This course introduces the idea of mathematics as a logically constructed axiomatic system, as developed by Euclid in the fourth century BC. It works through the first book of Euclid’s structure methodically, with exposition. In addition, a rich historical context is presented including political, military, and philosophical developments. The story of the development of geometry is fascinating and we miss a lot by considering it in isolation.
The first four parts of the course will work through all of the first book of the Elements, building up to a proof of the Pythagorean Theorem, and will constitute the first semester of the full course. Part 1 includes the definitions, postulates, and first 12 propositions of Euclid’s first book.
Classical Geometry – Mathematical Thinking in Context
The following sheet should be printed out as a reference while working through the proofs – Part 1
Each chapter should be about a week of work, working for around 1 hour per day. I will be posting a new chapter each week.
Part 1 –
- Chapter 1 – Propositions I.1-I.3
This course is a great introduction to logical thinking and Geometry if you are:
A parent of an advanced or gifted child in private or public school –
This course will challenge your advanced student to go beyond what is covered in a traditional geometry course. The focus is on the logical structure of the Elements, rather than just learning a set of “math facts” needed for a standardized test. Euclid’s Elements have been the catalyst for a love of math and science in many famous scholars historically. This is the perfect introduction to “real” mathematics and will give students a taste of the rich history and thought process behind the development of mathematics.
Homeschooling using a Classical Education –
The approach to Geometry in this course is Classical in every sense of the word. It follows the course of logical development that was the basis of mathematical education beyond calculation for over 2000 years. The course is designed to integrate logic, history, and mathematics in a way that will appeal to the classically educated student. The reading level is intended for those who are comfortable reading the great books, and the ideas are challenging and engaging.
Homeschooling using a Charlotte Mason based approach –
Charlotte Mason wrote about reading the works of real mathematicians, but she was writing in a time before we were saturated with textbooks aimed at children. This course is very much steeped in the philosophy of Charlotte Mason, presenting a real logical progression with a rich historical basis, rather than a watered-down method aimed at preparing children for standardized tests. If you have been following a Charlotte Mason approach, your student will be used to reading classical literature and thinking deeply about things. The ideas and reading level of this course will engage and challenge your student.
The philosophy of this course is embodied by this quote from Charlotte Mason:
“How interesting Arithmetic and Geometry might be if we gave a short history of their principal theorems, if the child were meant to be present at the labours of a Pythagoras, a Plato, a Euclid, or in modern times, of a Descartes, a Pascal, or a Leibnitz. Great theories instead of being lifeless and anonymous abstractions would become living human truths each with its own history like a statue by Michael Angelo or like a painting by Raphael.” CM Vol. 6 pg 110
An adult who is passionate about mathematics and logic, but is not familiar with Euclid –
This course focuses on a combination of providing a rich historical and mathematical context along side the direct translation of Euclid’s Elements. It provides a richer experience than you would receive just reading a direct translation, although that is also a good idea. If you are comfortable reading mathematics and would rather just dive in without all the historical context, I recommend:
The Green Tree version is a very bare-bones translation with all 13 books included. It makes a great reference.
An adult who always disliked math and never felt like they “got it” –
It is very likely that what you disliked was calculation, not real mathematics. Many professional mathematicians are not very good at calculation either, and don’t enjoy it. Mathematics is a game of logical thinking that often appeals to a very different group than those who enjoy mathematics in the K-12 curriculum. Give this course a try and see if it doesn’t help you think differently about math.