The Real Numbers

Abstract

0. In their constructions, the Egyptians use the rational approximation for the irrational π ≈ 22 7 number. π ≈ 3 141592. ...... a. What is the relative error of their approximation? 1. Consider the number. 3 a. Carefully explain the meaning of the number to an elementary school student: 3 is the number that 3 b. Using a compass and straightedge only, give a formal construction of (a segment with length) 3 c. Using pencil and paper only, approximate the decimal value of by bisection 3 (interval halving). Show all intermediate results.