"Our civilization has the odd habit of printing books full of lines. We call these notebooks "ruled". It's an orderly, lawful word, as befits an orderly, lawful document. Of course, in a ruled notebook, the rules are there to invite writing, drawing, and thinking. The rules are riverbanks, and the river flowing between them is whatever you want it to be. How might changing the lines change the flow of thoughts between them? What if the straight parallels gave way to curves, clusters, and criss-crosses? What if the once-identical pages began to individuate and develop personalities? What ideas might come to life, if the rules grew unruly? Mathematics, liked line notebooks, does not enjoy a reputation for playful spontaneity. If you want to create an unruly notebook for nonstandard thoughts, it might seem that algebra is the last place you'd turn. But creativity is not (as we sometimes imagine) a matter of shaking off all constraints. It is about playing against them. We need rules, if only for the sake of breaking them. Plotted, written, and overruled by mathematicians, educators, and popularizers Tim Chartier and Amy Langville, and with a foreword by Ben Orlin, this book reveals math's creative side. We will see how straight lines can form fractal crenelations; how circles can disrupt and unify; how waves can create complex landscapes and famous faces. The rules of mathematics, this book shows, are like the rules of a notebook: invitations to play"--