The Equation

Abstract

We begin with a history of counting in the Middle East, and how it began as a method of accounting for real things. These historical sections can be nested within the Social Sciences section of the Common Core Curriculum. We discuss flock numbers and field numbers, and the measurement of areas with a right triangle and the Pythagorean theorem. We show that the right angle is the most fundamental unit of measure in geometry, and that further application of the Pythagorean theorem makes it one of the most important formulas in understanding later sciences. We review algebraic ratios and proportions. We discuss measurements and proportions of ancient star lore. When we discuss Euclid’s axioms and the concepts of pure mathematical proof, we discuss the implications for students of moving from counting and measuring real things toward abstract principles of proof.