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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Direct product of spheres with constraint

Suppose we have a space which is a direct product of 1-spheres: $\mathbb{S}^1\times\mathbb{S}^1\times...\times\mathbb{S}^1 = \mathbb{T}^N$ (the total number of spheres = $N$), or 2-spheres:…
Philipp
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Distance Between Planes Splitting a Sphere

Consider two planes, which are parallel, intersecting a sphere of radius $1$, such that the volume between the planes is half the volume of the sphere. Then, compute the minimum distance between the two planes. Here is what I've done so far. I tried…
YDP
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How can I find Z on a hemisphere providing X/Y coordinates?

Forgive me as I am a programmer, not a mathematician. I have a rectangular plane that I am drawing shapes onto, I want to create an effect where coloured shapes traveling to the outer edges of this rectangle become more and more faded in an oblong…
James T
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Find the center and radius of a sphere

Find the center and radius of a sphere that has $(1,-2,4)$ and $(3,4,-12)$ as endpoints of a diameter. Okay. I Understand how to find radius. It is merely the distance formula applied to a sphere. However, I am having trouble trying to find the…
user152810
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Find Volume of Sphere w/ Radius of Spherical Cap

I'm trying to create a sphere around one known dimension - the radius of what would be a spherical cap. The spherical cap would have a volume equal to one-third the volume of the whole sphere. radius of spherical cap, r=692.820323
user208187
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If a point equally distant of the vertices of a regular tetrahedron, does this mean it is the center of the sphere circumscribed in that tetrahedron?

If a point equally distant of the vertices of a regular tetrahedron, does this mean it is the center of the sphere circumscribed in that tetrahedron? Hope one of you can help me! Thank you!
IONELA BUCIU
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Great Circle on unit sphere with $M=(0,0,0)$ and normal vector of great circle plane $(n_x,n_y,n_z)$

Given: a unit sphere S with $M:=(0,0,0)$ and a normal unit vector $n_0:=(n_x,n_y,n_z)$ to a plane E containing $M$, further a parameter $t \in [0,2\pi)$. The intersection of S and E defines a great circle C with center $M$. Wanted: a parametric…
peets
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Solving equation of a sphere for one variable. Is there an explicit solution?

I have the following equation: $$(q\sin(\phi)\cos(\theta)-a)^2 + (q \sin(\phi)\sin(\theta)-b)^2 + (q \cos(\phi) -c)^2 =r^2$$ I am given $q,r,a,b,c$. I am able to choose either $\phi$ or $\theta$ but not both. I then have to solve this equation for…
Stan Shunpike
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How to find the percentage change in size for a cylinder/sphere like object?

I have an object of more or less unknown shape and I'm trying to find the size change over time. The object is a cancer tumor and from each scan I get two numbers. Scan 1: 3.0 x 3.6 Scan 2: 1.5 x 1.3 Eyeballing the numbers I would say it is a >50%…
Gary
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Sufficient Condition on the existence of an intersection between N spheres

I have this problem to solve: Given N spheres with centers C : {$c_1, ..., c_n| c_i ∈ R^M$} and radiuses R : {$r_1, ..., r_n| r_i ∈ R$} I'm searching for a sufficient condition which states that exists a region that is part of each sphere. For N = 2…
NooneBug
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Sphere volume. Calculation formula from school textbook.

I had a question from the course of school stereometry: why is the volume of a ball calculated exactly according to the formula $V=\frac{4}{3} \pi R^3$, why is $4/3$ used? I did not find the necessary information in the textbook and on the…
Daria
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Lunar Landing Proof.

Given the size of sphere 1, the dimensions of one reference point, the visible curve on sphere 1. What size is sphere 2 at 238,900 mi away? [Picture from Apollo 11] https://images-assets.nasa.gov/image/6900994/6900994~orig.jpg [Moon Radius] Mean…
Anthony Meadows
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How can there be calculation methods other than the cross-sectional area and volume of the sphere using angles?

enter image description here How can there be calculation methods other than the cross-sectional area and volume of the sphere using angles? I am a very poor English speaker. But now it is very frustrating and there is nowhere to ask for help. It…
데구르
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The volume enclosed by a sphere of radius $r$ is $\frac{4}{3} \pi r^3$

The volume enclosed by a sphere of radius radius $r$ is $\frac{4}{3} \pi r^3$. The surface area of the same sphere is $4\pi r^2$. You may already have noticed that the volume is exactly $\frac{1}{3}r$ times the surface area. Explain why this…
Amy
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The centre of the sphere lies on the plane or not

An equation of the sphere is given:$$x^2+y^2+z^2+2x-4y-2z+1=0$$ then the centre of the sphere lies on the plane $2x-4y-2z+1=0$ or not ? My attempt - the the centre of the sphere is $(-1,2,1)$ which is not equal to DRS of the plane.So the centre of…
mSourav
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