Sphere, the Glossary
A sphere (from Greek) is a geometrical object that is a three-dimensional analogue to a two-dimensional circle.[1]
Table of Contents
205 relations: Abu Sahl al-Quhi, Affine sphere, Affine transformation, Albert Einstein, Alexander horned sphere, Algebraic surface, Analytic geometry, Ancient Greek, Angle, Antipodal point, Apollonius of Perga, Arc length, Archimedes, Astronomy, Australia, Axial symmetry, Axiom, Backscatter (photography), Ball, Ball (mathematics), Ball bearing, Bearing (navigation), Boundary (topology), Bubble (physics), Cavalieri's principle, Celestial sphere, Celestial spheres, Centre (geometry), Channel surface, Chebyshev distance, Circle, Circle of latitude, Circumference, Circumscribed circle, Colatitude, Collinearity, Compact space, Cone, Conic section, Coordinate system, Coplanarity, Cube, Curvature, Curve, Curved mirror, Cylinder, David Hilbert, Density, Derivative, Diameter, ... Expand index (155 more) »
- Elementary shapes
- Homogeneous spaces
- Spheres
Abu Sahl al-Quhi
(ابوسهل بیژن کوهی Abusahl Bijan-e Koohi) was a Persian mathematician, physicist and astronomer.
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Affine sphere
In mathematics, and especially differential geometry, an affine sphere is a hypersurface for which the affine normals all intersect in a single point. Sphere and affine sphere are differential geometry.
Affine transformation
In Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles.
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Albert Einstein
Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who is widely held as one of the most influential scientists. Best known for developing the theory of relativity, Einstein also made important contributions to quantum mechanics. His mass–energy equivalence formula, which arises from relativity theory, has been called "the world's most famous equation".
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Alexander horned sphere
The Alexander horned sphere is a pathological object in topology discovered by.
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Algebraic surface
In mathematics, an algebraic surface is an algebraic variety of dimension two.
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Analytic geometry
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.
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Ancient Greek
Ancient Greek (Ἑλληνῐκή) includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC.
Angle
In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Sphere and angle are Elementary geometry.
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Antipodal point
In mathematics, two points of a sphere (or n-sphere, including a circle) are called antipodal or diametrically opposite if they are the endpoints of a diameter, a straight line segment between two points on a sphere and passing through its center.
See Sphere and Antipodal point
Apollonius of Perga
Apollonius of Perga (Ἀπολλώνιος ὁ Περγαῖος) was an ancient Greek geometer and astronomer known for his work on conic sections.
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Arc length
Arc length is the distance between two points along a section of a curve.
Archimedes
Archimedes of Syracuse was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily.
Astronomy
Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos.
Australia
Australia, officially the Commonwealth of Australia, is a country comprising the mainland of the Australian continent, the island of Tasmania, and numerous smaller islands.
Axial symmetry
Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis.
Axiom
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
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Backscatter (photography)
In photography, backscatter (also called near-camera reflection) is an optical phenomenon resulting in typically circular artifacts on an image, due to the camera's flash being reflected from unfocused motes of dust, water droplets, or other particles in the air or water.
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Ball
A ball is a round object (usually spherical, but can sometimes be ovoid) with several uses.
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Ball (mathematics)
In mathematics, a ball is the solid figure bounded by a sphere; it is also called a solid sphere. Sphere and ball (mathematics) are spheres and topology.
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Ball bearing
A ball bearing is a type of rolling-element bearing that uses balls to maintain the separation between the bearing races.
Bearing (navigation)
In navigation, bearing or azimuth is the horizontal angle between the direction of an object and north or another object.
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Boundary (topology)
In topology and mathematics in general, the boundary of a subset of a topological space is the set of points in the closure of not belonging to the interior of.
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Bubble (physics)
A bubble is a globule of a gas substance in a liquid.
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Cavalieri's principle
In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows.
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Celestial sphere
In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. Sphere and celestial sphere are spheres.
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Celestial spheres
The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus, and others.
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Centre (geometry)
In geometry, a centre (British English) or center (American English) of an object is a point in some sense in the middle of the object. Sphere and centre (geometry) are Elementary geometry.
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Channel surface
In geometry and topology, a channel or canal surface is a surface formed as the envelope of a family of spheres whose centers lie on a space curve, its directrix. Sphere and channel surface are surfaces.
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Chebyshev distance
In mathematics, Chebyshev distance (or Tchebychev distance), maximum metric, or L∞ metric is a metric defined on a real coordinate space where the distance between two points is the greatest of their differences along any coordinate dimension.
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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. Sphere and circle are Elementary shapes.
Circle of latitude
A circle of latitude or line of latitude on Earth is an abstract east–west small circle connecting all locations around Earth (ignoring elevation) at a given latitude coordinate line.
See Sphere and Circle of latitude
Circumference
In geometry, the circumference (from Latin circumferens, meaning "carrying around") is the perimeter of a circle or ellipse.
Circumscribed circle
In geometry, a circumscribed circle for a set of points is a circle passing through each of them.
See Sphere and Circumscribed circle
Colatitude
In a spherical coordinate system, a colatitude is the complementary angle of a given latitude, i.e. the difference between a right angle and the latitude.
Collinearity
In geometry, collinearity of a set of points is the property of their lying on a single line.
Compact space
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. Sphere and compact space are topology.
Cone
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex. Sphere and cone are Elementary shapes and surfaces.
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Conic section
A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane.
Coordinate system
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
See Sphere and Coordinate system
Coplanarity
In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all.
Cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces. Sphere and cube are Elementary shapes.
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Curvature
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane.
Curve
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Sphere and curve are topology.
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Curved mirror
A curved mirror is a mirror with a curved reflecting surface.
Cylinder
A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. Sphere and cylinder are Elementary shapes and surfaces.
David Hilbert
David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician and one of the most influential mathematicians of his time.
Density
Density (volumetric mass density or specific mass) is a substance's mass per unit of volume.
Derivative
The derivative is a fundamental tool of calculus that quantifies the sensitivity of change of a function's output with respect to its input.
Diameter
In geometry, a diameter of a circle is any straight line segment that passes through the centre of the circle and whose endpoints lie on the circle. Sphere and diameter are Elementary geometry.
Diffeomorphism
In mathematics, a diffeomorphism is an isomorphism of differentiable manifolds.
Differential form
In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. Sphere and differential form are differential geometry.
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Differential geometry of surfaces
In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric. Sphere and differential geometry of surfaces are differential geometry and surfaces.
See Sphere and Differential geometry of surfaces
Dihedral angle
A dihedral angle is the angle between two intersecting planes or half-planes.
Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
Dionysodorus
Dionysodorus of Caunus (Διονυσόδωρος ὁ Καύνειος, c. 250 BC – c. 190 BC) was an ancient Greek mathematician.
Directional statistics
Directional statistics (also circular statistics or spherical statistics) is the subdiscipline of statistics that deals with directions (unit vectors in Euclidean space, Rn), axes (lines through the origin in Rn) or rotations in Rn.
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Disc integration
Disc integration, also known in integral calculus as the disc method, is a method for calculating the volume of a solid of revolution of a solid-state material when integrating along an axis "parallel" to the axis of revolution.
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Disk (mathematics)
In geometry, a disk (also spelled disc).
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Dupin cyclide
In mathematics, a Dupin cyclide or cyclide of Dupin is any geometric inversion of a standard torus, cylinder or double cone. Sphere and Dupin cyclide are surfaces.
Dyson sphere
A Dyson sphere is a hypothetical megastructure that encompasses a star and captures a large percentage of its solar power output.
Ellipse
In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. Sphere and ellipse are Elementary shapes.
Ellipsoid
An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation. Sphere and ellipsoid are surfaces.
Elliptic geometry
Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold.
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Embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. Sphere and embedding are differential topology.
Equator
The equator is a circle of latitude that divides a spheroid, such as Earth, into the Northern and Southern hemispheres.
Equirectangular projection
The equirectangular projection (also called the equidistant cylindrical projection or la carte parallélogrammatique projection), and which includes the special case of the plate carrée projection (also called the geographic projection, lat/lon projection, or plane chart), is a simple map projection attributed to Marinus of Tyre, who Ptolemy claims invented the projection about AD 100.
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Euclid's Elements
The Elements (Στοιχεῖα) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid 300 BC.
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Euclidean distance
In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them.
