Chapter 1. Introduction to MATLAB 1.1 The golden ratio What is the world's most interesting number? Perhaps you like T, or e, or 17. Some people might vote for o, the golden ratio, computed here by our first MATLAB phi =(1 sqrt(5))/2 Thi hi= 1.6180 Let's see more digits. format long phi 1.61803398874989 This didn't recompute it just displayed 15 significant digits instead of 5 The golden ratio shows up in many places in mathematics: we'll see several in this book. The golden ratio gets its name from the golden rectangle, shown in Figure 1. 1. The golden rectangle has the property that removing a square leaves a haller rectangle with the same shap Figure l.l. The golden rectangle Equating the aspect ratios of the rectangles gives a defining equation for o This equation says that you can compute the reciprocal of o by simply subtracting one. How many numbers have that property? Multiplying the aspect ratio equation by o produces the polynomial equation2 Chapter 1. Introduction to MATLAB 1.1 The Golden Ratio What is the world’s most interesting number? Perhaps you like π, or e, or 17. Some people might vote for φ, the golden ratio, computed here by our first Matlab statement. phi = (1 + sqrt(5))/2 This produces phi = 1.6180 Let’s see more digits. format long phi phi = 1.61803398874989 This didn’t recompute φ, it just displayed 15 significant digits instead of 5. The golden ratio shows up in many places in mathematics; we’ll see several in this book. The golden ratio gets its name from the golden rectangle, shown in Figure 1.1. The golden rectangle has the property that removing a square leaves a smaller rectangle with the same shape. φ φ − 1 1 1 Figure 1.1. The golden rectangle. Equating the aspect ratios of the rectangles gives a defining equation for φ: 1 φ = φ − 1 1 . This equation says that you can compute the reciprocal of φ by simply subtracting one. How many numbers have that property? Multiplying the aspect ratio equation by φ produces the polynomial equation φ 2 − φ − 1 = 0