There are three basic types of geometry: Euclidean, hyperbolic and elliptical. Although there are additional varieties of geometry, they are all based on combinations of these three basic types. Euclidean geometry is the original form, dating back to 300 BC, and it is the result of the work of the Greek Alexandrian mathematician Euclid, who developed the five postulates, or axioms, upon which his geometric theorems are built.Know More
Euclid's fifth postulate, known as the parallel postulate, went without an accompanying proof for thousands of years. The parallel postulate assumes that a straight line crossing through two other straight lines and forming two same-side interior angles of less than 90 degrees determines that those two lines, if extended far enough, will eventually meet on the side of the interior angles. This assumption, however, did not take into account the idea of curved space, which was first conceptualized by Albert Einstein in his 1915 General Theory of Relativity.
The idea of space existing with either a positive or a negative curvature introduced the idea of non-Euclidean geometry, in which the parallel postulate would not always hold true. In curved space, it cannot be assured that the two lines in question will ever meet, regardless of how far they might be extended. The geometry based on space with a negative curvature became known as hyperbolic geometry. Elliptical geometry refers to the type of geometry based on space with a positive curvature.Learn more about Geometry
In geometry, a plane is defined as a flat, infinite surface. It has infinite length and width but no thickness. A plane is thus a two-dimensional, boundless surface and a subset of space.Full Answer >
In geometry, a corollary is a statement that is proven true by another statement or considered to be a consequence of a statement's truth. Corollaries are believed to be true without additional proof besides the initial true statement.Full Answer >
Numerous mathematicians have studied geometry and made major contributions throughout history. Ancient geometers of importance include Pythagoras, Euclid, Hippocrates and Archimedes. More modern figures include Rene Descartes, Isaac Newton and Johann Bolyai.Full Answer >
Geometric forms and structures are abundant in nature, and many of the natural processes that drive growth obey rules that can be described with fractal geometry. Plants, animals and many landforms develop in ways that generate recognizable shapes solely as a result of forces such as natural selection or erosion.Full Answer >