Foreword During the Renaissance, algebra was resumed from Near Eastern sources, and geometry from the Greek. Scholars of the time became familiar with classical mathematics. When calculus was born in 1665, the new ideas spread quickly through the intellectual circles of Europe. Our history shows the importance of the diffusion of these mathematical ideas, and their effects upon the subsequent development of the sciences and technology. Today, there is a cultural resistance to mathematical ideas. Due to the widespread impression that mathematics is difficult to understand, or to a structural flaw in our educational system, or perhaps to other mechanisms, mathematics has become an esoteric subject. Intellectuals of all sorts now carry on their discourse in nearly total ignorance of mathematical ideas. We cannot help thinking that this is a critical situation, as we hold the view that mathematical ideas are essential for the future evolution of our society. The absence of visual representations in the curriculum may be part of the problem, contributing to mathematical illiteracy and the math-avoidance reflex. This book is based on the idea that mathematical concepts may be communicated easily in a format that combines visual, verbal, and symbolic representations in tight coordination. It aims to attack math ignorance with an abundance of visual representations. In sum, the purpose of this book is to encourage the diffusion of mathematical ideas by presenting them visually. ix