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[Texts]## 52A55: Spherical Geometry |

This section is supposed to be for "spherical and hyperbolic convexity" but it appears to be the only geometric area focusing on things spherical! So we use it to hold a few posts on spherical geometry.

Parent field: 52A: General convexity.
But there is not yet a page for that; see *its* parent page,
52: Convex and discrete geometry

There is a considerable collection of useful formulas for global navigation and so on at the Aviation Formulary.

- Geometry of spheres (e.g. Girard's Theorem).

- Here is a longish essay on spheres which discusses geometry, trigonometry, and topology. Here are just some comments on basic issues of spherical navigation and so on.
- Many answers -- take your pick -- to the incessantly-asked question, "What's the (great-circle) distance between two points on a sphere (such as Earth) given their latitude and longitude (spherical coordinates): Clairaut's formula.
- Citations and pointers for latitude/longitude calculations
- Numerically stable formula for distances on a sphere
- Where is the point on a sphere determined as being a certain geodesic distance along a fixed arc away from a given point?
- Given two points in spherical coordinates, what's the angle between the rays joining them to the center of the sphere?
- Given three angles as above and two points, where's the third point on the sphere making the appropriate angles? (shows the vector- and trig-calculations necessary).
- What is the relation between the angles as shown above and the angles at the vertices of the resulting spherical triangle?
- Surface area of spherical triangle in terms of sides of the triangle
- Curvature and areas of triangles in spherical/hyperbolic 2-D geometry
- How big is the sphere from which a cap was cut? (Spherical geometry)
- Clairaut's formula: how far north does a great circle pass?

Last modified 2002/01/14 by Dave Rusin. Mail: