AI & ChatGPT searches , social queries for SPHERICAL GEOMETRY
Search references for SPHERICAL GEOMETRY. Phrases containing SPHERICAL GEOMETRY
See searches and references containing SPHERICAL GEOMETRY!
Search references for SPHERICAL GEOMETRY. Phrases containing SPHERICAL GEOMETRY
See searches and references containing SPHERICAL GEOMETRY!SPHERICAL GEOMETRY
Geometry of the surface of a sphere
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
Spherical_geometry
Set of points equidistant from a center
on the sphere. Spherical geometry is a form of elliptic geometry, which together with hyperbolic geometry makes up non-Euclidean geometry. The sphere is
Sphere
Non-Euclidean geometry
Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel
Elliptic_geometry
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_trigonometry
Overview of and topical guide to geometry
Ruppeiner geometry Solid geometry Spherical geometry Symplectic geometry Synthetic geometry Systolic geometry Taxicab geometry Toric geometry Transformation
Outline_of_geometry
Coordinates comprising a distance and two angles
In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates
Spherical_coordinate_system
Polygon with one edge and one vertex
segment. Most definitions of a polygon in Euclidean geometry do not admit the monogon. In spherical geometry, a monogon can be constructed as a vertex on a
Monogon
Partition of a sphere's surface into polygons
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
Spherical_polyhedron
Section of a sphere
In geometry, a spherical cap or spherical dome is a portion of a sphere or of a ball cut off by a plane. It is also a spherical segment of one base, i
Spherical_cap
Three dimensional analogue of uniformization conjecture
one of three geometries (Euclidean, spherical, or hyperbolic). In three dimensions, it is not always possible to assign a single geometry to a whole topological
Geometrization_conjecture
Region between parallel planes intersecting a sphere
geometry, a spherical segment is the solid defined by cutting a sphere or a ball with a pair of parallel planes. It can be thought of as a spherical cap
Spherical_segment
Type of non-Euclidean geometry
rarely used sequence elliptic geometry (spherical geometry), parabolic geometry (Euclidean geometry), and hyperbolic geometry. In the former Soviet Union
Hyperbolic_geometry
Special mathematical functions defined on the surface of a sphere
scientific fields. The table of spherical harmonics contains a list of common spherical harmonics. Since the spherical harmonics form a complete set of
Spherical_harmonics
Shape with four equal sides and angles
balls for taxicab geometry and Chebyshev distance, two forms of non-Euclidean geometry. Although spherical geometry and hyperbolic geometry both lack polygons
Square
Branch of mathematics
of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by
Differential_geometry
Ancient Greek mathematician (fl. 300 BC)
set of axioms. He also wrote works on perspective, conic sections, spherical geometry, number theory, and mathematical rigour. In addition to the Elements
Euclid
Exterior angle of a triangle is greater than either of the remote interior angles
geometry is used (see Foundations of geometry) this assertion of Euclid can be proved. The exterior angle theorem is not valid in spherical geometry nor
Exterior_angle_theorem
Multiple proofs regarding Earth's approximately spherical shape
The roughly spherical shape of Earth can be empirically evidenced by many different types of observation, ranging from ground level, flight, or orbit
Empirical evidence for the spherical shape of Earth
Empirical_evidence_for_the_spherical_shape_of_Earth
Two geometries based on axioms closely related to those specifying Euclidean geometry
non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the
Non-Euclidean_geometry
Area on a sphere bounded by two semicircles joined at antipodal points
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. It is an
Spherical_lune
Relationship between two figures of the same shape and size, or mirroring each other
similarity and not congruence in Euclidean space. However, in spherical geometry and hyperbolic geometry (where the sum of the angles of a triangle varies with
Congruence_(geometry)
Branch of mathematics
Desargues in the 17th century, all the way back to the implicit use of spherical geometry to understand the Earth's geodesy and to navigate the oceans since
Geometry
Geometry without the parallel postulate
with elliptic geometry or spherical geometry: the notion of ordering or betweenness of points on lines, used to axiomatize absolute geometry, is inconsistent
