Some basic properties of bigeometric calculus and its applications in numerical analysis

Abstract

Objective of this paper is to visualize a new type of number line which will be called geometric number line based on geometric arithmetic introduced by Grossman and Katz in the book Non-Newtonian calculus (Grossman and Katz, Lee Press, Massachusetts, 1972). Then, we introduce different types of interpolation formulae for geometrically equal and geometrically unequal values of the argument. In our whole discussion, we’ll use geometric increment to the arguments instead of linear increments. We will apply the new formule to different problems of numerical analysis.