Sums of Squares

 In Class Work Homework Textbook: None. But I do recommend John Stillwell's Numbers and Geometry. Here is the course syllabus. Here is the daily agenda from the course. What is the Pythagorean Theorem? Why is it true? Is it true? Definition of Triangle on a Sphere Area of a Triangle on a Sphere Record of What We Did Find a proof of the Pythagorean Theorem. Present it to the class. Write it up and hand it in. Investigate Pythagoras of Samos. Investigate Euclid of Alexandria. What is Area? What is Volume? Dimensions X 1/2 = Volume X 1/8 Volume of a Tetrahedron Volume of a Cone Volume of a Sphere Surface Area of a Sphere Record of What We Did Find a proof of 4\pi r^2 using Calculus. Present it to the class. Investigate Archimedes of Syracuse. Investigate "hyperspheres". Re-submit your proof of Pythagorean Theorem. What is Space? Cartesian Coordinates Equation of a Circle Equation of a Line Intersection of Lines and Circles Record of What We Did Investigate René Descartes. Investigate Pierre de Fermat. Investigate equations of planes/lines in R^3. Choose your favorite mathematician. Write a one page summary. Distance betwenn points in R^3 Equation of a Sphere in R^3 Equation of a Plane/Line in R^3? What is a Vector? Equivalence of Vectors Addition/Subtraction of Vectors The Dot Product! Record of What We Did Read this history of vectors. Choose a topic for Independent Study 1. Go to the library and get a book for IS1. Submit a list of sources for IS1. Set up a meeting with me to discuss IS1. Re-submit PT and sketch of mathematician. Definition of the Dot Product When are two vectors perpendicular? The Law of Cosines Angles Between Vectors Methane Molecules Equation of a Plane in R^3 Parametrized Lines in R^3 Record of What We Did Find a proof of the Law of Cosines and be prepared to share it with us. Hand in a 1 or 2 page outline of your Independent Study 1, including bibliography. Hand in your Independent Study 1. Pythagorean Triples Euclid's Trick Diophantus' Trick Rational Points on Circles Fermat's Christmas Theorem Look up "Plimpton 322". Look up Diophantus of Alexandria. Write up your favorite proof of the Law of Cosines and hand it in. Look up Hypatia of Alexandria. Look up Fermat's Christmas Theorem. The Diophantus-Brahmagupta-Fibonacci Identity A Funny Multiplication on R^2 The Square Root of -1 De Moivre's Formula Rotations of the Plane Look up Brahmagupta. Look up Fibonacci. Look up De Moivre and his formula. Look up Hypatia of Alexandria. Look up Fermat's Christmas Theorem. Look up Carl Friedrich Gauss and the Fundamental Theorem of Algebra.