# The Geometric Representation of Numbers and Numeric Operations

Early Greek mathematics was largely based on geometry. The Greeks figured out how to add, subtract, and multiply geometrically. Here are a few ways to construct lines of specific lengths (such as √2) given a line that has a length of one. When a line has a length of one, we say it is unity.

René Descartes came up with this way to solve a special case of the quadratic equation geometrically.

Descartes Multiplication

René Descartes came up with this way to multiply geometrically.

Construct √2 Using Geometry

Geometry and numbers are closely related. Given a line segment of length 1, you can construct a line segment of length √2.

Construct √3 Using Geometry

Geometry and numbers are closely related. Given a line segment of length 1, you can construct a line segment of length √3.

Construct √5 Using Geometry

Geometry and numbers are closely related. Given a line segment of length 1, you can construct a line segment of length √5.

Construct √6 Using Geometry

Geometry and numbers are closely related. Given a line segment of length 1, you can construct a line segment of length √6.