Definition

1. Noun:
   • A branch of geometry: Spherical geometry is the mathematical study of figures, shapes, and properties on the surface of a sphere.
   • Non-Euclidean geometry: It is a type of geometry where the parallel postulate of Euclidean geometry does not hold, as it deals with curved, two-dimensional surfaces.

Usage Examples

• Noun:
  • In spherical geometry, the sum of the angles in a triangle is always greater than 180 degrees.
  • Navigators must understand spherical geometry to plot the shortest routes across the Earth's surface.
  • The course covered the basic principles of spherical geometry.

Advanced Usage

• "applications of spherical geometry": Refers to the practical uses of this mathematical field.

  • Astronomy and cartography are key fields that rely on applications of spherical geometry.

• "principles of spherical geometry": Denotes the fundamental rules and theorems of this system.

  • Understanding the principles of spherical geometry is essential for global positioning systems.

Variants and Related Words

• Spherical trigonometry (n): A specific branch of spherical geometry dealing with triangles on a sphere and their relationships between sides and angles.

  • Calculating great-circle distances requires the use of spherical trigonometry.

• Elliptic geometry (n): A broader term often used synonymously with spherical geometry, though technically it refers to the geometry of a space with constant positive curvature.

  • Spherical geometry is a simple model of elliptic geometry.

Synonyms

• Non-Euclidean geometry: A general term for geometries that differ from the flat-plane geometry of Euclid.
• Geometry of the sphere: A descriptive synonym.

Related Phrases

• Great circle: The largest possible circle that can be drawn on a sphere, representing the shortest path between two points in spherical geometry.

  • An airplane's flight path often follows a great circle.

• Spherical triangle: A triangle formed by arcs of great circles on a sphere's surface.

  • A spherical triangle has three angles and three sides measured as angles at the sphere's center.

Noun

1. (mathematics) the geometry of figures on the surface of a sphere