Dual Number Geometry

Similar to Complex numbers, dual numbers can be expressed as

where

and

$ϵ$ is an infinitesimal value such that its square equates to $ϵ$. but its value is not zero. This is because a small number say $0.0001$ when squared, gives an even smaller number $0.00000001$. Thus a small number $ϵ$ when squared, gives $0$.

Using maclaurin series for $e^x$ and Galilean trigo functions.

Used in general relativity and computational algorithms