This is mathematics in action, in context, in real life, and in detail. Begin the journey with Archimedes, and travel alongside the likes of Fermat, Fibonacci, Coxeter, and Adler. There is much to consider and opportunities to make links to things that might be "known", but maybe not well appreciated. On the way you will come across an angular wiggle and a radial shake that help in the sense making process. The enthusiasm of the author might be described as "infectious", in the best possible sense of the term. (Contains 5 figures.)