Absolute_geometry
Geometric shape; radial slice of a sphere
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). The angle
Spherical_wedge
Spherical triangle with three right angles
In geometry, an octant of a sphere is a spherical triangle with three right angles and three right sides. It is sometimes called a trirectangular (spherical)
Octant_of_a_sphere
Relation between sides of a right triangle
> c2. Here two cases of non-Euclidean geometry are considered—spherical geometry and hyperbolic plane geometry; in each case, as in the Euclidean case
Pythagorean_theorem
Relation used in geometry
affine geometries and Euclidean geometry is a special instance of this type of geometry. In some other geometries, such as hyperbolic geometry, lines
Parallel_(geometry)
Shape with three sides
tetrahedron. In non-Euclidean geometries, three "straight" segments also determine a "triangle", for instance, a spherical triangle or hyperbolic triangle
Triangle
Function used in computer graphics
In geometry, spherical linear interpolation, commonly abbreviated slerp, is a function which interpolates between two points on a sphere, such that spherical
Spherical linear interpolation
Spherical_linear_interpolation
Common point(s) shared by two lines in Euclidean geometry
[further explanation needed] In spherical and elliptic geometries, every pair of lines intersects, while in hyperbolic geometry there exist infinitely many
Line–line_intersection
Three-dimensional geometric shape
In geometry, a spherical shell (a ball shell) is a generalization of an annulus to three dimensions. It is the region of a ball between two concentric
Spherical_shell
Intersection of a sphere and cone emanating from its center
In geometry, a spherical sector, also known as a spherical cone, is a portion of a ball that is bounded by a spherical cap and the cone that connects
Spherical_sector
290 BC) – astronomy, spherical geometry Euclid (fl. 300 BC) – Elements, Euclidean geometry (sometimes called the "father of geometry") Apollonius of Perga
List_of_geometers
Hand-held device for reference or calculation
example, the "Curveasy" wheel chart displays information related to spherical geometry calculations, and the Prestolog calculator is used for cost/profit
Slide_chart
Mathematical expression of circle like slices of sphere
spherical geometry, a spherical circle (often shortened to circle) is the locus of points on a sphere at constant spherical distance (the spherical radius)
Spherical_circle
Transparent dry-erase sphere used to teach spherical geometry
writing surface for exploring spherical geometry, invented by Hungarian István Lénárt as a modern replacement for a spherical blackboard. It can be used
Lénárt_sphere
Equation for radii of tangent circles
definition of curvature, the theorem also applies in spherical geometry and hyperbolic geometry. In higher dimensions, an analogous quadratic equation
Descartes'_theorem
Spherical geometry analog of a straight line
great circle is a geodesic of the sphere, so that great circles in spherical geometry are the natural analog of straight lines in Euclidean space. For any
Great_circle
Mathematical function
continuous varieties, in one, two, and three dimensions, in Cartesian and spherical geometry, on surfaces and in volumes, on graphs, and in scalar, vector, and
Slepian_function
Natural number
degenerate, collapsing to a line segment between the two vertices. In spherical geometry, however, non-degenerate digons can exist. Two distinct points in
2
Shortest distance between two points on the surface of a sphere
distance Isoazimuthal Loxodromic navigation Meridian arc Rhumb line Spherical geometry Spherical trigonometry Versor Admiralty Manual of Navigation, Volume 1
Great-circle_distance
Basis used to express spherical tensors
and their applications, a spherical basis is the basis used to express spherical tensors.[definition needed] The spherical basis closely relates to the
Spherical_basis
Fundamental result in geometry
hypotenuse equals the sum of the squares of the other two sides. Spherical geometry does not satisfy several of Euclid's axioms, including the parallel
Sum_of_angles_of_a_triangle
oriented arrangement of linear nucleic acids in a three-dimensional, spherical geometry. This novel three-dimensional architecture is responsible for many
Spherical_nucleic_acid
Spherical tank
[citation needed] Today, spherical tanks are designed to codes such as ASME VIII, PD 5500, or EN 13445. The spherical geometry minimizes both the mechanical
