Everything about Sphere
Set of points equidistant from a center
A sphere is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the center of the sphere, and the distance r is the sphere's radius. The earliest known mentions of spheres appear in the work of the ancient Greek mathematicians. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: SphereA 5-minute orientation
- Skim a recent paper: Cooperative Coupling of H 2 O 2 Production and Organic Synthesis over a Floatable Polystyrene‐Sphere‐Supported TiO 2 /Bi 2 O 3 S‐Scheme PhotocatalystInfluential work since 2022
- Pick up a classic book: FlatlandThe most-reprinted book on the subject
- Read the landmark paper: HEALPix: A Framework for High‐Resolution Discretization and Fast Analysis of Data Distributed on the SphereCited 5,431 times
- Go sideways: Spherical circleA closely related topic
- Go sideways: Gaussian curvatureA closely related topic
📖 Definitions
Noun A surface in three dimensions consisting of all points equidistant from a center. .
Noun An object which appears to be bounded by a sphere; a round object, a ball.
Noun The celestial sphere: the edge of the heavens, imagined as a hollow globe within which celestial bodies appear to be embedded.
Noun Any of the concentric hollow transparent globes formerly believed to rotate around the Earth, and which carried the heavenly bodies; there were originally believed to be eight, and later nine and ten; friction between them was thought to cause a harmonious sound (the music of the spheres).
🏆 Landmark papers (most cited)
HEALPix: A Framework for High‐Resolution Discretization and Fast Analysis of Data Distributed on the Sphere
Dispersion on a Sphere
Rethinking the Public Sphere: A Contribution to the Critique of Actually Existing Democracy
Equation of motion for a small rigid sphere in a nonuniform flow
The lift on a small sphere in a slow shear flow
Phase Transition for a Hard Sphere System
Solutions for effective shear properties in three phase sphere and cylinder models
Control and information in the intrapersonal sphere: An extension of cognitive evaluation theory.
🆕 Influential since 2022
Cooperative Coupling of H 2 O 2 Production and Organic Synthesis over a Floatable Polystyrene‐Sphere‐Supported TiO 2 /Bi 2 O 3 S‐Scheme Photocatalyst
Selective Degradation of Electron-Rich Organic Pollutants Induced by CuO@Biochar: The Key Role of Outer-Sphere Interaction and Singlet Oxygen
Reflections and Hypotheses on a Further Structural Transformation of the Political Public Sphere
Transition Metal Catalysis Controlled by Hydrogen Bonding in the Second Coordination Sphere
Second and Outer Coordination Sphere Effects in Nitrogenase, Hydrogenase, Formate Dehydrogenase, and CO Dehydrogenase
📚 Books worth reading
FlatlandEdwin Abbott Abbott · 1884
BollandDionys Burger · 1957
Mine ventilation and air conditioningHoward L. Hartman · 1961
A beautiful questionFrank Wilczek · 2015
A treatise on the circle and the sphereCoolidge, Julian Lowell · 1916- 📕Spherical Geometry and Its ApplicationsMarshall A. Whittlesey · 2019
The music of the heavensBruce Stephenson · 1994- 📕The soul as sphere & androgyneKeith Critchlow · 1980
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Spherical circle In spherical geometry, a spherical circle (often shortened to circle) is the locus of points on a sphere at constant spherical distance (the spherical…
- Gaussian curvature In differential geometry, the Gaussian curvature or Gauss curvature (symbol Κ, named after Carl Friedrich Gauss) of a smooth surface in three-dimensional…
- Intersection (geometry) In geometry, an intersection between geometric objects (seen as sets of points) is a point, line, or curve common to two or more objects (such as lines…
- Cylinder A cylinder (from Ancient Greek κύλινδρος (kúlindros) 'roller, tumbler') has traditionally been a three-dimensional solid, one of the most basic of curvilinear…
- Analytic geometry In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts…
- Great circle In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a diametral plane, which is a plane passing through the sphere's…
- Circle A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point of…
- Coordinate system In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points…