One of my projects for 2016 (and beyond) is a walk through of one of the most important works in the mathematical world: Euclid’s Elements. I intend to walk through the proofs, providing explanations and insight into those proofs. If you are an aspiring mathematician I hope our journey will help you to develop the creativity and intuition that will take you far in your mathematical pursuits, as well as some respect for the abilities of those who came before us. Although this is an ancient text, which provided mental exercises in logic and thought for people throughout the ages, you will find that the approaches that we take will show up in many other mathematical disciplines.
The idea for this project came to me while reading a biography of Abraham Lincoln. It mentioned how he had worked his way through Euclid’s Elements, and I thought it would be fun to work my way through it myself. After I picked up a copy for myself I started to think about documenting my journey, and here we are.
A bit about me and my approach: I believe in the importance of the discovery of mathematics. In my opinion, students can only learn mathematics by participating and by thinking. You may not always come up with correct ideas at first, or perhaps the most efficient approach, but we do learn through trial and error. At the beginning of our journey I will discuss the upcoming proposition and any background information I think you will need, encouraging you to come up with your own ideas about proving that proposition.
There is no one correct approach to all mathematical problems, developing creativity and problem solving skills is most important. You may find that you take different approaches to proving some of the propositions and I want you to know that that’s OK. All I ask is that you try to understand whether my approach makes sense to you and then to determine which approach you like better. Have any questions? Feel free to leave a comment and we can talk it out.
The book I am using is Euclid’s Elements, which is published by Green Lion Press. This paperback edition contains all 13 books in one volume, and I highly recommend it. You can pick up a copy through the following link.
Thanks for checking out this site – George