Homology Groups of Graphs

Abstract

Ancient Greek mathematicians tried to establish their theory of area and volume by means of “geometric algebra”. Namely, in order to compare the area (or volume) of two figures, they made up an algebraic system with addition and subtraction performed among a class of figures, e.g., polygons or polyhedra. Figure 4.1 illustrates a way to prove using geometric algebra that the area of a triangle is equal to one-half of the area of a rectangle with the same base and height.