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	ABOUT: [Introduction][History][Related areas][Subfields] POINTERS: [Texts][Software][Web links][Selected topics here] 52A55: Spherical Geometry

Introduction

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.

History

Applications and related fields

Subfields

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

Textbooks, reference works, and tutorials

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

Software and tables

Other web sites with this focus

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

Selected topics at this site

• 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?