Geometry (Ancient Greek: γεωμετρία; geo- "earth", -metri "measurement") "Earth-measuring" is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Geometry is one of the oldest mathematical sciences. Initially a body of practical knowledge concerning lengths, areas, and volumes, in the 3rd century BC geometry was put into an axiomatic form by Euclid, whose treatment—Euclidean geometry—set a standard for many centuries to follow. Archimedes developed ingenious techniques for calculating areas and volumes, in many ways anticipating modern integral calculus. The field of astronomy, especially mapping the positions of the stars and planets on the celestial sphere and describing the relationship between movements of celestial bodies, served as an important source of geometric problems during the next one and a half millennia. A mathematician who works in the field of geometry is called a geometer.

The introduction of coordinates by René Descartes and the concurrent development of algebra marked a new stage for geometry, since geometric figures, such as plane curves, could now be represented analytically, i.e., with functions and equations. This played a key role in the emergence of infinitesimal calculus in the 17th century. Furthermore, the theory of perspective showed that there is more to geometry than just the metric properties of figures: perspective is the origin of projective geometry. The subject of geometry was further enriched by the study of intrinsic structure of geometric objects that originated with Euler and Gauss and led to the creation of topology and differential geometry.

In Euclid's time there was no clear distinction between physical space and geometrical space. Since the 19th-century discovery of non-Euclidean geometry, the concept of space has undergone a radical transformation, and the question arose which geometrical space best fits physical space. With the rise of formal mathematics in the 20th century, also 'space' (and 'point', 'line', 'plane') lost its intuitive contents, so today we have to distinguish between physical space, geometrical spaces (in which 'space', 'point' etc. still have their intuitive meaning) and abstract spaces. Contemporary geometry considers manifolds, spaces that are considerably more abstract than the familiar Euclidean space, which they only approximately resemble at small scales. These spaces may be endowed with additional structure, allowing one to speak about length. Modern geometry has multiple strong bonds with physics, exemplified by the ties between pseudo-Riemannian geometry and general relativity. One of the youngest physical theories, string theory, is also very geometric in flavour.

While the visual nature of geometry makes it initially more accessible than other parts of mathematics, such as algebra or number theory, geometric language is also used in contexts far removed from its traditional, Euclidean provenance (for example, in fractal geometry and algebraic geometry).

Adjective

geometric (comparative more geometric, superlative most geometric)

1. Of, or relating to geometry.
   • The architect used geometric techniques to design her home.
2. increasing or decreasing in a geometric progression.
   • Bacteria exhibit geometric increase in numbers when the environment is not limiting.
3. Using simple shapes such as circles, triangles and lines in a decorative object.
   • The building's profile was strikingly geometric.

Synonyms

• (of or relating to geometry): geometrical
• (using simple shapes): geometrical

Matching Results for Geometric:

Giuseppe Peano
Geometric calculus consists in a system of operations analogous to those of ... Geometric calculus consists in a system of operations analogous to those of ...

Wassily Kandinsky
Thus we look upon the geometric point as the ultimate and most singular union of ... The geometric point has, therefore, been given its material form, in the first ...

Omar Khayyám
This quotation has often been abridged in various ways, usually ending with "Algebras are geometric facts which are proved", thus altering the context significantly. ...

	New Location:
city:
state/region:
country:

Arts: Visual Arts: Personal Pages: K
This category in other languages: Danish (13) German (104) Artwork by David K. Klaren - Current work by David K. Klaren, contemporary visual artist based in Pinedale ...

---

Science: Math: Topology: Knot Theory
See also: Reference: Knots (83) Science: Math: Topology: Geometric Topology (6) Knots on the Web (Peter Suber) - A collection of knotting resources on the web.

---

Recreation: Kites: Plans: Flat and Bowed Kites
Abu dako - Japanese horsefly kite (plan at end of page), Arch - Straightforward design for arch of diamond kites.