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Euclidean geometry
Euclidean geometry is a mathematical system attributed to ancient Greek mathematician Euclid, which he described in his textbook on geometry, Elements. Sphere and Euclidean geometry are Elementary geometry.
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Euclidean plane
In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted \textbf^2 or \mathbb^2.
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Euclidean space
Euclidean space is the fundamental space of geometry, intended to represent physical space. Sphere and Euclidean space are Homogeneous spaces.
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Eudoxus of Cnidus
Eudoxus of Cnidus (Εὔδοξος ὁ Κνίδιος, Eúdoxos ho Knídios) was an ancient Greek astronomer, mathematician, doctor, and lawmaker.
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Euler angles
The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system.
Exotic sphere
In an area of mathematics called differential topology, an exotic sphere is a differentiable manifold M that is homeomorphic but not diffeomorphic to the standard Euclidean ''n''-sphere. Sphere and exotic sphere are differential topology and spheres.
Figure of the Earth
In geodesy, the figure of the Earth is the size and shape used to model planet Earth.
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Filling area conjecture
In differential geometry, Mikhail Gromov's filling area conjecture asserts that the hemisphere has minimum area among the orientable surfaces that fill a closed curve of given length without introducing shortcuts between its points. Sphere and filling area conjecture are differential geometry and surfaces.
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Focal surface
For a surface in three dimension the focal surface, surface of centers or evolute is formed by taking the centers of the curvature spheres, which are the tangential spheres whose radii are the reciprocals of one of the principal curvatures at the point of tangency. Sphere and focal surface are surfaces.
Focus (geometry)
In geometry, focuses or foci (focus) are special points with reference to which any of a variety of curves is constructed.
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Fused quartz
Fused quartz, fused silica or quartz glass is a glass consisting of almost pure silica (silicon dioxide, SiO2) in amorphous (non-crystalline) form.
Gauss map
In differential geometry, the Gauss map of a surface is a function that maps each point in the surface to a unit vector that is orthogonal to the surface at that point. Sphere and Gauss map are differential geometry and surfaces.
Gaussian curvature
In differential geometry, the Gaussian curvature or Gauss curvature of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, and, at the given point: K. Sphere and Gaussian curvature are differential geometry, differential topology and surfaces.
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Geodesic
In geometry, a geodesic is a curve representing in some sense the shortest path (arc) between two points in a surface, or more generally in a Riemannian manifold. Sphere and geodesic are differential geometry.
Geography
Geography (from Ancient Greek γεωγραφία; combining 'Earth' and 'write') is the study of the lands, features, inhabitants, and phenomena of Earth.
Geometry
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.
Gravity Probe B
Gravity Probe B (GP-B) was a satellite-based experiment to test two unverified predictions of general relativity: the geodetic effect and frame-dragging.
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Great circle
In mathematics, a great circle or orthodrome is the circular intersection of a sphere and a plane passing through the sphere's center point. Sphere and great circle are Elementary geometry.
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 arc between them.
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Greek mathematics
Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly from the 5th century BC to the 6th century AD, around the shores of the Mediterranean.
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Ground track
A ground track or ground trace is the path on the surface of a planet directly below an aircraft's or satellite's trajectory.
Gyroscope
A gyroscope (from Ancient Greek γῦρος gŷros, "round" and σκοπέω skopéō, "to look") is a device used for measuring or maintaining orientation and angular velocity.
Hand with Reflecting Sphere
Hand with Reflecting Sphere, also known as Self-Portrait in Spherical Mirror, is a lithograph by Dutch artist M. C. Escher, first printed in January 1935.
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Heine–Borel theorem
In real analysis the Heine–Borel theorem, named after Eduard Heine and Émile Borel, states: For a subset S of Euclidean space Rn, the following two statements are equivalent.
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Helicoid
The helicoid, also known as helical surface, is a smooth surface embedded in three-dimensional space. Sphere and helicoid are surfaces.
Hoberman sphere
A Hoberman sphere is a kinetic structure patented by Chuck Hoberman that resembles a geodesic dome, but is capable of folding down to a fraction of its normal size by the scissor-like action of its joints.
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Homology sphere
In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n\ge 1. Sphere and homology sphere are spheres.
