# Preface

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