Ancient Mathematics: How the Babylonians and Chinese may have found the correct formula for the area of a circle, , where is circumference and diameter. (Two different methods were shown.)
The incommensurability of the side and diagonal of a square.
Dunham Chap. 1: Two Preliminaries (Triangle to Rectangle, to Square), followed by Great Theorem and Proof 1: Hippocrates of Chios Squares the Lune
Proof: Euclid I-6
Proof: Euclid I-29, Euclid's first use of Postulate 5
Dunham Chap. 2:
One Preliminary (Euclid I-41), followed by Great Theorem and Proof 2: Euclid's Proof of I-47, the Pythagorean Theorem
Proof of Euclid I-48, the Pythagorean Theorem Converse
Proof: Euclid VI-12, "Construct , so that "
Dunham Chap. 3: Preliminaries (Defs of prime and composite), following by Great Theorem and Proof 3: Euclid's Proof of IX-20, infinitude of primes
Proof: Euclid XII-2, Circles to diameters-squared (Method of Exhaustion)
Eratosthenes, Circumference of the Earth
Archimedes "On the Equilibrium of Planes". Proof: Proposition 6, The Law of the Lever (Commensurable case only)
Dunham Chap. 4: Four Preliminaries (See Class notes), followed by Great Theorem and Proof 4: Archimedes "On the Measurement of The Circle", Proposition 1, The Area of a Circle
Archimedes "The Method", Proposition 1, Area of a Parabolic Segment: Ideas of 1st Proof: By the Law of the Lever
Apollonius Proposition I-33, drawing a tangent to a parabola
Archimedes' Trisection of an Angle with a marked straightedge
Ptolemy's Theorem and Proof
Diophantus Arithmetica, problems I-28 and II-13
Chinese Remainder Problem and solution
The three famous Greek construction problems and the restrictions under which they were to be solved.
The Greek distinction between Numbers (The Discrete) and Magnitude (The Continuous)
Statement & Explanation: Euclid's five postulates. Statement: Euclid's five common notions
Statement: Euclid II-4, Example of Geometric Algebra
Statement & Use: Euclidean Algorithm, gcd of two numbers
Statements and Meaning: Euclid IX-35, Euclid X-1, Euclid X-9
Proof Explication of some not previously seen result