Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects like the point ,
line , circle , triangle ,
and polygon ), solid geometry
(dealing with objects like the line , sphere ,
and polyhedron ), and spherical
geometry (dealing with objects like the spherical
triangle and spherical polygon ). Geometry
was part of the quadrivium taught in medieval universities.
A mathematical pun notes that without geometry, life is pointless. An old children's joke asks, "What does an acorn say when it grows up?" and answers, "Geometry" ("gee, I'm a tree").
Historically, the study of geometry proceeds from a small number of accepted truths (axioms or postulates ), then
builds up true statements using a systematic and rigorous step-by-step proof .
However, there is much more to geometry than this relatively dry textbook approach,
as evidenced by some of the beautiful and unexpected results of projective
geometry (not to mention Schubert's powerful but questionable enumerative
geometry ).
The late mathematician E. T. Bell has described geometry as follows (Coxeter and Greitzer 1967, p. 1): "With a literature much vaster than those of
algebra and arithmetic
combined, and at least as extensive as that of analysis ,
geometry is a richer treasure house of more interesting and half-forgotten things,
which a hurried generation has no leisure to enjoy, than any other division of mathematics."
While the literature of algebra , arithmetic ,
and analysis has grown extensively since Bell's day,
the remainder of his commentary holds even more so today.
Formally, a geometry is defined as a complete locally homogeneous Riemannian manifold . In ,
the possible geometries are Euclidean planar, hyperbolic planar, and elliptic planar.
In , the possible geometries include Euclidean,
hyperbolic, and elliptic, but also include five other types.
See also Absolute Geometry ,
Affine Geometry ,
Analytic Geometry ,
Cartesian
Coordinates ,
Combinatorial Geometry ,
Computational Geometry ,
Differential
Geometry ,
Discrete Geometry ,
Enumerative
Geometry ,
Finsler Geometry ,
Inversive
Geometry ,
Kawaguchi Geometry ,
Nil
Geometry ,
Non-Euclidean Geometry ,
Ordered Geometry ,
Plane
Geometry ,
Projective Geometry ,
Sol
Geometry ,
Solid Geometry ,
Spherical
Geometry ,
Stochastic Geometry ,
Thurston's
Geometrization Conjecture Explore
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F. Famous
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Cite this as:
Weisstein, Eric W. "Geometry." From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/Geometry.html
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