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Homotopy groups of spheres
In the mathematical field of algebraic topology, the homotopy groups of spheres describe how spheres of various dimensions can wrap around each other. Sphere and homotopy groups of spheres are spheres.
See Sphere and Homotopy groups of spheres
Homotopy sphere
In algebraic topology, a branch of mathematics, a homotopy sphere is an n-manifold that is homotopy equivalent to the n-sphere.
See Sphere and Homotopy sphere
Hyperbolic geometry
In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry.
See Sphere and Hyperbolic geometry
Implicit curve
In mathematics, an implicit curve is a plane curve defined by an implicit equation relating two coordinate variables, commonly x and y. For example, the unit circle is defined by the implicit equation x^2+y^2.
Inscribed figure
An inscribed triangle of a circle In geometry, an inscribed planar shape or solid is one that is enclosed by and "fits snugly" inside another geometric shape or solid. Sphere and inscribed figure are Elementary geometry.
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Integer
An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.
Integral
In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations.
Integral curve
In mathematics, an integral curve is a parametric curve that represents a specific solution to an ordinary differential equation or system of equations. Sphere and integral curve are differential geometry.
Isoperimetric inequality
In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume.
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King (playing card)
The king is a playing card with a picture of a king displayed on it.
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Lénárt sphere
A Lénárt sphere is a educational manipulative and writing surface for exploring spherical geometry, invented by Hungarian István Lénárt as a modern replacement for a spherical blackboard.
Lens
A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction.
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Line (geometry)
In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature, an idealization of such physical objects as a straightedge, a taut string, or a ray of light. Sphere and line (geometry) are Elementary geometry.
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Locus (mathematics)
In geometry, a locus (plural: loci) (Latin word for "place", "location") is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions. Sphere and locus (mathematics) are Elementary geometry.
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Longitude
Longitude is a geographic coordinate that specifies the east–west position of a point on the surface of the Earth, or another celestial body.
M. C. Escher
Maurits Cornelis Escher (17 June 1898 – 27 March 1972) was a Dutch graphic artist who made woodcuts, lithographs, and mezzotints, many of which were inspired by mathematics.
Manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.
Map projection
In cartography, a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane.
Martian spherules
Martian spherules (also known as hematite spherules, blueberries, & Martian blueberries) are small spherules (roughly spherical pebbles) that are rich in an iron oxide (grey hematite, α-Fe2O3) and are found at Meridiani Planum (a large plain on Mars) in exceedingly large numbers.
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Mathematics
Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.
Mean curvature
In mathematics, the mean curvature H of a surface S is an extrinsic measure of curvature that comes from differential geometry and that locally describes the curvature of an embedded surface in some ambient space such as Euclidean space. Sphere and mean curvature are differential geometry and surfaces.
Mercator projection
The Mercator projection is a conformal cylindrical map projection presented by Flemish geographer and cartographer Gerardus Mercator in 1569.
See Sphere and Mercator projection
Meridian (geography)
In geography and geodesy, a meridian is the locus connecting points of equal longitude, which is the angle (in degrees or other units) east or west of a given prime meridian (currently, the IERS Reference Meridian).
See Sphere and Meridian (geography)
Method of exhaustion
The method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape.
See Sphere and Method of exhaustion
Metric circle
In mathematics, a metric circle is the metric space of arc length on a circle, or equivalently on any rectifiable simple closed curve of bounded length.
Metric space
In mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. Sphere and metric space are topology.
Minimal surface
In mathematics, a minimal surface is a surface that locally minimizes its area. Sphere and minimal surface are differential geometry.
See Sphere and Minimal surface
N-sphere
In mathematics, an -sphere or hypersphere is an -dimensional generalization of the -dimensional circle and -dimensional sphere to any non-negative integer. Sphere and n-sphere are spheres.
Napkin ring problem
In geometry, the napkin-ring problem involves finding the volume of a "band" of specified height around a sphere, i.e. the part that remains after a hole in the shape of a circular cylinder is drilled through the center of the sphere.
See Sphere and Napkin ring problem
Natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, etc., possibly excluding 0.
Navigation
Navigation is a field of study that focuses on the process of monitoring and controlling the movement of a craft or vehicle from one place to another.
Non-Euclidean geometry
In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.
