Null geometric algebra with geometric interpretation

Null geometric algebra (NGA) refers to a basis-free version of Clifford algebra where the base vector space is spanned by vectors whose inner product with itself equals zero. It provides powerful tools for manipulating expressions in conformal geometric algebra (CGA) when making symbolic reasoning in classical geometry. This paper develops several new techniques in NGA and uses them to explore the geometric interpretations of basic algebraic objects in NGA—null monomials, their scalar parts and pseudo-scalar parts, centred null binomials—and illustrates how these objects are used in making geometric reasoning for problems in classical geometry. This article is part of the theme issue ‘Modern applications of geometric algebra’.