Show that the set of all positive integers is equivalent to the set of all positive even integers. Describe the characteristics of each, and give examples. Describe the arithmetic, geometric, and heronian mean of two numbers.
Ontogeny recapitulates phylogony.
Give one or more of your favorite proofs of the pythagorean theorem. Define the concepts congruent by addition and congruent by subtraction. Explain how Pappus's theorem is a generalization of the pythagorean theorem, and prove it. Monday January 29 Show how sums, differences, products, quotients, and square roots can be found geometrically. Wednesday January 31 Prove that the square root of 2 is not rational.