geometry

Geometry was humanity's first success in understanding how the world worked without resorting to spirits, gods, and devils.

The granddaddy of all sciences, geometry probably arose out of techniques developed in Ancient Egypt to re-survey land after the Nile River's annual flood. Although appropriated as a pseudoscience by the Pythagoreans, a group of Classical Greek mystics, geometry was developed into a systematic science by Euclid, who worked in Alexandria during Hellenistic times.

The actual postulates and theorems presented by Euclid are eclipsed by the systematic method he used to develop geometry, building up from postulates (aka axioms) and proceeding with absolute rigor to the inexorable conclusions of those axioms. Preserved during the Dark Ages as one of the Quadrivium of Liberal Arts, this method had consequences reaching far beyond geometry itself. The axiomatic method was eventually used to systematize other branches of mathematics, and gave Isaac Newton the idea that he could systematize mathematical principles of natural philosophy (aka 'physics'). Thomas Jefferson's inspiration for the American Declaration of Independence is said to have been a copy of Euclid's Elements that he encountered while visiting the home of his neighbor James Madison. (Gz)

Common geometric formulas
Geometric shapes

First:
parallel postulate
Euclid's Elements
Euclidean Geometry
Euclidean Space
Affine Geometry
analytic geometry (needs to be filled!)
Euclidean vector space
Trigonometry

Then:
Non-Euclidean
Non-Euclidean geometry
(Non-Euclidian geometry)
----
Gram-Schmidt Theorem
Noncommutative Geometry
Spherical Geometry

0D (yes, very odd...), the 0th dimension
mathematical point
point
zero-dimensional

1D
Line
one-dimensional
Point

2D, Two dimensional , Two-dimensional
Central Dilatation
Circle
collinear
coordinate geometry
diamond
Flatland
Flatland: A Romance of Many Dimensions
Golden ratio
Homologous point
Homothetic position
Parallelogram
perpendicular bisector
polar geometry
Quadrature of the circle
Quadrilateral
Rectangle
Similitude center
Square
The golden ratio
Trapezium
Trapezoid
Triangle
two-dimensional

3D Three dimensional
Cone
Cube
Dodecahedron

Ge*om"e*try (?), n; pl. Geometries (#) [F. g'eom'etrie, L. geometria, fr. Gr. , fr. to measure land; , , the earth + to measure. So called because one of its earliest and most important applications was to the measurement of the earth's surface. See Geometer.]

1.

That branch of mathematics which investigates the relations, properties, and measurement of solids, surfaces, lines, and angles; the science which treats of the properties and relations of magnitudes; the science of the relations of space.

2.

A treatise on this science.

Analytical or Coordinate, geometry, that branch of mathematical analysis which has for its object the analytical investigation of the relations and properties of geometrical magnitudes. -- Descriptive geometry, that part of geometry which treats of the graphic solution of all problems involving three dimensions. -- Elementary geometry, that part of geometry which treats of the simple properties of straight lines, circles, plane surface, solids bounded by plane surfaces, the sphere, the cylinder, and the right cone. -- Higher geometry, that pert of geometry which treats of those properties of straight lines, circles, etc., which are less simple in their relations, and of curves and surfaces of the second and higher degrees.

© Webster 1913.