See Sphere and Non-Euclidean geometry
Norm (mathematics)
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin.
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Normal (geometry)
In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. Sphere and normal (geometry) are surfaces.
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Northern Hemisphere
The Northern Hemisphere is the half of Earth that is north of the Equator.
See Sphere and Northern Hemisphere
Octahedron
In geometry, an octahedron (octahedra or octahedrons) is a polyhedron with eight faces.
On the Sphere and Cylinder
On the Sphere and Cylinder (Περὶ σφαίρας καὶ κυλίνδρου) is a treatise that was published by Archimedes in two volumes c. 225 BCE.
See Sphere and On the Sphere and Cylinder
Orthogonal group
In mathematics, the orthogonal group in dimension, denoted, is the group of distance-preserving transformations of a Euclidean space of dimension that preserve a fixed point, where the group operation is given by composing transformations.
See Sphere and Orthogonal group
Orthogonality
In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.
Parallel postulate
In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry. Sphere and parallel postulate are Elementary geometry.
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Parametric equation
In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.
See Sphere and Parametric equation
Plane (mathematics)
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. Sphere and plane (mathematics) are surfaces.
See Sphere and Plane (mathematics)
Point (geometry)
In geometry, a point is an abstract idealization of an exact position, without size, in physical space, or its generalization to other kinds of mathematical spaces. Sphere and point (geometry) are Elementary geometry.
See Sphere and Point (geometry)
Point at infinity
In geometry, a point at infinity or ideal point is an idealized limiting point at the "end" of each line.
See Sphere and Point at infinity
Polar orbit
A polar orbit is one in which a satellite passes above or nearly above both poles of the body being orbited (usually a planet such as the Earth, but possibly another body such as the Moon or Sun) on each revolution.
Pressure vessel
A pressure vessel is a container designed to hold gases or liquids at a pressure substantially different from the ambient pressure.
See Sphere and Pressure vessel
Principal curvature
In differential geometry, the two principal curvatures at a given point of a surface are the maximum and minimum values of the curvature as expressed by the eigenvalues of the shape operator at that point. Sphere and principal curvature are surfaces.
See Sphere and Principal curvature
Pseudosphere
In geometry, a pseudosphere is a surface with constant negative Gaussian curvature. Sphere and pseudosphere are spheres and surfaces.
Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
See Sphere and Pythagorean theorem
Quadric
In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).
Quartic function
In algebra, a quartic function is a function of the form where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.
See Sphere and Quartic function
Radius
In classical geometry, a radius (radii or radiuses) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. Sphere and radius are spheres.
Real projective plane
In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface. Sphere and real projective plane are surfaces.
See Sphere and Real projective plane
Refraction
In physics, refraction is the redirection of a wave as it passes from one medium to another.
Reuleaux tetrahedron
The Reuleaux tetrahedron is the intersection of four balls of radius s centered at the vertices of a regular tetrahedron with side length s. The spherical surface of the ball centered on each vertex passes through the other three vertices, which also form vertices of the Reuleaux tetrahedron.
See Sphere and Reuleaux tetrahedron
Riemann sphere
In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane (also called the closed complex plane): the complex plane plus one point at infinity. Sphere and Riemann sphere are spheres.
Riemannian geometry
Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, defined as smooth manifolds with a Riemannian metric (an inner product on the tangent space at each point that varies smoothly from point to point). Sphere and Riemannian geometry are differential geometry.
See Sphere and Riemannian geometry
Rolling
Rolling is a type of motion that combines rotation (commonly, of an axially symmetric object) and translation of that object with respect to a surface (either one or the other moves), such that, if ideal conditions exist, the two are in contact with each other without sliding.
Rotation
Rotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation.
Semi-major and semi-minor axes
In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter.
See Sphere and Semi-major and semi-minor axes
Similarity (geometry)
In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other.
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Soap bubble
A soap bubble (commonly referred to as simply a bubble) is an extremely thin film of soap or detergent and water enclosing air that forms a hollow sphere with an iridescent surface.
Solid angle
In geometry, a solid angle (symbol) is a measure of the amount of the field of view from some particular point that a given object covers.
Solid geometry
Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space).
Specific surface area
Specific surface area (SSA) is a property of solids defined as the total surface area (SA) of a material per unit mass, (with units of m2/kg or m2/g).
