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Straight path on a curved surface or a Riemannian manifold
In geometry, a geodesic (/ˌdʒiː.əˈdɛsɪk, -oʊ-, -ˈdiːsɪk, -zɪk/) is a curve representing in some sense the locally shortest path (arc) between two points
Geodesic
Spherical shell structure based on a geodesic polyhedron
A geodesic dome is a hemispherical thin-shell structure (lattice-shell) based on a geodesic polyhedron. The rigid triangular elements of the dome distribute
Geodesic_dome
Topics referred to by the same term
A geodesic is a curve representing in some sense the shortest path between two points on a surface. Look up geodesic in Wiktionary, the free dictionary
Geodesic_(disambiguation)
Generalization of straight line to a curved space time
In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from
Geodesics in general relativity
Geodesics_in_general_relativity
Shortest paths on a bounded deformed sphere-like quadric surface
The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth
Geodesics_on_an_ellipsoid
geodesic convexity is a natural generalization of convexity for sets and functions to Riemannian manifolds. It is common to drop the prefix "geodesic"
Geodesic_convexity
Polyhedron made from triangles that approximates a sphere
A geodesic polyhedron is a convex polyhedron made from triangles which approximates a sphere. They usually have icosahedral symmetry, such that they have
Geodesic_polyhedron
18th-century expedition to present-day Ecuador
The Spanish-French Geodesic Mission (French: Expédition géodésique française en Équateur), also called the French Geodesic Mission to Peru, was an 18th-century
French Geodesic Mission to the Equator
French_Geodesic_Mission_to_the_Equator
Bending of trajectories in general relativity by a tidal force
called a geodesic. The geodesic deviation equation relates the Riemann curvature tensor to the relative acceleration of two neighboring geodesics. In differential
Geodesic_deviation
Spatial grid based on a geodesic polyhedron
A geodesic grid is a spatial grid based on a geodesic polyhedron or Goldberg polyhedron. The earliest use of the (icosahedral) geodesic grid in geophysical
Geodesic_grid
Type of curve in geometry
In mathematics, a prime geodesic on a hyperbolic surface is a primitive closed geodesic: one whose parametrization is not obtained by going repeatedly
Prime_geodesic
American philosopher, architect and inventor (1895–1983)
known geodesic dome; carbon molecules known as fullerenes were later named by scientists for their structural and mathematical resemblance to geodesic spheres
Buckminster_Fuller
In mathematics, a complex geodesic is a generalization of the notion of geodesic to complex spaces. Let (X, || ||) be a complex Banach space and let B
Complex_geodesic
In mathematics, the geodesic equations are second-order non-linear differential equations, and are commonly presented in the form of Euler–Lagrange equations
Geodesics as Hamiltonian flows
Geodesics_as_Hamiltonian_flows
Procedure in mathematics
Solving the geodesic equations is a procedure used in mathematics, particularly Riemannian geometry, and in physics, particularly in general relativity
Solving the geodesic equations
Solving_the_geodesic_equations
A geodesic circle is either "the locus on a surface at a constant geodesic distance from a fixed point" or a curve of constant geodesic curvature. A geodesic
Geodesic_circle
Paths of particles in the Schwarzschild solution to Einstein's field equations
In general relativity, Schwarzschild geodesics describe the motion of test particles in the gravitational field of a central fixed mass M , {\textstyle
Schwarzschild_geodesics
differential geometry and dynamical systems, a closed geodesic on a Riemannian manifold is a geodesic that returns to its starting point with the same tangent
Closed_geodesic
differential geometry—a geodesic map (or geodesic mapping or geodesic diffeomorphism) is a function that "preserves geodesics". More precisely, given
Geodesic_map
Mathematics of smooth surfaces
a geodesic of sufficiently short length will always be the curve of shortest length on the surface which connects its two endpoints. Thus, geodesics are
Differential geometry of surfaces
Differential_geometry_of_surfaces
Mathematical measure in Riemannian geometry
geometry, the geodesic curvature k g {\displaystyle k_{g}} of a curve γ {\displaystyle \gamma } measures how far the curve is from being a geodesic. For example
Geodesic_curvature
