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Everything about Spherical trigonometry
Geometry of figures on the surface of a sphere
Spherical trigonometry is the branch of spherical geometry and trigonometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Spherical trigonometryA 5-minute orientation
- Skim a recent paper: Efficiency Comparison of Quaternions and Spherical Trigonometry Formulas for 3D RotationsInfluential work since 2022
- Pick up a classic book: A treatise on spherical trigonometryThe most-reprinted book on the subject
- Read the landmark paper: Revisiting Spherical Trigonometry with Orthogonal ProjectorsCited 19 times
- Go sideways: Tangent half-angle formulaA closely related topic
- Go sideways: Solution of trianglesA closely related topic
📖 Definitions
Noun A branch of trigonometry pertaining to spherical triangles.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Revisiting Spherical Trigonometry with Orthogonal Projectors
Remembering spherical trigonometry
Plane and Spherical Trigonometry.
Plane and Spherical Trigonometry.
Rotations by spherical trigonometry
New formulas of spherical trigonometry
C53. Partial correlation and spherical trigonometry
LXXIV. Spherical trigonometry reduced to plane
🆕 Influential since 2022
Efficiency Comparison of Quaternions and Spherical Trigonometry Formulas for 3D Rotations
A Mathematical Approach in Ship Navigation: The Integration of Trigonometry and Spherical Triangles in STEM Contexts
SING SPHERICAL TRIGONOMETRY AS A TOOL IN SOLVING TRIANGLES
Implementation of Spherical Trigonometry Qibla Direction Formula with Modern Calculating Tools
The Application of Spherical Trigonometry in Maritime Navigation: From Celestial Observations to Modern Positioning Systems
📚 Books worth reading
A treatise on spherical trigonometryWilliam J. M'Clelland · 1886
The elements of plane and spherical trigonometryJohn Hind · 1828
The Construction of the Wonderful Canon of LogarithmsJohn Russell Napier, William Rae Macdonald · 1889
A short practical treatise on spherical trigonometryOliver Byrne · 1835
Heavenly MathematicsGlen Van Brummelen · 2012
Spherical trigonometryIsaac Todhunter · 1859- 📕The elements of plane and spherical trigonometryJohn Charles Snowball · 1848
- 📕A treatise of plane and spherical trigonometry, in theory and practiceFrancis Nichols · 1811
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Tangent half-angle formula In trigonometry, tangent half-angle formulas relate the tangent of half of an angle to trigonometric functions of the entire angle. The tangent of half…
- Solution of triangles Solution of triangles (Latin: solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths…
- Law of tangents In trigonometry, the law of tangents or tangent rule is a statement about the relationship between the tangents of two angles of a triangle and the lengths…
- Mollweide's formula In trigonometry, Mollweide's formula is a pair of relationships between sides and angles in a triangle. A variant of one of the expressions in more geometrical…
- Law of cosines In trigonometry, the law of cosines (also known as the cosine formula or cosine rule or Al-Kashi’s theorem) relates the lengths of the sides of a triangle…
- Law of sines Law of sines In trigonometry, the law of sines (sometimes called the sine formula or sine rule) is a mathematical equation relating the lengths of the…
- Spherical law of cosines In spherical trigonometry, the law of cosines (or, more specifically, the law of cosines for sides) is a theorem relating the three sides and one of the…
- Hyperbolic triangle In hyperbolic geometry, a hyperbolic triangle is a triangle in the hyperbolic plane. It consists of three line segments called sides or edges and three…