spherical triangle: meaning, definition, pronunciation and examples
LowTechnical / Scientific
Quick answer
What does “spherical triangle” mean?
A figure formed on the surface of a sphere by three arcs of great circles that intersect pairwise.
Audio
Pronunciation
Definition
Meaning and Definition
A figure formed on the surface of a sphere by three arcs of great circles that intersect pairwise.
In spherical geometry, any triangle whose sides are segments of great circles (geodesics) on a sphere, with angles and sides measured in angular units. It is the spherical analogue of a planar triangle in Euclidean geometry.
Dialectal Variation
British vs American Usage
Differences
No significant lexical or definitional differences. Spelling of related terms may follow regional conventions (e.g., centre/center).
Connotations
Identical technical connotations in both varieties.
Frequency
Equally low frequency in specialised academic and technical contexts in both regions.
Grammar
How to Use “spherical triangle” in a Sentence
[Spherical triangle] + [verb: has, is defined by, can be solved][Adjective: right, equilateral] + spherical trianglespherical triangle + [preposition: on, in] + [sphere, celestial sphere]Vocabulary
Collocations
Examples
Examples of “spherical triangle” in a Sentence
adjective
British English
- The spherical-triangle properties were essential for the calculation.
American English
- The spherical triangle properties were essential for the calculation.
Usage
Meaning in Context
Business
Not used.
Academic
Used in university-level mathematics, astronomy, geodesy, and cartography courses and research.
Everyday
Extremely rare; only in highly specific discussions (e.g., advanced navigation).
Technical
Core term in spherical trigonometry, used in astronomy for celestial navigation, satellite geometry, and geodesy.
Vocabulary
Synonyms of “spherical triangle”
Neutral
Weak
Vocabulary
Antonyms of “spherical triangle”
Watch out
Common Mistakes When Using “spherical triangle”
- Treating its side lengths as linear units instead of angular measures.
- Assuming the angle sum is 180 degrees.
- Confusing it with a triangle that is simply 'triangle-shaped' but drawn on a sphere, rather than one bounded by great circles.
FAQ
Frequently Asked Questions
Only if its sides are segments of great circles (the largest possible circles on the sphere, like the equator or lines of longitude). If drawn arbitrarily, it is just a triangle on a curved surface.
Yes, this is possible on a sphere. For example, a triangle with one vertex at the North Pole and two vertices on the equator, separated by 90 degrees of longitude, will have two right angles.
It is used in astronomy (mapping celestial objects), satellite orbital mechanics, global positioning systems (GPS), and long-range aviation and maritime navigation.
The key laws are the Law of Sines and the Law of Cosines for sides and angles, analogous to but different from their plane triangle counterparts. Napier's rules are used specifically for right spherical triangles.
A figure formed on the surface of a sphere by three arcs of great circles that intersect pairwise.
Spherical triangle is usually technical / scientific in register.
Spherical triangle: in British English it is pronounced /ˈsfɛrɪkəl ˈtraɪæŋɡl/, and in American English it is pronounced /ˈsfɪrɪkəl ˈtraɪæŋɡl/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think of slicing an orange: the lines you cut along the peel's surface between three points create a curved, spherical triangle.
Conceptual Metaphor
THE SURFACE OF A SPHERE IS A PLANE (allowing the extension of triangle concepts to a curved surface).
Practice
Quiz
What is a defining property of a spherical triangle?