Horton_sphere
Property of segments that have the same length and the same direction
In Euclidean geometry, equipollence is a homogeneous relation between directed line segments. Two segments are said to be equipollent when they have the
Equipollence_(geometry)
Subclass of manifold
the following sections. The spherical manifolds are exactly the manifolds with spherical geometry, one of the eight geometries of Thurston's geometrization
Spherical_3-manifold
Triangle in hyperbolic geometry
some properties that are analogous to those of triangles in spherical or elliptic geometry: Two triangles with the same angle sum are equal in area. There
Hyperbolic_triangle
Quadrilateral with four right angles
and not all equal, though opposite angles are equal. Other geometries, such as spherical, elliptic, and hyperbolic, have so-called rectangles with opposite
Rectangle
Compact astronomical body
event occurred. For non-rotating black holes, the geometry of the event horizon is precisely spherical, while for rotating black holes, the event horizon
Black_hole
Curve on the sphere analogous to an ellipse or hyperbola
Publication No. 112. Higgs, Peter W. (1979). "Dynamical symmetries in a spherical geometry I". Journal of Physics A: Mathematical and General. 12 (3): 309–323
Spherical_conic
Mathematics of smooth surfaces
In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most
Differential geometry of surfaces
Differential_geometry_of_surfaces
differential geometry Metric tensor Riemannian manifold Pseudo-Riemannian manifold Levi-Civita connection Non-Euclidean geometry Elliptic geometry Spherical geometry
List of differential geometry topics
List_of_differential_geometry_topics
Spherics (sometimes spelled sphaerics or sphaerica) is a term used in the history of mathematics for historical works on spherical geometry, exemplified
Spherics
Quadrilateral symmetric across a diagonal
quadrilateral. The fourth angle is acute in hyperbolic geometry and obtuse in spherical geometry. Every kite is an orthodiagonal quadrilateral, meaning
Kite_(geometry)
Quadrilateral whose vertices lie on a circle
circumcenter and the point where the diagonals intersect. In spherical geometry, a spherical quadrilateral formed from four intersecting greater circles
Cyclic_quadrilateral
Spherical polyhedron composed of lunes
In spherical geometry, an n-gonal hosohedron is a tessellation of lunes on a spherical surface, such that each lune shares the same two polar opposite
Hosohedron
Property of geometry, also used to generalize the notion of "distance" in metric spaces
example. Thus, in Euclidean geometry, the shortest distance between two points is a straight line. In spherical geometry, the shortest distance between
Triangle_inequality
Ancient Greek astronomer and mathematician
astronomer and mathematician from Bithynia who wrote the Spherics, a treatise about spherical geometry, as well as several other books on mathematics and astronomy
Theodosius_of_Bithynia
Study of geometries as axiomatic systems
Foundations of geometry is the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean
Foundations_of_geometry
Topics referred to by the same term
refer to: Vertex (graph theory), a vertex in a mathematical graph Vertex (geometry), a point where two or more curves, lines, or edges meet. Node (autonomous
Node
Topological invariant in mathematics
pentagonal and 20 hexagonal panels. The result is a truncated icosahedron spherical geometry. An example is the Adidas Telstar. The n-dimensional sphere has singular
Euler_characteristic
Measure of distance in physical space
geometry used in general relativity is an example of such a geometry. In spherical geometry, length is measured along the great circles on the sphere and
Length
Triangle area in terms of side lengths
L'Huilier's formula relates the area of a triangle in spherical geometry to its side lengths. For a spherical triangle with side lengths a , {\displaystyle
Heron's_formula
Ancient Greek spherical geometry treatise
The Spherics (Greek: τὰ σφαιρικά, tà sphairiká) is a three-volume treatise on spherical geometry written by the Hellenistic mathematician Theodosius of
Theodosius'_Spherics
Topics referred to by the same term
hyperbolic planes, elliptic planes two-dimensional spherical geometry. Plane curve Inversive geometry Geometrography This disambiguation page lists mathematics
Plane geometry (disambiguation)
Plane_geometry_(disambiguation)
algebraic geometry. Elliptic geometry a type of non-Euclidean geometry (it violates Euclid's parallel postulate) and is based on spherical geometry. It is
