# Questions tagged [spheres]

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

1,028 questions
Filter by
Sorted by
Tagged with
16 views

### Nearest intersection point to the center of multiple spheres

I have multiple spheres with the same radius r, and I need to find the nearest intersection point to the center of all the spheres. I also know that all the spheres intersect together. I'm using ...
30 views

7 views

### Derive expression for surface area $(n-1)$-sphere in hyperbolic space

The answer is $A(r) = n \frac{\pi^{n/2}}{\Gamma(n/2)}\sinh^{n-1}(r)$ as is given in (3.2) of this paper or in eqn III.4.2 of Riemannian Geometry: A Modern Introduction. However, neither source offers ...
24 views

### The plane x+2y+3z=12 cuts the coordinate axes A,B,C Find the equation of circle circumscribing the triangle ABC.

The plane x+2y+3z=12 cuts the coordinate axes A,B,C Find the equation of circle circumscribing the triangle ABC. IN my textbook they are using equation of circle as x^2+y^2+z^2+2ux+2vy+2wz+d=0. but to ...
30 views

### Trigonometric functions as a ball

I cannot stop thinking how these trigonometric functions look like the surface of a sphere in 2D... could this mean that where functions are not defined or are as infinite or minus infinite, we can ...
56 views

### What is the distance between the centre of the sphere and the vertex of the cone?

A hollow right circular cone rests on a sphere as shown in the figure. The height of the cone is $4$ metres and the radius of the base is $1$ metre. The volume of the sphere is same as that of the ...
17 views

### The radius of a sphere is measured as 5 cm ± 0·1 cm. Use differentiation to find the volume of the sphere in the form Vcm^3 ± bcm^3.

I have tried: V = 4/3πr^3 If the radius is 5 ± 0·1, then V = 4/3π(5 ± 0·1) ^3 giving V = 555.65 or V = 492.81 The provided solution is (524 ± 31) cm^3 but I am not sure how you derive this result. ...
6 views

### Compute ND Triangulation from Pairwise Distance Matrix

Is there a way to compute a triangulation of points (e.g. triangles that approximate the surface of a 2-sphere) from a pairwise distance matrix in n-dimensions? So far, what I've found is from ...
38 views

44 views

### volume of intersection of a plane and a sphere [closed]

given a,b,c,d in R. what's the volume of: $ax+by+cz<d; x^2+y^2+z^2<1$. I've tried using polar coordinates, but got a really hard integral. Is there a way to solve it with integrals?
177 views

### How to find the distance along a sphere from an angle?

Imagine there are two points on planet Earth and a light is shone from one to the other by reflecting off an object 500km up (think of this as a mirror oriented parallel to the surface right below it)....
13 views

36 views

### Manipulating the product of the dot product of multiple vectors is producing a paradox

Unless otherwise indicated all defined vectors lie on the surface of the unit sphere (i.e their norm is 1). Let's take the following expression: $(V\cdot Z_1)(V\cdot Z_2) = V^TZ_1V^TZ_2$ Given that ...
22 views

### About points in the circle of sphere surface

here is the image Hey guys! I’m so sorry for the silly question but my math skills are very poor and I just need this problem fixed. I made a simple image about it and I hope it won’t confused you. ...
35 views

### Distance between points maximally distributed on n-dimensional unit sphere?

This problem arose in some of my own personal data science research and I am wondering if anyone has encountered this before. Consider $k$ points that lie on an $n$-dimensional unit sphere such that ...
34 views

### Hairy ball theorem for $S^2$ [duplicate]

It is well-known that there is "no" nowhere vanishing continuous tangent vector field on $S^2$, by the so-called Hairy-ball theorem. But then, is there a continuous tangent vector field on $S^2$ which ...
8 views

### Number of points on a sphere with known average diameter and distance between points

I try to find the best solution of a mathematical problem. I know the diameter of a sphere, lets say 10 +- 1 cm. I would like to estimate the number of points on the surface of this sphere, with a ...
49 views

