spherical triangle: meaning, definition, pronunciation and examples

Low
UK/ˈsfɛrɪkəl ˈtraɪæŋɡl/US/ˈsfɪrɪkəl ˈtraɪæŋɡl/

Technical / Scientific

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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

strong
solve a spherical trianglearea of a spherical triangleright spherical triangleoblique spherical triangleangles of a spherical triangle
medium
spherical triangle on a globeproperties of a spherical trianglevertices of a spherical trianglespherical triangle formula
weak
navigation spherical triangleastronomical spherical triangledraw a spherical trianglegeometry spherical triangle

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

spherical trigon

Weak

triangle on a spherenon-Euclidean triangle

Vocabulary

Antonyms of “spherical triangle”

plane triangleEuclidean triangleflat 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

Fill in the gap
In celestial navigation, the position of a star relative to an observer forms one vertex of a that can be solved using spherical trigonometry.
Multiple Choice

What is a defining property of a spherical triangle?