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# Great circle

A great circle, also known as an orthodrome, of a sphere is the intersection of the sphere and a plane that passes through the center point of the sphere. 

## Antipodal point

In mathematics, the antipodal point of a point on the surface of a sphere is the point which is diametrically opposite to it — so situated that a line drawn from the one to the other passes through the center of the sphere and forms a true diameter.

## Astronomical object

An astronomical object or celestial object is a naturally occurring physical entity, association, or structure that exists in the observable universe.

## Calculus of variations

Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.

## Celestial equator

The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth.

## Celestial sphere

In astronomy and navigation, the celestial sphere is an abstract sphere with an arbitrarily large radius concentric to Earth.

## Centre (geometry)

In geometry, a centre (or center) (from Greek κέντρον) of an object is a point in some sense in the middle of the object.

## Circle

A circle is a simple closed shape.

## Circle of a sphere

A circle of a sphere is a circle that lies on a sphere.

## Circumference

In geometry, the circumference (from Latin circumferentia, meaning "carrying around") of a circle is the (linear) distance around it.

## Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.

## Earth

Earth is the third planet from the Sun and the only astronomical object known to harbor life.

## Ecliptic

The ecliptic is the circular path on the celestial sphere that the Sun follows over the course of a year; it is the basis of the ecliptic coordinate system.

## Equator

An equator of a rotating spheroid (such as a planet) is its zeroth circle of latitude (parallel).

## Euclidean geometry

Euclidean geometry is a mathematical system attributed to Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements.

## Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

## Euler–Lagrange equation

In the calculus of variations, the Euler–Lagrange equation, Euler's equation, or Lagrange's equation (although the latter name is ambiguous—see disambiguation page), is a second-order partial differential equation whose solutions are the functions for which a given functional is stationary.

## Figure of the Earth

The figure of the Earth is the size and shape of the Earth in geodesy.

## Functional (mathematics)

In mathematics, the term functional (as a noun) has at least two meanings.

## Funk transform

In the mathematical field of integral geometry, the Funk transform (also known as Minkowski–Funk transform, Funk–Radon transform or spherical Radon transform) is an integral transform defined by integrating a function on great circles of the sphere.

## Geodesic

In differential geometry, a geodesic is a generalization of the notion of a "straight line" to "curved spaces".

## Geodesics on an ellipsoid

The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks.

## Great-circle distance

The great-circle distance or orthodromic distance is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior).

## Great-circle navigation

Great-circle navigation or orthodromic navigation (related to orthodromic course; from the Greek ορθóς, right angle, and δρóμος, path) is the practice of navigating a vessel (a ship or aircraft) along a great circle.

## Hemispheres of Earth

In geography and cartography, the hemispheres of Earth refer to any division of the globe into two hemispheres (from Ancient Greek ἡμισφαίριον hēmisphairion, meaning "half of a sphere").

## Horizontal coordinate system

The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane.

## Land and water hemispheres

The land and water hemispheres of Earth, sometimes capitalised as the Land Hemisphere and Water Hemisphere, are the hemispheres of Earth containing the largest possible total areas of land and ocean, respectively.

## N-sphere

In mathematics, the n-sphere is the generalization of the ordinary sphere to spaces of arbitrary dimension.

## Plane (geometry)

In mathematics, a plane is a flat, two-dimensional surface that extends infinitely far.

## Rhumb line

In navigation, a rhumb line, rhumb, or loxodrome is an arc crossing all meridians of longitude at the same angle, that is, a path with constant bearing as measured relative to true or magnetic north.

## Riemannian circle

In metric space theory and Riemannian geometry, the Riemannian circle is a great circle equipped with its great-circle distance.

## Riemannian geometry

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point.

## Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

## Spherical coordinate system

In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.

## Wolfram Demonstrations Project

The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields.

## References

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