In geometric data analysis and statistical shape analysis, principal geodesic analysis is a generalization of principal component analysis to a non-Euclidean
Principal_geodesic_analysis
In mathematics, a geodesic metric space, or a geodesic space, is a concept in metric geometry and metric space theory that formalizes the idea of a space
Geodesic_metric_space
Type of aircraft structure
aeronautical engineer Barnes Wallis in the 1930s (who sometimes spelt it "geodesic"). Earlier, it was used by Prof. Schütte for the Schütte Lanz Airship SL
Geodetic_airframe
Horizontal angle from north or other reference cardinal direction
of the spheroid; geodetic azimuth (or geodesic azimuth) is the angle between north and the ellipsoidal geodesic (the shortest path on the surface of the
Azimuth
Science of measuring the shape, orientation, and gravity of Earth
The general solution is called the geodesic for the surface considered, and the differential equations for the geodesic are solvable numerically. On the
Geodesy
Vector field in Riemannian geometry
a geodesic γ {\displaystyle \gamma } in a Riemannian manifold describing the difference between the geodesic and an "infinitesimally close" geodesic. In
Jacobi_field
Key results in general relativity on gravitational singularities
the time-like geodesics into the future, it is impossible for the boundary of the region they form to be generated by the null geodesics from the surface
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
Concept in geometry/topology
(a geodesic) then it is called a geodesic metric space. For instance, the Euclidean plane is a geodesic space, with line segments as its geodesics. The
Intrinsic_metric
Existence of geodesic circles on surfaces
geodesics (i.e. three embedded geodesic circles). The result can also be extended to quasigeodesics on a convex polyhedron, and to closed geodesics of
Theorem of the three geodesics
Theorem_of_the_three_geodesics
Generalization of Riemannian manifolds
many concepts in Riemannian geometry still exist, including length, geodesics, curvature, connections, covariant derivative, and Cartan structural equations
Finsler_manifold
geometry, a geodesic bicombing distinguishes a class of geodesics of a metric space. The study of metric spaces with distinguished geodesics traces back
Geodesic_bicombing
Indian children's magazine
literature, until his death in August 1980. In 2007, Chandamama was acquired by Geodesic, a Mumbai-based software services company, with plans to transition the
Chandamama
Structure that resembles a geodesic dome
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
Hoberman_sphere
Multi-purpose venue in Jeddah
record previously held by the Caesars Superdome, and the world’s largest geodesic dome. Notable Events List of largest buildings "Jeddah Superdome: Say hello
Jeddah_Super_Dome
Riemannian manifold in which geodesics extend infinitely in all directions
In mathematics, a complete manifold (or geodesically complete manifold) M is a (pseudo-) Riemannian manifold for which, starting at any point p of M, there
Complete_manifold
This is a list of selected geodesic polyhedra and Goldberg polyhedra, two infinite classes of polyhedra. Geodesic polyhedra and Goldberg polyhedra are
List of geodesic polyhedra and Goldberg polyhedra
List_of_geodesic_polyhedra_and_Goldberg_polyhedra
Iranian mathematician (1977–2017)
Slightly more formally, a curve is a geodesic if no slight deformation can make it shorter. Closed geodesics are geodesics which are also closed curves—that
Maryam_Mirzakhani
Proposed airborne habitats
created from giant geodesic spheres, which might be made to levitate by slightly heating the air inside above the ambient temperature. Geodesic spheres become
Cloud_Nine_(sphere)
In differential geometry
viewpoint is that conjugate points tell when the geodesics fail to be length-minimizing. All geodesics are locally length-minimizing, but not necessarily
Conjugate_points
Theorem in differential geometry
with boundary ∂M. Let K be the Gaussian curvature of M, and let kg be the geodesic curvature of ∂M. Then ∫ M K d A + ∫ ∂ M k g d s = 2 π χ ( M ) , {\displaystyle
Gauss–Bonnet_theorem
manifold Geodesic is a curve which locally minimizes distance. Geodesic equation is the differential equation whose local solutions are the geodesics. Geodesic
Glossary of Riemannian and metric geometry
Glossary_of_Riemannian_and_metric_geometry
Set of points where the shortest paths from a specific starting point cease to be unique
the manifold that are connected to p by two or more distinct shortest geodesics. More generally, the cut locus of a closed set X on the manifold is the
