• Pythagoras of Samos (approx 569-475 BC)
• Pythagorean triples
• many proofs of the Pythagorean Theorem
• an annotated animated proof of the Pythagorean Theorem
• Zeno of Elea (approx 490-425 BC) -- originally a Pythagorean. Most famous for his paradoxes about infinity.
• Meno, one of Plato's dialogues. Using leading questions, Socrates prompts Meno's slave into "remembering" the Pythagorean Theorem.

• Theodorus of Cyrene (approx 465-398 BC) -- apparently learned of incommensurables from the Pythagoreans
• Theaetetus of Athens (approx 417-369 BC), student of Theodorus, extended results on incommensurables; his ideas found their way into Euclid's Elements
• Plato (427-347 BC)
• Eudoxus of Cnidus (408-355 BC) -- invented a method of comparing 2 cross-ratios, so that it was possible to study the ratio of two incommensurable magnitudes.

• How to bisect an angle
• An Introduction to the Works of Euclid With an Emphasis on the Elements by Donald Lancon, Jr.
• David Joyce's animated Euclid
  • Euclid, Book VI, Proposition 12 -- this is the construction used in Lemma 1a, page 10, of Hadlock's book
  • Euclid, Book VI, Proposition 13 -- this is the construction used in Lemma 1b, page 13, of Hadlock's book
• Interactive Miscellany: geometry
• Some interesting geometry computer programs with free downloadable demos. Geometer's Sketchpad and Cabri Geometer.
• straightedge unnecessary for classical constructions

• Decimal numbers -- for integers and for fractions -- were introduced by many mathematicians over a period of many years, from around 1000 AD to around 1600 AD, starting in India and the Moslem world and later spreading to Europe.

• a timeline about solving polynomial equations and explaining real numbers
• Fourier believed that every function could be represented as a sum of a trigonometric series; here is the sum of the first few terms of the series that approximates a square wave.

Still under construction: Following are some links that I may use later in the course; they're not entirely sorted out yet.

• Pythagorean theorem equivalent to parallel postulate
• Georg Friedrich Bernhard Riemann (1826-1866)
• Review of a biography of Riemann
• Non-Euclidean geometries
• NonEuclid free software for non-Euclidean geometry
• The Geometry Center's gallery of illustrations of hyperbolic geometry
• Dodecahedra: in Euclidean space and in hyperbolic space
• Models of the Hyperbolic Plane
• Hyperbolic.m: A general-purpose hyperbolic geometry package -- free software for manipulating hyperbolic objects (in any dimensional hyperbolic space) such as points, lines, vectors, polyhedra, and other structures. Available for unix or macintosh; requires Mathematica 2.0 or greater.
• The Geometry Center's public software ftp directory and a description of its contents.

• The Galileo Project -- information on the life and work of Galileo Galilei (1564-1642) and the science of his time.

• A few quotes about the meaning of modern mathematics
• Formalizing mathematics -- Principia Mathematica (1910, 1912, 1913), by Whitehead and Russell; and more recently, automatic theorem-proving systems such as Isabelle