationally faster way exists?
aleksv
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Distance between point on sphere

I have a sphere and 2 points on it. I know everything about these points to be able to define them in 3 dimensional space with both cartesian coordinate system and polar coordinate system (x, y and z position of the points; angles and radius). I…
Bálint
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