Cut_locus
Formula for the great-circle distance between two points on a sphere
open-source geodesic calculation software GeographicLib, assuming the WGS84 ellipsoid. See Karney, Charles F. F. (2013). "Algorithms for geodesics". Journal
Haversine_formula
German-born theoretical physicist (1879–1955)
like a black hole, to be a geodesic. Both physicists and philosophers have often repeated the assertion that the geodesic equation can be obtained from
Albert_Einstein
Length of shortest path between two nodes of a graph
edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance or shortest-path distance. Notice that
Distance_(graph_theory)
Nonlinear dimensionality reduction method
and extends metric multidimensional scaling (MDS) by incorporating the geodesic distances imposed by a weighted graph. To be specific, the classical scaling
Isomap
topology, Busemann functions are used to study the large-scale geometry of geodesics in Hadamard spaces and in particular Hadamard manifolds (simply connected
Busemann_function
Reference frame for measuring location
believe Earth was prolate (narrower at the equator). The subsequent French geodesic missions (1735-1739) to Lapland and Peru corroborated Newton, but also
Geodetic_datum
Mathematical finite graph-associated function
taken over all prime closed geodesics p {\displaystyle p} of the graph G = ( V , E ) {\displaystyle G=(V,E)} , where geodesics which differ by a cyclic rotation
Ihara_zeta_function
Historic house in Illinois, United States
only geodesic dome Fuller lived in, as well as the only property he ever owned. Fuller, a prolific architect and engineer, popularized the geodesic dome
R. Buckminster Fuller and Anne Hewlett Dome Home
R._Buckminster_Fuller_and_Anne_Hewlett_Dome_Home
Fixed surveying station used in geodetic surveying
A triangulation station, also known as a trigonometrical point, and sometimes informally as a trig, is a fixed surveying station, used in geodetic surveying
Triangulation_station
First-order method for approximating parallel transport of a vector along a curve
transport of a vector along a curve using only affinely parametrized geodesics. The method is named for Alfred Schild, who introduced the method during
Schild's_ladder
United States historic place
The ASM International Headquarters and Geodesic Dome, at the Materials Park campus in Russell Township, Geauga County, Ohio, United States, are the headquarters
ASM Headquarters and Geodesic Dome
ASM_Headquarters_and_Geodesic_Dome
Gives equivalent statements about the geodesic completeness of Riemannian manifolds
The Hopf–Rinow theorem is a set of statements about the geodesic completeness of Riemannian manifolds. It is named after Heinz Hopf and his student Willi
Hopf–Rinow_theorem
Temporary shelter which can be easily dismantled and which is portable
living area, with up to four tunnel extensions to provide sleeping areas. Geodesic tents are essentially dome tents with two or more extra poles which criss-cross
Tent
Architectural element similar to the hollow upper half of a sphere; there are many types
designed many geodesic domes and patented them in the United States. Geodesic dome in Jena, Germany Geodesic dome of the Montreal Biosphere Geodesic dome home
Dome
Smooth manifold with an inner product on each tangent space
{\displaystyle \gamma '(0)=v} exists, one obtains a geodesic called a maximal geodesic of which every geodesic satisfying γ ( 0 ) = p {\displaystyle \gamma (0)=p}
Riemannian_manifold
Relation used in geometry
equidistant curves, parallel geodesics and geodesics sharing a common perpendicular, respectively. While in Euclidean geometry two geodesics can either intersect
Parallel_(geometry)
Weatherproof structures enclosing antennea that emits radiation
rotating antennas. Radomes can be constructed in several shapes – spherical, geodesic, planar, etc. – depending on the particular application, using various
Radome
A geodesic polyarene in organic chemistry is a polycyclic aromatic hydrocarbon with curved convex or concave surfaces. Examples include fullerenes, nanotubes
Geodesic_polyarene
1959 architectural proposal
The Dome over Manhattan was a 1959 proposal for a 3-kilometer-diameter geodesic domed city covering Midtown Manhattan by the architects Buckminster Fuller
Dome_over_Manhattan
Concept in mathematics
space X {\displaystyle X} is geodesic, i.e. any two points x , y ∈ X {\displaystyle x,y\in X} are end points of a geodesic segment [ x , y ] {\displaystyle
