Geometry

Geometry is the branch of mathematics that deals with properties of shapes and spatial relationships. In its modern form, it is the pure mathematics of points and lines and curves and surfaces. It is one of the two most basic branches of mathematics, the other being algebra, the study of relationships between numbers. Primarily, the subject may be divided into six branches:

• Euclidean geometry studies geometry where the parallel postulate is valid.

• Non-Euclidean geometry studies geometry where the parallel postulate is false.

• Differential geometry studies properties of smooth shapes called differentiable manifolds by analyzing their curvature properties.

• Algebraic geometry studies properties of shapes defined by algebraic equations, by making use of the additional structures these objects inherit from their algebraic nature.

• Topology, broadly speaking, studies properties of shapes invariant under continuous functions.

• Riemannian geometry, a geometry developed by Riemann.

There are a few main types of spatial forms:

• Points, an infinitely small dot.
• Lines, an infinitely long set of points expanding in two opposite directions.
• Planes, an infinitely wide set of lines, stretching out in four directions.
• Space, all of the 3-dimensional space that points, lines, and planes exist ons.