geometry as on the surface of a sphere, where "lines" are great circles and any pair of lines must intersect
Questions tagged [spherical-geometry]
889 questions
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c.s.a of a hemisphere
Here is a question which I would like to understand. I want to know
How to prove that c.s.a of a hemisphere is $2\pi r^2$ ?
I'm a 10th CLASS average student,so please keep it simple.
Thank you....
user88232
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Verify whether the centre of a sphere is outside a pyramid whose vertices are given
I have a maths question where the equation of a sphere $S$ is said to be $x^2+y^2+z^2-12x-6y-4z = 0$, and I'm asked to show that the centre is outside the pyramid whose vertices are $A(12,0,0)$, $B (0,6,0)$, $C (0,0,4)$ and the origin. Edit: These 4…
Sebastian
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Equation of a sphere passing 3 points and tangential to a line
I got a maths question that gives you 3 points, $A (6,0,0)$ and $B (6,6,0)$ and $C (0,6,0)$ and a line DG, D being $(0,0,6)$ and $G (0,6,6)$ so the equation of DG is $\vec r$ = 6$\hat i$ -$6t\hat j$ . You're then asked to find the equation of the…
Sebastian
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spherical geometry
A mobile, on the surface of the earth, is at a point A. Travels 200 km south arriving at a point B. Later moves 200 km west arriving at a point C. Finally moves over 200 kilometers to the north, back to point A. Assuming that the surface of the…
Jorge Augusto
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Do two points on the surface of a sphere uniquely describe a great cirlce?
I had a debate with a buddy about this. He said you could get a chord by drawing the triangle formed by the two points and the center of the sphere and that chord corresponds to a single great circle arc. I can get to the chord but then projecting…
Frank Conry
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Longitude, Latitude Question. Converting distance in miles to longitude and latitude
Let's say I have some points on a map. Point one is at a longitude of -48.6 and a latitude of 38.8. Point 2 on the map is at a longitude of 52.1 and a latitude of 30.3. A line between these two points can be called A.
I would like to find 2 point…
tfr950
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Closure condition of spherical polygons
Given an open spherical polygon of geodesic edge length $L_i$ ($i=0,..,n$) and anterior spherical angles $A_i$ ($i=0,..,n-1$). My question is what are sufficient and nessecary conditions on the lengths of arcs $L_i$ and on $A_i$ for the closure of…
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Given a spherical triangle ABC and a point P, find (u, v) for slerping
Hmm. Where am I going wrong? Firstly, I apologise, I'm only a programmer, and skinny also, not a maths bod.
Everything is on the unit sphere
I have a spherical equilateral triangle ABC and a 2D co-ordinate (u, v). I construct P using slerp:
D =…
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to find volume of spherical tetrahedron and triangle area
I have two question though they are different in some way
Could any one tell me how to find area of spherical triangle in a easiest way?
How to find the volume of Spherical tetrahedron! which is in $S^3$ embedded in $\mathbb{R}^4$
Thank you for…
Myshkin
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Spherical geometry beginner exercise
Let $x,y \in \mathbb{R}^3: x = (0,0,-1) , y = (0,1,0)$ . Find the Great Circle that contains $x,y$.
From theory, a Great Circle is the intersection of $S^2 = \{x \in \mathbb{R}^3: ||x|| = 1\}$ and the plane $P = ax+by+cz=0, |a|+|b|+|c|\neq0,…
Alex Matt
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Spherical Geometry (SG) Vs Euclidean Geometry(EG)
Could any one tell me what are the fundamental contrasts with postulates of Euclidean Geometry and Spherical Geometry?
I myself see these things, please tell me if there are more:
Lines in EG are great Circles in SG, we can extend infinitely a line…
Myshkin
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Are Lines of Lattitude Exceptions to Parallel Postulate on Spheres?
The definition of spherical geometry is that there are no parallel lines (as far as I know). But isn't that definiton violated with lines such as lines of lattitude? Or are lines of lattitude in fact not straight?
Rory M. Tims
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How do I bound a circle on the surface of a sphere using coordinates?
Suppose I have a sphere of radius $R$ with a longitude/latitude system on it (i.e. great circle lines for longitude, constant $z$ lines for latitude). Then I place a circle on the surface of the sphere with radius $r < \frac{\pi}{4}R$.
What set of…
Sean Lake
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Three points on a sphere define eight spherical triangles
reading a book of spherical astronomy I've read this:
Three great circles pass through three points on a sphere. If for each great circle we consider only one of the two parts in which it is divided by the two points that determine it, we will have…
C.Baroni
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How fast do great circles on a sphere converge?
Given a sphere with two great circles.
The distance where points on the circles are furthest apart is small compared to the radius.
How do I calculate how fast the two lines converge?
First approximation. They converge linearly. We know at 90…