Hyperbolic_metric_space
Special coordinate system in differential geometry
covariant derivative reduces to a partial derivative (at p only), and the geodesics through p are locally linear functions of t (the affine parameter). This
Normal_coordinates
German-Russian mathematician (1806–1885)
invariance of geodesic curvature. He studied ruled surfaces, developable surfaces and surfaces of revolution and determined geodesics on the pseudosphere
Ferdinand_Minding
Local coordinates that are adapted to a geodesic
adapted to a geodesic. In a second, more general one, they are local coordinates that are adapted to any world line, even not geodesical. Take a future-directed
Fermi_coordinates
Equations that describe the behavior of a physical system
}}}} and the geodesic equation is a second-order differential equation in the coordinates. The general solution is a family of geodesics: d 2 x μ d s
Equations_of_motion
Branch of geometry
a Riemannian n-manifold M {\displaystyle M} , consider its unit-speed geodesic curves (i.e. parameterized by arc length). This produces a transport of
Contact_geometry
Depictions of a spatial anomaly
In the episode "Inside Man" an artificially created wormhole was named geodesic fold. In the 2009 Star Trek film, red matter is used to create artificial
Wormholes_in_fiction
US scientific research station at the South Pole, Antarctica
station was moved in 1975 to the newly constructed Buckminster Fuller geodesic dome 160 feet (50 m) wide by 52 feet (16 m) high, with 46 by 79 feet (14 m
Amundsen–Scott South Pole Station
Amundsen–Scott_South_Pole_Station
Relates sectional curvature of a Riemannian manifold to the rate geodesics spread apart
which geodesics spread apart. Intuitively, it states that for positive curvature, geodesics tend to converge, while for negative curvature, geodesics tend
Rauch_comparison_theorem
Monument park in Ecuador
takes its name) and commemorates the eighteenth-century Franco-Spanish Geodesic Mission which fixed its approximate location; they also contain the Museo
Ciudad_Mitad_del_Mundo
to or the same length as the side AB, although it will be straight (a geodesic). A parallelogram in Euclidean geometry can be constructed as follows:
Levi-Civita_parallelogramoid
Branch of differential geometry
diverse results concerning the geometry of surfaces and the behavior of geodesics on them, with techniques that can be applied to the study of differentiable
Riemannian_geometry
Light motion in curved spacetime
assumed to propagate in a vacuum along a null geodesic in a pseudo-Riemannian manifold. Besides the geodesics principle in a classical field theory there
Fermat's and energy variation principles in field theory
Fermat's_and_energy_variation_principles_in_field_theory
Type of traversable wormhole
point in space, but if set in motion by some disturbance will follow a geodesic of an equatorial cross section at constant speed, as would also a photon
Ellis_wormhole
Partition of Earth's surface into subdivided cells
reference ellipsoid. A simplified Geoid: sometimes an old geodesic standard (e.g. SAD69) or a non-geodesic surface (e. g. perfectly spherical surface) must be
Discrete_global_grid
Triangle comparison theorem in Riemannian geometry
K\geq \delta \,.} Let pqr be a geodesic triangle, i.e. a triangle whose sides are geodesics, in M, such that the geodesic pq is minimal and if δ > 0, the
Toponogov's_theorem
Mathematical expression of circle like slices of sphere
on the sphere (the pole or spherical center). It is a curve of constant geodesic curvature relative to the sphere, analogous to a line or circle in the
Spherical_circle
end of a geodesic either meets a boundary of the band at a right angle or is asymptotic to the midline; the midline itself is the only geodesic that does
Band_model
Theorem in general relativity
A ray is a family of geodesic light-like curves. That is tangent vector field l a {\displaystyle l^{a}} is null and geodesic: l a l a = 0 {\displaystyle
Goldberg–Sachs_theorem
Type of metric space in mathematics
d)} be a geodesic metric space, i.e. a metric space for which every two points x , y ∈ X {\displaystyle x,y\in X} can be joined by a geodesic segment,
CAT(k)_space
theoretical motivation for general relativity, including the motivation for the geodesic equation and the Einstein field equation, can be obtained from special
Theoretical motivation for general relativity
Theoretical_motivation_for_general_relativity
System of moving vectors in differential geometry
