The I, Mathematician section of my website is my writings on being a Mathematician. The articles here will contain more personal opinion than in the Counting on my Fingers section and will be more about my approach to Mathematics. Some of the articles in the Counting on my Fingers section should be in this section. To avoid dead links, I'm not going to change their URLs but I'll list them here as well.
Part of being a Mathematician is doing Mathematics, and part of doing Mathematics is being a Mathematician, so there will inevitably be a significant intersection between these two parts of my website. Putting an article here is my way of signalling that it is more about my approach and less about the objective Mathematics.
I'll see how it evolves.
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These are articles that I wrote before creating this section but which would now be classified as more about my approach to Mathematics than the Mathematics itself.
Euler's equation consistently tops the list of "most beautiful equation". I think that this is ill-deserved. This is my explanation as to why.
This is my contribution over the semi-annual debate as to which angle deserves a symbol of its own. There can only be One True Right Angle.
The author of the Math with Bad Drawings posted an interesting article about a combinatorial interpretation of Fermat's Last Theorem. It got me thinking. This is the result of those thoughts.
There are many, many proofs of Pythagoras' Theorem and amongst them I've found one that I particularly like. It has ingredients that closely relate to what Pythagoras' Theorem is really about (how lengths behave in Euclidean Space), and extends to a proof of the cosine rule.
This is a summary of my thinking about Pythagoras' Theorem and how it relates (or not) to the concept of area. It also details my attempts to find an area-based proof of the Intersecting Chords Theorem.
I originally wrote this way back in 2011 for a course where students were required to prove results rigorously. I used it as the basis for this answer on Mathematics.SE, and so am reposting it here.
There's something about mathematical puzzles that I find not quite to my liking. Two puzzles that recently came my way gave me the opportunity to try to figure out why that is.