sitedownload.blogg.se - Non euclidean geometry in geography

Euclid ’s parallel postulate may also be stated as one and only one parallel to a given line goes through a given point not on the line.Įlliptic geometry uses a modification of Postulate II. Hyperbolic geometry is based on changing Euclid ’s parallelpostulate, which is also referred to as Euclid ’s fifth postulate, the last of the five postulates of Euclidian Geometry. Although there are different types of non-Euclidean geometry which do not use all of the postulates or make alterations of one or more of the postulates of Euclidean geometry, hyperbolic and elliptic are usually most closely associated with the term non-Euclidean geometry. If a transversal falls on two lines in such a way that the interior angles on one side of the transversal are less than two right angles, then the lines meet on the side on which the angles are less than two right angles.Ī consistent logical system for which one of these postulates is modified in an essential way is non-Euclidean geometry.All right angles are equal to one another.

A circle may be described with any point as center and any distance as a radius.

A finite straight line can be produced continuously in a straight line.

A straight line can be drawn from any point to any point.

The first five postulates of Euclidean geometry will be listed in order to better understand the changes that are made to make it non-Euclidean. 265 BC), what is called Euclid ’s geometry or Euclidean geometry. These geometries deal with more complex components of curves in space rather than the simple plane or solids used as the foundation for the geometry invented by Euclid of Alexandria (c. There are other types of geometry that do not assume all of Euclid ’s postulates such as hyperbolic geometry, elliptic geometry, spherical geometry, descriptive geometry, differential geometry, geometric algebra, and multidimensional geometry.

Non-Euclidean geometry refers to certain types of geometry that differ from plane geometry and solid geometry, which dominated the realm of mathematics for several centuries.