This book is about creating art based on the properties of the number pi. The symbol mathematicians use to represent pi is π. What is π you ask? π is an irrational number that shows up in many areas of mathematics. It probably first entered human consciousness when someone tried to calculate either the area of a circle or the length of its circumference. Indeed you can define π as being equal to the ratio of the circumference to the diameter of a circle. This is true for any circle no matter how small or large. In terms of area, the ratio of the area of a circle with radius equal to 1, to the area of a square with sides of length 1, is equal to π. We could also simply say that π is the area of a circle with radius equal to 1.
The definition of π in terms of areas brings up another property of π that may be of interest to artists. In addition to being irrational, π is also transcendental. Mathematically, this means that there is no polynomial with rational coefficients that has π as one of its roots. In terms of areas it means that it is impossible to draw a square with the same area as a given circle in a finite number of steps using only a straight edge and compass.
People have been engaged in calculating the value of π since antiquity. In modern times it has almost become something of a sport to see who can calculate more digits of π. The value of π is now known to trillions of digits. Still there seems to be no discernible pattern to the digits. Indeed the digits appear to be random under statistical tests.
What we have discovered, however, and what this book is about, is the fact that rational approximations to π do encode many intricate patterns that can be turned into interesting drawings. We have collected 357 of these drawings together in this book. This is an art book meant to stimulate your creativity and imagination. There is no mathematics required. We have included two appendices that contain a very short explanation of some of the mathematics behind π and how the images are created, indexed by name. More detailed information on how to create the images can be found in our book: Pattern Generation for Computational Art
May you find these images stimulating and inspirational, as we have found them.
Stefan Hollos and Richard Hollos Exstrom Laboratories LLC Longmont, Colorado Sept 3, 2014