notion of a metric geodesic, while the latter is provided by a connection, leading to the notions of parallel transport and affine geodesics. Let us consider
Parallel_transport
Theorem in differential geometry
curvature of a surface in terms of the circumference of a geodesic circle, or the area of a geodesic disc. The theorem is named for Joseph Bertrand, Victor
Bertrand–Diguet–Puiseux theorem
Bertrand–Diguet–Puiseux_theorem
Environment museum in Montreal, Quebec
the grounds of Parc Jean-Drapeau on Saint Helen's Island. The museum's geodesic dome was designed by Buckminster Fuller. The structure was originally built
Montreal_Biosphere
Convex polyhedron made from hexagons and pentagons
enantiomorphs of each other. A Goldberg polyhedron is a dual polyhedron of a geodesic polyhedron. A consequence of Euler's polyhedron formula is that a Goldberg
Goldberg_polyhedron
Geodætisk Institut (1928–1987) was a Danish state-run cartographic institute. It was created by law number 82, of 31 March[citation needed] 1928, combining
Geodætisk_Institut
Satellites where the payload follows a geodesic path through space
satellites or drag-free satellites are satellites where the payload follows a geodesic path through space only affected by gravity and not by non-gravitational
Zero-drag_satellite
Partitioned topological space
foliation. A geodesic lamination of a 2-dimensional hyperbolic manifold is a closed subset together with a foliation of this closed subset by geodesics. These
Lamination_(topology)
Graph operation
it is an extension of concepts introduced by the Goldberg polyhedra and geodesic polyhedra. The GC construction is primarily studied in organic chemistry
Goldberg–Coxeter_construction
Diffeomorphism that has a hyperbolic structure on the tangent bundle
flow comes from the realization that g t {\displaystyle g_{t}} is the geodesic flow on P and Q. Lie vector fields being (by definition) left invariant
Anosov_diffeomorphism
South African-born mathematician
University Princeton University Institute for Advanced Study Thesis Prime geodesic theorems (1980) Doctoral advisor Paul Cohen Doctoral students Andrew Booker
Peter_Sarnak
Four-dimensional analog of the icosahedron
Moreover, in 4-space there are geodesics on the 3-sphere which do not lie in central planes at all. There are geodesic shortest paths between two 600-cell
600-cell
Object in differential geometry
the geometry of geodesics. Given a system of parametrized geodesics, one can specify a class of affine connections having those geodesics, but differing
Torsion_tensor
Shape with three sides
A geodesic triangle is a region of a general two-dimensional surface enclosed by three sides that are straight relative to the surface (geodesics). A
Triangle
Tensor field in Riemannian geometry
observable via the geodesic deviation equation. The curvature tensor represents the tidal force experienced by a rigid body moving along a geodesic in a sense
Riemann_curvature_tensor
Hotel resort at Waikiki, Honolulu, Hawaii, USA
of the Hawaiian Village Hotel. In 1957, the modern Ocean Tower and the Geodesic Dome were added. Conrad Hilton bought half of the resort from Henry J.
Hilton_Hawaiian_Village
Formula in classical differential geometry
through the point P {\displaystyle P} . The relation remains valid for a geodesic on an arbitrary surface of revolution. A statement of the general version
Clairaut's relation (differential geometry)
Clairaut's_relation_(differential_geometry)
Geodesic dome in Paris, France
48.89444°N 2.38861°E / 48.89444; 2.38861 La Géode is a mirror-finished geodesic dome that holds an Omnimax theatre in Parc de la Villette at the Cité des
La_Géode
GEODESIC
GEODESIC
GEODESIC
GEODESIC
Boy/Male
Muslim
Religion, Faith, Belief
Boy/Male
Muslim/Islamic
Praised
Girl/Female
Bengali, Indian, Muslim
Spiritual
Boy/Male
English Teutonic
Thorn wood/clearing; from Thor's meadow.
Girl/Female
Tamil
Raktima | ரகà¯à®¤à¯€à®®à®¾à®‚Â
Pleasing
Girl/Female
Afghan, Arabic, Muslim
Affection; Sympathy
Girl/Female
Tamil
Ansika | அநà¯à®¸à¯€à®•à®¾
Minute particle, Beautiful
Male
English
Middle English form of Anglo-Saxon Eadric, EDRIC means "rich ruler."
Boy/Male
Biblical American Hebrew
Watchman; making bare; pouring out.
Girl/Female
Indian
Goddess Laxmi
GEODESIC
GEODESIC
GEODESIC
GEODESIC
GEODESIC
a.
Of or pertaining to geodesy; geodetic.
n.
A geodetic line or curve.
a.
Of or pertaining to geodesy; obtained or determined by the operations of geodesy; engaged in geodesy; geodesic; as, geodetic surveying; geodetic observers.
a.
Alt. of Geodesical