ABSTRACT
This chapter derives various traits of Pascal’s triangle and proves them by applying the Definition of Combinations and by Induction. It examines Definition of Combinations in the horizontal direction to analyze the triangle’s Horizontally Oriented Identities and in the diagonal direction to examine the triangle’s Diagonally Oriented Identities. To obtain the triangle’s Horizontally Oriented Identities, the triangle figure is decomposed into blue and red horizontal rows (the blue rows are even-ordered rows and the red rows are odd-ordered rows). The chapter depicts the triangle’s Pascal’s Identity by adding two neighboring horizontal terms in each row. It analyzes an example that renders the triangle’s Symmetry Identity.
