spherical triangle
Definition
Noun: A spherical triangle is a geometric figure on the surface of a sphere, formed by connecting three points with the arcs of three great circles. Unlike a triangle in plane (Euclidean) geometry, its sides are measured as angular distances (e.g., in degrees) and its angles sum to more than 180 degrees.
Usage
The term is used in spherical geometry, astronomy, and navigation to describe and calculate relationships on a curved surface. - In astronomy, the celestial sphere is often divided into spherical triangles for mapping the positions of stars. - Navigators used the properties of a spherical triangle to calculate a ship's position from celestial observations.
Advanced Usage
- Solving a spherical triangle: Refers to the process of finding unknown sides or angles using formulas like the spherical law of sines or cosines.
- To determine the shortest flight path, the pilot had to solve the spherical triangle defined by the departure city, the destination, and the North Pole.
Variants and Related Words
- Spherical trigonometry (n): The branch of mathematics dealing with the relationships between the sides and angles of spherical triangles.
- Understanding spherical trigonometry is essential for precise global positioning.
- Spherical polygon (n): A more general term for a closed figure on a sphere formed by arcs of great circles.
- A spherical triangle is the simplest type of spherical polygon.
Synonyms
- Spherical trigon (n): A less common, synonymous term.
Related Concepts (Not Phrasal Verbs or Idioms)
- Great circle: A circle on the surface of a sphere whose center is the sphere's center. The sides of a spherical triangle are arcs of great circles.
- Spherical excess: The amount by which the sum of a spherical triangle's angles exceeds 180 degrees.
Noun
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a spherical polygon formed by the arcs of 3 great circles