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Geometric object
In four-dimensional geometry, the spherinder, or spherical cylinder or spherical prism, is a geometric object, defined as the Cartesian product of a 3-ball
Spherinder
Dutch graphic artist (1898–1972)
The Hague, pointed out that Parmigianino (1503–1540) had explored spherical geometry and reflection in his 1524 Self-portrait in a Convex Mirror, depicting
M._C._Escher
Timurid sultan, astronomer and mathematician (1394–1449)
his work in astronomy-related mathematics, such as trigonometry and spherical geometry, as well as his general interests in the arts and intellectual activities
Ulugh_Beg
4th-century BC Ancient Greek astromer, mathematician and geographer
works On the Moving Sphere and On Risings and Settings, both about spherical geometry. Autolycus was born in Pitane, a town of Aeolis within Ionia, Asia
Autolycus_of_Pitane
Mathematical treatise by Euclid
It is this property that allows distinguishing Euclidean geometry from spherical geometry "P.Oxy. LXXXII 5299. Euclid, Elements 1.4 (Diagram), 8–11,
Euclid's_Elements
Characterizes spherical triangles with fixed base and area
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
Lexell's_theorem
Study of geometry using a coordinate system
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts
Analytic_geometry
In geometry and coding theory, a spherical code with parameters (n,N,t) is a set of N points on the unit hypersphere in n dimensions for which the dot
Spherical_code
Metastable excited state of a nuclide
This geometry can result in quantum-mechanical states where the distribution of protons and neutrons is so much further from spherical geometry that de-excitation
Nuclear_isomer
Sphere with radius one, usually centered on the origin of the space
of the unit sphere. The unit sphere is often used as a model for spherical geometry because it has constant sectional curvature of 1, which simplifies
Unit_sphere
Pair of diametrically opposite points on a circle, sphere, or hypersphere
results in spherical geometry depend on choosing non-antipodal points, and degenerate if antipodal points are allowed; for example, a spherical triangle
Antipodal_point
Generalized sphere of dimension n (mathematics)
n} -sphere is the setting for n {\displaystyle n} -dimensional spherical geometry. Considered extrinsically, as a hypersurface embedded in ( n + 1
N-sphere
Framework of distances and directions
framework. In the 19th and 20th centuries mathematicians began to examine geometries that are non-Euclidean, in which space is conceived as curved, rather
Space
Type of geometry
In mathematics, a Klein geometry is a type of geometry motivated by Felix Klein in his influential Erlangen program. More specifically, it is a homogeneous
Klein_geometry
American-Danish nuclear physicist (1926–2022)
physicist. He won the 1975 Nobel Prize in Physics for his work on the non-spherical geometry of atomic nuclei. Mottelson was born in Chicago, Illinois, on 9 July
Ben_Roy_Mottelson
Plane of reference that divides the sphere into two hemispheres
The fundamental plane in a spherical coordinate system is a plane of reference that divides the sphere into two hemispheres. The geocentric latitude of
Fundamental plane (spherical coordinates)
Fundamental_plane_(spherical_coordinates)
Global electromagnetic resonances, generated and excited by lightning discharges
into the formula), a characteristic attributed to the atmosphere's spherical geometry. The peaks exhibit a spectral width of approximately 20% due to the
Schumann_resonances
Movement with a fixed point is rotation
is named after Leonhard Euler, who proved it in 1775 by means of spherical geometry. The axis of rotation is known as an Euler axis, typically represented
Euler's_rotation_theorem
Circle-packing on the surface of a sphere
Interesting Geometry. New York: Penguin Books. pp. 31. ISBN 0-14-011813-6. Bagchi, Bhaskar (1997). "How to Stay Away from Each Other in a Spherical Universe"
Tammes_problem
Hyperbolic geometry is a non-Euclidean geometry where the first four axioms of Euclidean geometry are kept but the fifth axiom, the parallel postulate
Constructions in hyperbolic geometry
Constructions_in_hyperbolic_geometry
Chess variants played on spherical boards
The other pieces have the moves from standard chess adapted to the spherical geometry. For example, the rook can move any number of fields orthogonally
Spherical_chess
Spherical triangle used in astronavigation
The navigational triangle or PZX triangle is a spherical triangle used in astronavigation to determine the observer's position on the globe. It is composed