See Sphere and Specific surface area
Sphere
A sphere (from Greek) is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. Sphere and sphere are differential geometry, differential topology, Elementary geometry, Elementary shapes, Homogeneous spaces, spheres, surfaces and topology.
Sphere eversion
In differential topology, sphere eversion is the process of turning a sphere inside out in a three-dimensional space (the word eversion means "turning inside out"). Sphere and sphere eversion are differential topology.
See Sphere and Sphere eversion
Sphere packing
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. Sphere and sphere packing are spheres.
Spherical cap
In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane.
Spherical conic
In mathematics, a spherical conic or sphero-conic is a curve on the sphere, the intersection of the sphere with a concentric elliptic cone.
See Sphere and Spherical conic
Spherical coordinate system
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a given point in space is specified by three numbers, (r, θ, φ): the radial distance of the radial line r connecting the point to the fixed point of origin (which is located on a fixed polar axis, or zenith direction axis, or z-axis); the polar angle θ of the radial line r; and the azimuthal angle φ of the radial line r.
See Sphere and Spherical coordinate system
Spherical cow
Comic of a spherical cow as illustrated by a 1996 meeting of the American Astronomical Association, in reference to astronomy modeling The spherical cow is a humorous metaphor for highly simplified scientific models of complex phenomena.
Spherical Earth
Spherical Earth or Earth's curvature refers to the approximation of the figure of the Earth as a sphere. Sphere and Spherical Earth are spheres.
See Sphere and Spherical Earth
Spherical lune
In spherical geometry, a spherical lune (or biangle) is an area on a sphere bounded by two half great circles which meet at antipodal points.
Spherical polyhedron
In geometry, a spherical polyhedron or spherical tiling is a tiling of the sphere in which the surface is divided or partitioned by great arcs into bounded regions called spherical polygons. Sphere and spherical polyhedron are spheres.
See Sphere and Spherical polyhedron
Spherical sector
In geometry, a spherical sector, also known as a spherical cone, is a portion of a sphere or of a ball defined by a conical boundary with apex at the center of the sphere.
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Spherical segment
In geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes.
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Spherical trigonometry
Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. Sphere and spherical trigonometry are spheres.
See Sphere and Spherical trigonometry
Spherical wedge
In geometry, a spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge's base).
See Sphere and Spherical wedge
Sphericity
Sphericity is a measure of how closely the shape of an object resembles that of a perfect sphere. Sphere and Sphericity are spheres.
Spheroid
A spheroid, also known as an ellipsoid of revolution or rotational ellipsoid, is a quadric surface obtained by rotating an ellipse about one of its principal axes; in other words, an ellipsoid with two equal semi-diameters. Sphere and spheroid are surfaces.
Spiral
In mathematics, a spiral is a curve which emanates from a point, moving farther away as it revolves around the point.
Stefan Cohn-Vossen
Stefan Cohn-Vossen (28 May 1902 – 25 June 1936) was a mathematician, who was responsible for Cohn-Vossen's inequality and the Cohn-Vossen transformation is also named after him.
See Sphere and Stefan Cohn-Vossen
Surface (topology)
In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Sphere and surface (topology) are surfaces.
See Sphere and Surface (topology)
Surface area
The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies.
Surface of revolution
A surface of revolution is a surface in Euclidean space created by rotating a curve (the generatrix) one full revolution around an axis of rotation (normally not intersecting the generatrix, except at its endpoints).
See Sphere and Surface of revolution
Surface tension
Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible.
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Tangent
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is, intuitively, the straight line that "just touches" the curve at that point. Sphere and tangent are differential geometry, differential topology and Elementary geometry.
Tangent indicatrix
In differential geometry, the tangent indicatrix of a closed space curve is a curve on the unit sphere intimately related to the curvature of the original curve. Sphere and tangent indicatrix are differential geometry.
See Sphere and Tangent indicatrix
Taxicab geometry
Taxicab geometry or Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined to be the sum of the absolute differences of their respective Cartesian coordinates, a distance function (or metric) called the taxicab distance, Manhattan distance, or city block distance.