### A geodesic on a unit sphere

Points $A(\cos\alpha,0,\sin\alpha)$ and $B(0,\cos\beta,\sin\beta)$, $(0<\alpha$ and $\beta<\pi/2)$ are on a unit sphere and $l$ is the shortest line (geodesic) between $A$ and $B$ on the sphere. ...
14 views

### Angle of horizontal polarization on a sphere

Given the following geometrical problem: linear polarized waves arrive with a certain angle on a sphere. Dependent of the location on the sphere, the angle of the incoming plane wave varies (see ...
107 views

### Curse of dimensionality $2^d +1$ hyperspheres inside a hypercube

Consider a $d-$dimensional hypercube $Q$ of side length $l ∈ R, i. e. |x_i − y_i | ≤ l$ for all $x, y ∈ Q$ and all $i ∈ [d]$. Note that $Q$ has $2^d$ corners. We fill $Q$ with ($L_2-)$hyperballs the ...
27 views

### Minimizing costs of a specific geometry shape

I have geometry mathematical problem. I have a shape that is made of a cylinder and two half spheres as to top and bottom. How can I minimize the cost of this shape when the volume is known and the ...
20 views

### How many parameters does the set of all spheres, which satisfy the given condition, depend on?

How many parameters does the set of all spheres, which satisfy the given condition, depend on? (i) Spheres that pass through the given point. (ii) Spheres that touch the given line (iii) Spheres that ...
52 views

### Why is the surface area of a sphere not $2 ( \pi r)^2$?

I was trying to derive the formula for the surface area of a sphere and thought of deriving it this way. If we have a circle with radius $r$ and we rotate it along its center by $180$ degrees, the ...
25 views

### How many points on a sphere whose distance is greater than $\epsilon$

I have a "simple" question, but my first researches are not very successful. Given a dimension $d$ and a distance $\epsilon$, is there a standard lower bound on the number of points $N(d,\epsilon)$ ...
37 views

### Find longitude intersection of known latitude at z=0 for a globe?

I have a globe image that is centered at lat,lon. At this lat,lon, by definition x=0, y=0, z=1. A line of latitude drawn on this map can either be completely visible (in which case it would be drawn ...
14 views

### Given a matrix nxd, what is the radius of its hypersphere?

Given the matrix: Centered on μ=0 What would be the radius of its hypersphere?
15 views

### When rotation a sphere $90^{\circ}$ away from you and then $90^{\circ}$ counter-clockwise, what point is either fixed or sent to its antipode?

There's a theorem in Algebraic Topology that says any continuous map $f \colon S^{2n} \rightarrow S^{2n}$ has either fixed points or sends a point to its antipode. Let $f$ be the function described ...
54 views

### Homotopy groups of $S^\infty$

I have seen that it is possible to see $S^\infty$ is contractible, which gives trivial homotopy groups $\pi_k(S^\infty)=0$ for all $k\geq1$. Are there different proofs to show the homotopy groups are ...
47 views

### Curvature and torsion of coordinate curve on the sphere [closed]

find the curvature and torsion of a $v=v_0$ (= constant) coordinate curve on the sphere $x(u,v)= (a.\cos u.\sin v$, $a.\sin u .\sin v$, $a.\cos v$), $\;0 < u < 2\pi$ , $0 < v < \pi$ I ...
7 views

46 views

### Haar measure on unit sphere

I am reading a paper where weak solutions to the Euler equations should be found by using the concept of convex integration. Therefore the proofs are very short and I've got some problems ...
38 views

### A sphere can be everted, but a spherical vector field can not - why?

As can be seen here a sphere can be smoothly and continuously turned inside-out by a process called "sphere eversion". Let's call this scenario A. On the other hand a 3d-unit-vector-field defined on ...
46 views

### A different perspective of sphere eversion?

Usually the process of sphere eversion starts with a sphere whose normals are pointing outward, undergoes some spatial transformation without creasing or pinching (a homotopy), usually using a halfway-...