geometry as on the surface of a sphere, where "lines" are great circles and any pair of lines must intersect

# Questions tagged [spherical-geometry]

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### Do the $2^n$ hyper-octants of a $n$-sphere always have a $n$-dimensional right angle? Is $\pi/2$ only fundamental in $2$ and $3$ dimensions?

In $2$ dimensions, a $2$-sphere can be divided into $2^2 = 4$ congruent pieces, the $4$ quadrants, each of angle $\pi/2$ radians.
In $3$ dimensions, a $3$-sphere can be divided into $2^3 = 8$ congruent pieces, the $8$ octants, each of angle…

Sargas

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### How can I calculate my position, if I have 3 points coordinates and distance?

How can I calculate my position, if I have 3 points coordinates and distance from every coordinate to my position. All coordinates by longitude and latitude.This is example

Ahmed Safanov

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### Angle between two position vectors on a sphere

I'm trying to find a general formula for the dot product of two position vectors of two points on a unit sphere given their latitude and longitude coordinates but I'm not sure how to find the angle between the vectors. Could someone help me figure…

FarmerZee

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### 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. In the image you can see
1. There is a Sphere with…

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### Determine orientation of spherical polygon without trig functions

Is there a way of testing the orientation of a spherical polygon given an ordered list of its vertices that doesn’t involve computing (inverse) trigonometric functions? The polygon is not necessarily convex but it partitions the sphere in a way that…

taylor swift

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### Isometry on the sphere

We know that an isometry $A$ on the sphere is an involution if $A^2=I$. My question would be if the product of two involutions is an involution?
I think is not but I do not know how to prove it.

Mark S

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### How to find radius?

When I am given centre of circle and a tangent of the circle. How can I get radius? I know radius is perpendicular to tangent so I applied distance foormula but what I got is ^2 of actual answer

user163054

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### solving spherical right triangle

How would I go about solving a spherical (right) triangle in the ambiguous case? There are two answers for $m\angle ABC$. I am given the following for:
$m\angle ACB = 90^\circ$, $AC = 2$, $BC = 1$ and $C$ is the midpoint of $AD$.
Using spherical…

user237975

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### Find all Equiangular Platonic triangles

A spherical triangle A is called equiangular if its 3 angles are equal. A is called Platonic if copies of A tile the unit sphere. I need to find all such triangles. Don't we have an infinite amount of them? Any input would be appreciated.

John.P

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### Determining North-South Line Via Watch Method: Theory & Reason

I recently read that if you're in the northern hemisphere and have an analog watch, then you can point the hour hand at the sun and know that a south line lies between (bisection) the hour hand and the 12 o'clock position:
Apparently the trick…

user266250

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### Lines through a point on sphere intersecting at antipodal points

Consider a line through a point p on a sphere, now take another line passing through that point. It is found that the second line always intersects the first line in antipodal points. How do I write a mathematical proof that this is always the…

A plate of momos

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