See Sphere and Taxicab geometry
Tennis ball theorem
In geometry, the tennis ball theorem states that any smooth curve on the surface of a sphere that divides the sphere into two equal-area subsets without touching or crossing itself must have at least four inflection points, points at which the curve does not consistently bend to only one side of its tangent line.
See Sphere and Tennis ball theorem
Theorema Egregium
Gauss's Theorema Egregium (Latin for "Remarkable Theorem") is a major result of differential geometry, proved by Carl Friedrich Gauss in 1827, that concerns the curvature of surfaces. Sphere and Theorema Egregium are differential geometry and surfaces.
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Three-dimensional space
In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates) are required to determine the position of a point.
See Sphere and Three-dimensional space
Topological manifold
In topology, a branch of mathematics, a topological manifold is a topological space that locally resembles real n-dimensional Euclidean space.
See Sphere and Topological manifold
Topology
Topology (from the Greek words, and) is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself.
Torus
In geometry, a torus (tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle. Sphere and torus are surfaces.
See Sphere and Torus
Transfinite number
In mathematics, transfinite numbers or infinite numbers are numbers that are "infinite" in the sense that they are larger than all finite numbers.
See Sphere and Transfinite number
Trigonometric functions
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
See Sphere and Trigonometric functions
Trigonometry
Trigonometry is a branch of mathematics concerned with relationships between angles and side lengths of triangles. Sphere and Trigonometry are Elementary geometry.
Umbilical point
In the differential geometry of surfaces in three dimensions, umbilics or umbilical points are points on a surface that are locally spherical. Sphere and umbilical point are surfaces.
See Sphere and Umbilical point
Unit sphere
In mathematics, a unit sphere is a sphere of unit radius: the set of points at Euclidean distance 1 from some center point in three-dimensional space. Sphere and unit sphere are spheres.
Viviani's curve
In mathematics, Viviani's curve, also known as Viviani's window, is a figure eight shaped space curve named after the Italian mathematician Vincenzo Viviani.
See Sphere and Viviani's curve
Volume
Volume is a measure of regions in three-dimensional space.
Volume element
In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates.
Wiley (publisher)
John Wiley & Sons, Inc., commonly known as Wiley, is an American multinational publishing company that focuses on academic publishing and instructional materials.
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Zenodorus (mathematician)
Zenodorus (Ζηνόδωρος; c. 200 – c. 140 BC) was an ancient Greek mathematician.
See Sphere and Zenodorus (mathematician)
Zoll surface
In mathematics, particularly in differential geometry, a Zoll surface, named after Otto Zoll, is a surface homeomorphic to the 2-sphere, equipped with a Riemannian metric all of whose geodesics are closed and of equal length. Sphere and Zoll surface are surfaces.
3-sphere
In mathematics, a 3-sphere, glome or hypersphere is a higher-dimensional analogue of a sphere. Sphere and 3-sphere are spheres.
3D rotation group
In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space \R^3 under the operation of composition.
See Sphere and 3D rotation group
See also
Elementary shapes
- Capsule (geometry)
- Circle
- Circles
- Cone
- Cube
- Cubes
- Cuboid
- Cuboids
- Cylinder
- Decagon
- Dodecagon
- Ellipse
- Hendecagon
- Heptagon
- Hexagon
- Kite (geometry)
- Nonagon
- Octagon
- Oval
- Parallelogram
- Pentagon
- Rectangle
- Rhombus
- Sphere
- Spheres
- Square
- Trapezoid
- Triangles
Homogeneous spaces
- Clifford–Klein form
- Complex hyperbolic space
- Erlangen program
- Euclidean space
- Hermitian symmetric space
- Homogeneous space
- Hyperbolic space
- Iwasawa manifold
- Klein geometry
- Kostant's convexity theorem
