Lines and Cross-Ratios

Abstract

At this stage of this monograph we enter a significant didactic problem. There are three concepts that are intimately related and that unfold their full power only if they play together. These concepts are performing calculations with geometric objects, determinants and determinant algebra, and geometric incidence theorems. The reader should understand that in a beginner’s text that makes few assumptions about prior knowledge, these concepts must be introduced sequentially. Therefore we will sacrifice some mathematical beauty for clarity of exposition. Still, we highly recommend that the following chapters be read (at least) twice, so that the reader may obtain an impression of the interplay of the different concepts.