Search results
Results From The WOW.Com Content Network
Compared to Euclidean geometry, hyperbolic geometry presents numerous difficulties for a coordinate system: the sum of the angles of a quadrilateral is always less than 360 degrees; there are no equidistant lines, so a proper Euclidean rectangle would need to be enclosed by two lines and two hypercycles; parallel-transporting a line segment ...
The mathematical derivation of an idealized Hubble's law for a uniformly expanding universe is a fairly elementary theorem of geometry in 3-dimensional Cartesian/Newtonian coordinate space, which, considered as a metric space, is entirely homogeneous and isotropic (properties do not vary with location or direction). Simply stated, the theorem ...
Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems. Classically, it studies zeros of multivariate polynomials; the modern approach generalizes this in a few different aspects. The fundamental objects of study in algebraic geometry are algebraic ...
A ray through the unit circle x 2 + y 2 = 1 in the point (cos a, sin a), where a is twice the area between the ray, the circle, and the x-axis. Figure 4-1b. A ray through the unit hyperbola x 2 − y 2 = 1 in the point (cosh a , sinh a ) , where a is twice the area between the ray, the hyperbola, and the x -axis.
Geometrical optics. Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances. The simplifying assumptions of geometrical optics include that light rays:
Geometric topology as an area distinct from algebraic topology may be said to have originated in the 1935 classification of lens spaces by Reidemeister torsion, which required distinguishing spaces that are homotopy equivalent but not homeomorphic. This was the origin of simple homotopy theory. The use of the term geometric topology to describe ...
Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space). [1] A solid figure is the region of 3D space bounded by a two-dimensional surface; for example, a solid ball consists of a sphere and its interior . Solid geometry deals with the measurements of volumes of various solids, including pyramids, prisms ...
Newton's law of universal gravitation, part of classical mechanics, does not provide for their existence, since that law is predicated on the assumption that physical interactions propagate instantaneously (at infinite speed) – showing one of the ways the methods of Newtonian physics are unable to explain phenomena associated with relativity.