The geometry of ancient Greece, as characterized by Euclid's famous book, the Elements, has formed the basis of much of modern mathematical thought. For example, the Greek insistence on strict methods of proof has survived to this day. The...

Plane (or Euclidean) geometry is the branch of mathematics that studies figures (such as points, lines, and angles) constructed only with the use of the straightedge and the compass. It is primarily concerned with such problems as determining the areas...

The ancient Greeks felt that the line and the circle are the basic figures and the straightedge and compass are their physical analogues. Hence they were interested in what can be done with a straightedge and compass, i.e. what figures are Euclidean...

Euclid's axioms are five postulates about the behavior of geometric objects; they constitute the foundation upon which Euclid built the entire edifice of geometry that is known today as Euclidean geometry. Before Euclid wrote his famous book The...

Euclidean geometry, sometimes called parabolic geometry, is a geometry that follows a set of propositions that are based on Euclid's five postulates (see Euclid's axioms), as defined in his book The Elements. More specifically, Euclidean geometry is...

Plane geometry is that subsection of geometry that deals with figures in a two-dimensional plane. Euclidean geometry, sometimes called parabolic geometry, is divided into two subsections: plane geometry, geometry dealing with figures in a plane, and...

Study of points, lines, angles, surfaces, and solids based on Euclid's axioms. Its importance lies less in its results than in the systematic method Euclid used to develop and present them. This axiomatic method has been the model for many systems of...

Euclidean geometry is a mathematical system attributed to the Greek mathematician Euclid of Alexandria. Euclid's text Elements is the earliest known systematic discussion of geometry. It has been one of the most influential books in history, as much for...