In 1916, Albert Einstein published his theory of general relativity, which provided a unified description of gravity as a geometric property of space and time.

One often cited description that Mandelbrot published to describe geometric fractals is " a rough or fragmented geometric shape that can be split into parts, each of which is ( at least approximately ) a reduced-size copy of the whole "; this is generally helpful but limited.

General relativity, or the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1916 and the current description of gravitation in modern physics.

General relativity generalises special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime.

The first step is the realization that classical mechanics and Newton's law of gravity admit of a geometric description.

The result is a geometric formulation of Newtonian gravity using only covariant concepts, i. e. a description which is valid in any desired coordinate system.

However, the most important contribution of Minkowski's geometric viewpoint of spacetime turned out to be in Einstein's later development of general relativity, since the correct description of the effect of gravitation on space and time was found to be most easily visualized as a " warp " or stretching in the geometrical fabric of space and time, in a smooth and continuous way that changed smoothly from point-to-point along the spacetime fabric.

In multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis.

MetaPost excels at producing diagrams in the PostScript programming language from a geometric / algebraic description.

and interact between the algebraic and geometric description of those via this duality.

The connection of quantum field theories to a physical geometric description is less obvious than the connection between the classical equations ( i. e. non-quantum mechanical descriptions of gravity and electromagnetism ) and geometry.

" In such a linguistic system, the concept of linear progress of time, geometric shapes, and even conventional methods of description are lost altogether or altered.

The first example of this restriction appeared in the 1984 article Potentials and Symmetries of General Gauged N = 2 Supergravity: Yang-Mills Models by Bernard de Wit and Antoine Van Proeyen, while a general geometric description of the underlying geometry, called special geometry, was present by Andrew Strominger in his 1990 paper Special Geometry.

In mathematics, an abstract simplicial complex is a purely combinatorial description of the geometric notion of a simplicial complex, consisting of a family of finite sets closed under the operation of taking subsets.

The translated ancient Roman and Greek accounts give a vivid description of the tomb both geometrically and aesthetically ; The tomb's geometric shape has changed little over the years, still maintaining a large stone of quadrangular form at the base, followed by a pyramidal succession of smaller rectangular stones, until after a few slabs, the structure is curtailed by an edifice, with an arched roof composed of a pyramidal shaped stone, and a small opening or window on the side, where the slenderst man could barely squeeze through.

In mathematics, sheaf cohomology is the aspect of sheaf theory, concerned with sheaves of abelian groups, that applies homological algebra to make possible effective calculation of the global sections of a sheaf F. This is the main step, in numerous areas, from sheaf theory as a description of a geometric problem, to its use as a tool capable of calculating dimensions of important geometric invariants.

a geometric description of the location and rotation of each part, and the exact path of each wire connecting them.

With the help of Riemannian geometry, Einstein formulated a geometric description of gravity in which Minkowski's spacetime is replaced by distorted, curved spacetime, just as curved surfaces are a generalization of ordinary plane surfaces.

His work contains a detailed description of the geometric dioptrics for uncentered systems.

Digital DATCOM requires an input file containing a geometric description of an aircraft, and outputs its corresponding dimensionless stability derivatives according to the specified flight conditions.

While this ' geometric ' description related to the kinematic solution ( using the Bragg condition ) is very powerful and useful for orientation and texture analysis, it only describes the geometry of the crystalline lattice and ignores many physical processes involved within the diffracting material.

The bridge inventory is developed with the purpose of having a unified database for bridges, including identification information, bridge types and specifications, operational conditions, bridge data including geometric data and functional description, inspection data, etc.

Drawing further upon the analogy with geometric Newtonian gravity, it is natural to assume that the field equation for gravity relates this tensor and the Ricci tensor, which describes a particular class of tidal effects: the change in volume for a small cloud of test particles that are initially at rest, and then fall freely.

Having formulated the relativistic, geometric version of the effects of gravity, the question of gravity's source remains.

Physical optics is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics.

Other causes of a UHI are due to geometric effects.

This stage may consist of visual effects, with an intensification of colors and the appearance of geometric patterns that can be seen with one ’ s eyes closed.

3D graphics are created via the process of designing imagery from geometric shapes, polygons or NURBS curves to create three-dimensional objects and scenes for use in various media such as film, television, print, rapid prototyping, games / simulations and special visual effects.

Diffraction effects from wave optics and the finite aperture of a lens can be included in the circle of least confusion ; the more general circle of confusion for out-of-focus points is often computed in terms of pure ray ( geometric ) optics.

Several uncertainties contribute to the determination of a precise value for critical masses, including ( 1 ) detailed knowledge of cross sections, ( 2 ) calculation of geometric effects.

While many users of lower doses of 2C-E have reported that the compound produces mainly closed-eye visuals, users of higher doses have compared its open-eye visuals with those produced by LSD ; a significant proportion of these comparisons have favored the visual effects of 2C-E in terms both of their geometric complexity and in the variety of colors seen during an experience.

The visual distortions produced by 2C-E are comparable in some respects to those produced by mescaline, and some users of both drugs have reported that the visual effects of 2C-E are more emphatic of color than are mescaline's corresponding effects, while mescaline's visuals are more emphatic of geometric structure.

However, sound radiated from an infinite plane source is not attenuated due to geometric spreading, but is affected by other sound propagation effects.

String theory, a leading candidate for a quantum theory of gravity, uses the term quantum geometry to describe exotic phenomena such as T-duality and other geometric dualities, mirror symmetry, topology-changing transitions, minimal possible distance scale, and other effects that challenge our usual geometrical intuition.

The tactical egg shows the effects of gravity on manoeuvringThe turning battle of a dogfight can be executed in an infinite number of geometric planes.

All metric theories satisfy the Einstein equivalence principle, which in modern geometric language states that in a very small region ( too small to exhibit measurable curvature effects ), all the laws of physics known in special relativity are valid in local Lorentz frames.

This feature can be used to create geometric elements at runtime of the renderer, procedural textures, bump and displacement maps, atmosphere and volume effects, environments, camera lenses, and light sources.

For simplicity we will consider only the geometric effects on as we get further from the ionizing source ( a source of flux ), so we have an inverse square law:

* A shift operator, which effects a geometric translation.

The listed chapel in the style of High Victorian Gothic Revival is noted for polychrome effects, geometric tiling and an unusual gallery, supported on marble pillars.

In this context, it is an intermediate method between geometric optics, which ignores wave effects, and full wave electromagnetism, which is a precise theory.

SqueeZoom DVE effects could be seen during CBS ' broadcast of the 1978 Grammy Awards, where album cover art would flip and tumble ( on the " X " and " Y " geometric axis ) as nominees names would be announced.