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Prior to the 1940s, algebraic geometry worked exclusively over the complex numbers, and the most fundamental variety was projective space. The geometry of projective space is closely related to the theory of perspective, and its algebra is described by homogeneous polynomials. All other varieties were defined as subsets of projective space.
Outer space (or simply space) is the expanse that exists beyond Earth's atmosphere and between celestial bodies. [1] It contains ultra-low levels of particle densities , constituting a near-perfect vacuum [ 2 ] of predominantly hydrogen and helium plasma , permeated by electromagnetic radiation , cosmic rays , neutrinos , magnetic fields and dust .
Space is a three-dimensional continuum containing positions and directions. [1] In classical physics , physical space is often conceived in three linear dimensions . Modern physicists usually consider it, with time , to be part of a boundless four-dimensional continuum known as spacetime . [ 2 ]
Figure 1: The four charts each map part of the circle to an open interval, and together cover the whole circle. After a line, a circle is the simplest example of a topological manifold. Topology ignores bending, so a small piece of a circle is treated the same as a small piece of a line.
This glossary of biology terms is a list of definitions of fundamental terms and concepts used in biology, the study of life and of living organisms.It is intended as introductory material for novices; for more specific and technical definitions from sub-disciplines and related fields, see Glossary of cell biology, Glossary of genetics, Glossary of evolutionary biology, Glossary of ecology ...
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements , it was the three-dimensional space of Euclidean geometry , but in modern mathematics there are Euclidean spaces of any positive integer dimension n , which are called Euclidean n -spaces when one wants to specify their ...
For example, a 1-dimensional line may be studied in isolation —in which case the ambient space of is , or it may be studied as an object embedded in 2-dimensional Euclidean space —in which case the ambient space of is , or as an object embedded in 2-dimensional hyperbolic space —in which case the ambient space of is .
A homogeneous space of N dimensions admits a set of 1 / 2 N(N + 1) Killing vectors. [5] For three dimensions, this gives a total of six linearly independent Killing vector fields; homogeneous 3-spaces have the property that one may use linear combinations of these to find three everywhere non-vanishing Killing vector fields ξ ( a )
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