After writing my book Divine Proportions: Rational trigonometry to Universal Geometry in 2005, I thought I would likely write another book on Rational Trigonometry (RT). Over the years since, I have spent a lot of research time and effort remodelling hyperbolic geometry in the direction of RT, and vaguely had this idea of writing a book on that subject.
After all, writing books is what academics do, when they are not writing papers or preparing classes. But book writing is not what it used to be in academy, unfortunately.
Since 2005, lots of my thinking has changed. I have become an ardent YouTube creator. I have engaged a lot more with the foundations of mathematics and both the challenges and opportunities there. I have created MOOCs, both on my own, and for UNSW. I have been busy making online materials for first year courses in the School of Mathematics and Statistics.
So now I have a different idea of what is the best use of my time. Why spend so much time writing primarily for a limited, rarified academic audience, which is often just a handful of people if one is being honest? Rather, I want to engage with big directions using a platform that is large scale and international, and that has a less formal structure, that has more room for modification and improvement, and that has more of a visual aspect. The internet is where I intend to do most of my publishing from now on!
And this website will be a big part of that hopefully. I want to provide a platform for a wide range of ideas, mathematical gems, instructive examples, enticing diagrams and clear explanations. A place where we can exchange views, discuss, watch videos, listen to podcasts and read interesting tidbits.
I would like to make more space for mathematical thinking: open up new possibilities, create room for alternative thoughts and theories, even critical ones. The status quo needs shaking up, and we are going to do a bit of that here!
But equally important, I want to provide a forum where ordinary people can come and just be exposed to interesting mathematics, to learn, review or discover something useful or special. And ask questions, and voice their opinions too, if they like.
Welcome, and please be patient with a work in progress.