- Nilmanifold
- Parabolic geometry (differential geometry)
- Quaternion-Kähler symmetric space
- Quaternionic projective space
- Sphere
- Stiefel manifold
- Symmetric space
- Weakly symmetric space
Spheres
- 3-sphere
- Ball (mathematics)
- Berger's sphere
- Bounding sphere
- Celestial globe
- Celestial sphere
- Chinese puzzle ball
- Circumscribed sphere
- Close-packing of equal spheres
- Dandelin spheres
- Exotic sphere
- Globe
- Hemispheres
- Homology sphere
- Homotopy groups of spheres
- Ideal polyhedron
- Inscribed sphere
- Kepler conjecture
- Klerksdorp sphere
- Midsphere
- N-sphere
- Pseudosphere
- Quasi-sphere
- Radius
- Riemann sphere
- Science On a Sphere
- Sfera (satellite)
- Sphere
- Sphere (venue)
- Sphere packing
- Sphere packing in a cube
- Sphere packing in a cylinder
- Sphere packing in a sphere
- Spherical Earth
- Spherical geometry
- Spherical polyhedron
- Spherical trigonometry
- Spherical wave transformation
- Sphericity
- Ulam's packing conjecture
- Unit sphere
References
[1] https://en.wikipedia.org/wiki/Sphere
Also known as 1-sphere, 2-sphere, Area of sphere, Curve on a sphere, Globose, Hemisphere (geometry), Hemispherical, Maschler space, Orb (shape), Perfect sphere, Sphere (geometry), Spheres, Spherical, Spherical curve, Spherical region, Spherical surface, Spherical volume, Spherule, Surface area of a sphere, Surface area of the sphere, S², Topological sphere, Two-dimensional sphere, Two-sphere, Volume Of A Sphere, Volume of sphere, X^2+y^2+z^2=r^2, .
, Diffeomorphism, Differential form, Differential geometry of surfaces, Dihedral angle, Dimension, Dionysodorus, Directional statistics, Disc integration, Disk (mathematics), Dupin cyclide, Dyson sphere, Ellipse, Ellipsoid, Elliptic geometry, Embedding, Equator, Equirectangular projection, Euclid's Elements, Euclidean distance, Euclidean geometry, Euclidean plane, Euclidean space, Eudoxus of Cnidus, Euler angles, Exotic sphere, Figure of the Earth, Filling area conjecture, Focal surface, Focus (geometry), Fused quartz, Gauss map, Gaussian curvature, Geodesic, Geography, Geometry, Gravity Probe B, Great circle, Great-circle distance, Greek mathematics, Ground track, Gyroscope, Hand with Reflecting Sphere, Heine–Borel theorem, Helicoid, Hoberman sphere, Homology sphere, Homotopy groups of spheres, Homotopy sphere, Hyperbolic geometry, Implicit curve, Inscribed figure, Integer, Integral, Integral curve, Isoperimetric inequality, King (playing card), Lénárt sphere, Lens, Line (geometry), Locus (mathematics), Longitude, M. C. Escher, Manifold, Map projection, Martian spherules, Mathematics, Mean curvature, Mercator projection, Meridian (geography), Method of exhaustion, Metric circle, Metric space, Minimal surface, N-sphere, Napkin ring problem, Natural number, Navigation, Non-Euclidean geometry, Norm (mathematics), Normal (geometry), Northern Hemisphere, Octahedron, On the Sphere and Cylinder, Orthogonal group, Orthogonality, Parallel postulate, Parametric equation, Plane (mathematics), Point (geometry), Point at infinity, Polar orbit, Pressure vessel, Principal curvature, Pseudosphere, Pythagorean theorem, Quadric, Quartic function, Radius, Real projective plane, Refraction, Reuleaux tetrahedron, Riemann sphere, Riemannian geometry, Rolling, Rotation, Semi-major and semi-minor axes, Similarity (geometry), Soap bubble, Solid angle, Solid geometry, Specific surface area, Sphere, Sphere eversion, Sphere packing, Spherical cap, Spherical conic, Spherical coordinate system, Spherical cow, Spherical Earth, Spherical lune, Spherical polyhedron, Spherical sector, Spherical segment, Spherical trigonometry, Spherical wedge, Sphericity, Spheroid, Spiral, Stefan Cohn-Vossen, Surface (topology), Surface area, Surface of revolution, Surface tension, Tangent, Tangent indicatrix, Taxicab geometry, Tennis ball theorem, Theorema Egregium, Three-dimensional space, Topological manifold, Topology, Torus, Transfinite number, Trigonometric functions, Trigonometry, Umbilical point, Unit sphere, Viviani's curve, Volume, Volume element, Wiley (publisher), Zenodorus (mathematician), Zoll surface, 3-sphere, 3D rotation group.