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)
^up
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
And look what we've got now...
Angle
Compass
computational geometry
Curve
Degree
differential geometry
distinct non-parallel straight lines
Equiangular
Geometric
Geometry
Line
metric space
Metric Topology
Orthogonal
Orthographic
Parallel
Perpendicular
Pi
Point
Pythagorean
Pythagorean Theorem
Pythagorean Triple
Shape
Side
Spiral
Straight-edge
The three geometric problems of antiquity
Topological Space
Trisection of the angle
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
How to carve a dodecahedron out of a cube
How to construct a dodecahedron
Helix
moebius strip
Platonic solid
Polar
Polar geometry
Polygon
Rational box
Sphere
Tetrahedron
three-dimensional
4D
ana
curved space
four-dimensional
Hypercube
Hypersphere
kata
Klein Bottle
Minkowski Space
Tesseract
The fourth dimension (no, really)
4D Transverse Wave
5D, fifth dimension.
What your looking for is probably listed under 4D, or maybe it just hasn't been noded yet...
If you're into multiple dimentions, you might want to look into Superstring Theory.
I'm sure there's many more, /msg me with additions. No nodeshells, please.