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Everything about Spherical circle
Mathematical expression of circle like slices of sphere
In spherical geometry, a spherical circle is the locus of points on a sphere at constant spherical distance from a given point on the sphere. It is a curve of constant geodesic curvature relative to the sphere, analogous to a line or circle in the Euclidean plane; the curves analogous to straight lines are called great circles, and the curves analogous to planar circles are called small circles or lesser circles. If the sphere is embedded in three-dimensional Euclidean space, its circles are the intersections of the sphere with planes, and the great circles are intersections with planes passing through the center of the sphere. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Spherical circleA 5-minute orientation
- Skim a recent paper: Circle packing on spherical capsInfluential work since 2022
- Pick up a classic book: A treatise on spherical trigonometry, by W.J. M'Clelland and T. PrestonThe most-reprinted book on the subject
- Read the landmark paper: Great Circle Tidal Streams: Evidence for a Nearly Spherical Massive Dark Halo around the Milky WayCited 411 times
- Go sideways: Great circleA closely related topic
- Go sideways: SphereA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Great Circle Tidal Streams: Evidence for a Nearly Spherical Massive Dark Halo around the Milky Way
Generalized optical design of two-spherical-mirror multi-pass cells with dense multi-circle spot patterns
A Small Circle of Best Fit for Spherical Data and Areas of Vulcanism
Aberration-reduced holographic spherical gratings for Rowland circle spectrographs
Transition from spherical circle packing to covering: geometrical analogues of chemical isomerization
Establishment and application of drilling sealing model in the spherical grouting mode based on the loosing-circle theory
Circle of least confusion of a spherical reflector
Squaring the circle – A curious phenomenon of fcc single crystals in spherical microindentation
🆕 Influential since 2022
Circle packing on spherical caps
Great circle theorem and the application of the spherical cosine rule to estimate distances on a globe
Combinatorial Calabi flows for ideal circle patterns in spherical background geometry
Constructing geometrical models of spherical analogs of the involute of a circle and cycloid
A New Earth System Spatial Grid Extending the Great Circle Arc QTM: The Spherical Geodesic Degenerate Octree Grid
📚 Books worth reading
A treatise on spherical trigonometry, by W.J. M'Clelland and T. PrestonWilliam John M 'Clelland, Thomas Preston · 1886- 📕al- Maqālah al-thālithah min al-qānūn al-MasʻūdīMuhammad Ibn Ahmad, Abu al-Raihan al-Biruni. · 1965
A treatise on spherical trigonometry, by W.J. M'Clelland and T. PrestonWilliam John M 'Clelland, Thomas Preston · 1885
A Treatise on TrigonometryJames Edward Oliver , George William Jones · 1890- 📕Si ku ti yao zhu lu cong shuXuan Zheng, Dong Hui · 2010
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Sphere A sphere (from Ancient Greek σφαῖρα (sphaîra) 'ball') is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that…
- Spherical geometry Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two-dimensional surface of a sphere or the n-dimensional surface of…
- Lexell's theorem In spherical geometry, Lexell's theorem holds that every spherical triangle with the same surface area on a fixed base has its apex on a small circle,…
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- Great-circle distance The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle…
- Horocycle In hyperbolic geometry, a horocycle (from Greek roots meaning "boundary circle"), sometimes called an oricycle or limit circle, is a curve of constant…
- Beltrami–Klein model In geometry, the Beltrami–Klein model, also called the projective model, Klein disk model, and Cayley–Klein model, is a model of hyperbolic geometry in…