spherical geometry

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spherical geometry

A student draws a triangle on a globe to illustrate spherical geometry.

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.
spherical geometry

A student draws a triangle on a globe to illustrate spherical geometry.

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