Definitions

Author:Christina Tran

To help you better understand the rational geometry system, definitions are given below. 2-D Definitions

A rational point is any element of

or a point of the form

such that

, and

are rational numbers. A rational line can be written

where

and

are rational numbers. A rational segment lies on a rational line and has rational endpoints. Rational polygons are defined by rational segments. A rational circle is the set of rational points satisfying

, where

, and

are rational. 3-D Definitions

A rational point is any element of

or a point of the form

where

and

are rational. A rational vector is a vector that connects two rational points. A rational line can be written

where

and

are rational numbers. A rational plane is the set of all the rational points that satisfy the equation

for rational

. A sphere is the set of rational points satisfying

, where

and

are rational. Functions A rational function can be expressed as

where

and

are polynomials with rational coefficients. Transformations A rational transformation is a rational function that maps one set of points to another.

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