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Spherical geometry obeys two of Euclid's postulates: the second postulate (" to produce a finite straight line continuously in a straight line ") and the fourth postulate (" that all right angles are equal to one another ").
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Spherical and geometry
Spherical geometry is similar to elliptical geometry.
* Spherical geometry
Spherical geometry is the geometry of the two-dimensional surface of a sphere.
Spherical geometry is not elliptic geometry but shares with that geometry the property that a line has no parallels through a given point.
* Spherical geometry
Spherical trigonometry is a branch of spherical geometry which deals with polygons ( especially triangles ) on the sphere and the relationships between the sides and the angles.
* Spherical geometry
Category: Spherical geometry
Spherical and two
* Spherical coordinate system represents a point in three space by the distance from the origin and two angles measured from two reference lines which intersect the origin.
Spherical buildings arise in two quite different ways in connection with the affine building X for SL < sub > n </ sub >( Q < sub > p </ sub >):
* Spherical roller thrust bearings consists of two rings and assymetrical rollers of spherical shape.
Spherical and ("
* Fritz Koenig-Great Spherical Caryatid (" The Sphere "), designed for the World Trade Center, now in Battery Park, NYC
Spherical and produce
Spherical mirrors are easier to make than parabolic mirrors and they are often used to produce approximately collimated light.
Spherical and all
Spherical lenses have a single power in all meridians of the lens, such as + 1. 00 D, or − 2. 50 D.
When it was all completed ( in + 725 ) it was called the ' Water-Driven Spherical Bird's-Eye-View Map of the Heavens ( Shui Yun Hun Thien Fu Shih Thu ) or ' Celestial Sphere Model Water-Engine ' and was set up in front of the Wu Chheng Hall ( of the Palace ) to be seen by the multitude of officials.
Spherical and are
Spherical concave backing surfaces support the diaphragm when excessive pressures are applied and prevent the stresses within the diaphragm from exceeding the elastic limit.
Spherical errors occur when errors have both uniform variance ( homoscedasticity ) and are uncorrelated with each other.
Spherical fullerenes are also called buckyballs, and they resemble the balls used in soccer.
Spherical mechanisms are constructed by connecting links with hinged joints such that the axes of each hinge passes through the same point.
Spherical coordinates, projected on the celestial sphere, are analogous to the geographic coordinate system used on the surface of the Earth.
Spherical waves are waves whose amplitude depends only upon the radial distance r from a central point source.
Spherical harmonics are often used to approximate the shape of the geoid.
Spherical harmonics are important in many theoretical and practical applications, particularly in the computation of atomic orbital electron configurations, representation of gravitational fields, geoids, and the magnetic fields of planetary bodies and stars, and characterization of the cosmic microwave background radiation.
Spherical codes are higher-dimensional analogues of Tammes problem, which arose as an attempt to explain the distribution of pores on pollen grains.
which regular solutions for positive energies are given by so-called Bessel functions of the first kind ' so that the solutions written for R are the so-called Spherical Bessel function
Spherical coordinates are one of the most used curvilinear coordinate systems in such fields as Earth sciences, cartography, and physics ( in particular quantum mechanics, relativity ), engineering, etc.
Spherical 3-manifolds are sometimes called elliptic 3-manifolds or Clifford-Klein manifolds.
Spherical tokamaks are not limited by the same instabilities as tokamaks and as such the area is receiving considerable experimental attention.
Spherical astronomy is the branch of astronomy that is concerned with where celestial objects are located and how they move on the celestial sphere.
Spherical groups with a radially fibrous structure and bristled with crystals on the surface are not uncommon.
Spherical and another
Spherical mirrors may be used for direction finding by moving the sensor rather than the mirror ; another unusual example is the Arecibo Observatory ; see also
geometry and two
This choice gives us two alternative forms of geometry in which the interior angles of a triangle add up to exactly 180 degrees or less, respectively, and are known as Euclidean and hyperbolic geometries.
In 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.
In Riemannian geometry, the metric tensor is used to define the angle between two tangents.
In geometry an Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices.
Analytic geometry, or analytical geometry has two different meanings in mathematics.
The second book moves onto two dimensional geometry, i. e. the construction of regular polygons.
Pascal was an important mathematician, helping create two major new areas of research: he wrote a significant treatise on the subject of projective geometry at the age of sixteen, and later corresponded with Pierre de Fermat on probability theory, strongly influencing the development of modern economics and social science.
Brass instruments may also be characterised by two generalizations about geometry of the bore, that is, the tubing between the mouthpiece and the flaring of the tubing into the bell.
* Chord ( geometry ), a line segment joining two points on a curve
The weak and the strong cosmic censorship hypothesis are two conjectures concerned with the global geometry of spacetimes.
) Conversely, it is often helpful to use the geometry of Cartesian coordinates in two or three dimensions to visualize algebraic relationships between two or three of many non-spatial variables.
Diatomic molecules cannot have any geometry but linear, as any two points always lie in a line.
In Euclidean geometry, the ellipse is usually defined as the bounded case of a conic section, or as the set of points such that the sum of the distances to two fixed points ( the foci ) is constant.
In projective geometry, an ellipse can be defined as the set of all points of intersection between corresponding lines of two pencils of lines which are related by a projective map.
For over two thousand years, the adjective " Euclidean " was unnecessary because no other sort of geometry had been conceived.
Euclidean geometry has two fundamental types of measurements: angle and distance.
The two figures on the left are congruent, while the third is Similarity ( geometry ) | similar to them.
At the turn of the 20th century, Otto Stolz, Paul du Bois-Reymond, Giuseppe Veronese, and others produced controversial work on non-Archimedean models of Euclidean geometry, in which the distance between two points may be infinite or infinitesimal, in the Newton – Leibniz sense.
One of the basic tenets of Euclidean geometry is that two figures ( that is, subsets ) of the plane should be considered equivalent ( congruent ) if one can be transformed into the other by some sequence of translations, rotations and reflections.
In the field of numerical relativity, powerful computers are employed to simulate the geometry of spacetime and to solve Einstein's equations for interesting situations such as two colliding black holes.
In geometry, a prismatoid is a polyhedron where all vertices lie in two parallel planes.
In geometry, the truncated icosahedron is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids whose faces are two or more types of regular polygons.
In Minkowski geometry the world lines of inertially moving bodies maximize the proper time elapsed between two events.
0.298 seconds.