Navigational_triangle
German physicist
moderator in a nuclear reactor. They conducted experiments with a spherical geometry (hollow spheres) of uranium surrounded by heavy water. Trial L-I was
Klara_Döpel
Complement of latitude; polar angle
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
Colatitude
Portuguese designer and author (born 1978)
his third point, Lima hypothesizes on how the circular framing and spherical geometry of our visual field, which cause a distortion similar to a "fish-eye
Manuel_Lima
German mathematician (1794–1874)
examined the model of geometry on a "sphere" of imaginary radius, which he called "logarithmic-spherical" (now called hyperbolic geometry). He published his
Franz_Taurinus
Model of hyperbolic geometry
analogous to the gnomonic projection of spherical geometry, in that geodesics (great circles in spherical geometry) are mapped to straight lines. This model
Beltrami–Klein_model
Branch of differential geometry and differential topology
Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds
Symplectic_geometry
In the theory of analytic geometry for real three-dimensional space, the curve formed from the intersection between a sphere and a cylinder can be a circle
Sphere–cylinder_intersection
Fundamental object of 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
Point_(geometry)
Indian mathematician and astronomer (1444–1544)
expansions of trigonometric functions and problems of algebra and spherical geometry. Grahapariksakrama is a manual on making observations in astronomy
Nilakantha_Somayaji
Nuclear accident in Leipzig, Germany
from the L-IV trial, in the first half of 1942, indicated that the spherical geometry, with five tonnes of heavy water and 10 tonnes of metallic uranium
Leipzig L-IV experiment accident
Leipzig_L-IV_experiment_accident
2D surface which extends indefinitely
Euclidean geometry (which has zero curvature everywhere) is not the only geometry that the plane may have. The plane may be given a spherical geometry by using
Plane_(mathematics)
SPHERICAL GEOMETRY
SPHERICAL GEOMETRY
Boy/Male
Greek
Greek surname. Euclid was an early developer of geometry theories.
Girl/Female
Indian, Tamil
The Sun is the Star at the Centre of the Solar System; It is Almost Perfectly Spherical and Consists of Hot Plasma Interwoven with Magnetic Fields; Sun
SPHERICAL GEOMETRY
SPHERICAL GEOMETRY
Boy/Male
Irish
domhan “â€worldâ€â€ and all “â€mightyâ€â€ implying “â€ruler of the world.â€â€ “â€Donal Ogâ€â€ (“â€Young Donalâ€â€) is the title of a fifteenth-century love song that is still popular among Irish traditional musicians and singers.
Girl/Female
Hindu, Indian, Marathi
Goddess Lakshmi
Biblical
he that resists Baal; rebellion
Girl/Female
German
Snake; Lime tree; linden tree. : From the Old German Betlindis, which is derived from the word...
Surname or Lastname
English
English : perhaps a variant of Yelling, a habitational name from Yelling in Cambridgeshire (formerly in Huntingdonshire), probably named with the Old English personal name Giella + -ingas ‘people of’.Jewish (Ashkenazic) : variant of Jelen.
Girl/Female
Hindu, Indian, Marathi
Intelligent Girl
Boy/Male
Hindu, Indian
Garland of Lights
Boy/Male
Arabic, Muslim
Faithful
Boy/Male
Scottish American
God has been gracious; has shown favor. Based on John or Jacques.
Boy/Male
Tamil
Bhavyansh | பாவà¯à®¯à®‚à®·Â
Bigger part
SPHERICAL GEOMETRY
SPHERICAL GEOMETRY
SPHERICAL GEOMETRY
SPHERICAL GEOMETRY
SPHERICAL GEOMETRY
a.
Round; circular; spherical.
n.
The eye, as luminous and spherical.
n.
A rudimentary form of crystallite, spherical in shape.
a.
Spherical.
a.
Having the form of a globe; spherical.
a.
Globular; spherical; orbicular.
a.
Alt. of Spheric
a.
Having the form of a sphere; like a sphere; globular; orbicular; as, a spherical body.
v. t.
To form into roundness; to make spherical, or spheral; to perfect.
a.
Exactly spherical; globular.
a.
See Spheroidal.
a.
Alt. of Schetical
a.
Having the form of a bunch of grapes; like a cluster of grapes, as a mineral presenting an aggregation of small spherical or spheroidal prominences.
n.
Freedom from spherical aberration.
adv.
Spherically.
n.
The doctrine of the sphere; the science of the properties and relations of the circles, figures, and other magnitudes of a sphere, produced by planes intersecting it; spherical geometry and trigonometry.
a.
Spherical; orbicular; orblike; circular.
a.
Made convex; protuberant in a spherical form.
n.
A portion of a spherical or other convex surface.
a.
Round; spherical; starlike.