Ideas in Geometry

This learning project is meant to be an aid for teachers and students of a college mathematics course using the text "Ideas in Geometry". This text, licensed under the Creative Commons Attribution-ShareAlike License, is freely available its University of Illinois course website. Ideas in Geometry includes a few of the topics found in standard Euclidean Geometry, however it mostly covers slightly more advanced geometric topics, as well as topics in probability, logic, and other mathematical areas. The goal is not so much to teach proficiency in common geometric procedures, but rather to convey the spirit of mathematics.

The project will break down the topics of this text into amounts suitable for a single hour class. Each of these lessons will be treated by a student in the Fall 2010 semester of this course at Illinois. Students will also use some of the problems from the book as instructive examples to accompany the lessons.

Math 119

• Lesson One: Euclid's Axioms
• Lesson Two: Spherical Geometry
• Lesson Three: The Parallel Postulate
• Lesson Four: Algebraic Geometry
• Lesson Five: Analytic Geometry
• Lesson Six: Introduction to City Geometry
• Lesson Seven: More City Geometry
• Lesson Eight: Hyperbolic Geometry
• Lesson Nine: Mapping the Globe
• Lesson 9: Set Theory
• Lesson 10 Logic
• Lesson Eleven: The Pythagorean Theorem
• Lesson Twelve: The Pythagorean Theorem
• Lesson Thirteen: Proofs by Picture
• Lesson Fourteen: Proofs by Picture II
• Lesson Fifteen: Proof by Picture III
• Lesson Eighteen: Center of Triangles
• Lesson Eighteen: Area
• Lesson Nineteen: Triangles
• Lesson Twenty: Area
• Lesson Twenty One: Continued Fractions
• Lesson twenty two: Areas and Ratios
• Lesson Twenty Three: Wacky Dice
• Lesson Twenty-Four: Probability Paradoxes
• Lesson Twenty Five: Fibonacci Numbers
• Lesson twenty six: Constructions I
• Lesson Twenty six triangles
• Lesson twenty seven: Constructions II
• Lesson Twenty Nine: Introduction to Constructible Numbers
• Lesson Twenty-Nine: Constructible Polygons and Impossibilities
• Lesson Thirty: Fields
• Lesson Thirty One: Constructible Polygons
• Lesson Thirty Two: Symmetry Groups
• Lesson Thirty Three: Origami Constructions
• Lesson Thirty Four: Geometry of the Complex Numbers
• Lesson Thirty Five: Geometry of the (Polar) Complex Numbers
• Lesson Thirty Six: Transformations of the Complex Plane

A series of communication problems explained by MATH 119 student groups.

• Instructive examples