Linked from

The 30 pages that link to Spherical geometry, each with the reason it gives.

• Euclidean geometryBroader topic: Great-circle triangles demonstrate how curvature changes Euclidean angle and distance rules.

• Pythagorean theoremBroader topic: Spherical right triangles obey a trigonometric relation rather than the Euclidean sum of squared sides.

• Euclidean spaceCompared with: Its curved surface gives triangle angles and geodesics unlike Euclidean geometry.

• Non-Euclidean geometryBroader topic: It provides a concrete setting where triangle angles exceed 180 degrees.

• Hyperbolic geometryCompared with: It has positive curvature, contrasting with hyperbolic geometry’s negative curvature.

• Solid angleNarrower topic: Solid-angle regions are spherical areas, so spherical geometry describes their shape.

• Great circleNarrower topic: Great circles serve as the spherical geometry’s counterpart to straight lines.

• Plane (geometry)Compared with: A sphere curves, so its surface is not a Euclidean plane.

• Parallel postulateBroader topic: It provides a concrete model in which the Euclidean parallel postulate fails.

• Greek mathematicsRelated: It supported calculations on the celestial sphere and the Earth.

• Triangle geometryCompared with: Spherical triangles have angle sums greater than 180 degrees, altering familiar relations.

• Spherical trigonometryNarrower topic: Spherical trigonometry is the triangle-focused part of this broader geometry.

• Euclidean planeCompared with: On a sphere, straightest paths and parallel behavior differ from those in the plane.

• PendentiveRelated: A pendentive’s curved surface is shaped as part of a sphere.

• Elliptic geometryCompared with: Unlike elliptic geometry, its spherical model keeps antipodal points distinct.

• Nikolai LobachevskyCompared with: It shows that changing Euclid’s parallel postulate can yield a different geometry, though not Lobachevsky’s.

• Platonic solidRelated: Projecting a polyhedron's vertices onto a sphere reveals its symmetry and angle structure.

• Geometric proofBroader topic: Its triangles demonstrate that familiar Euclidean angle and parallel results are not universal.

• Great-circle distanceNarrower topic: Great-circle distance is the spherical analogue of straight-line distance in a plane.

• Spherical law of cosinesNarrower topic: The law belongs to a geometry where straight paths are great-circle arcs.

• Spherical triangleNarrower topic: Spherical triangles are the basic polygonal figures of this geometry.

• Spherical excessNarrower topic: Spherical excess is a basic consequence of this geometry’s positive curvature.

• IcosahedronRelated: Projecting the icosahedron's vertices onto a sphere produces a highly symmetric spherical arrangement.

• Anthemius of TrallesRelated: Its curved-surface problems illuminate the geometry relevant to domed architecture.

• Jørn UtzonRelated: A shared sphere made the Opera House's roof segments geometrically compatible.

• Playfair's axiomCompared with: Great-circle lines have no parallels, illustrating a model that violates the axiom.

• Regular icosahedronRelated: Projecting its vertices onto a sphere connects the solid to spherical triangles and symmetry.

• Square degreeNarrower topic: It supplies the surface-area relationships behind angular regions on the sky.

• Filling area conjectureRelated: The hemisphere's curvature and boundary geometry raise questions about rigidity of equality cases.

• Hjelmslev's theoremCompared with: It offers a contrasting curved setting with different triangle angle and congruence behavior.