The book is in 3 chapters, the first looks at mathematical series and shows how we can get the sum of arithmetic and geometric series and how the theorem of series can be applied towards the solution of convergence and divergence. In the second chapter we look at the Newton expansion and how it can be used to accurately and quickly evaluate pi to high precision. We are introduced to the opensource GMP arbitrary precision package that massively quickens our calculations and we show how pi can be calculated to phenomenal accuracy very quickly on a modest pc. In the third chapter we look at regular convex polyhedra and we show why there are only 5 of such. we show how we can construct them from their base regular polygons. We show their visualisation in 3D design software.