^{5}Let’s just chat for a minute why it’s . Look back at Figure 1.7 and imagine that the
wheel has rotated 45^{∘}, then draw a right triangle where the hypotenuse is a line connecting the
centre of the wheel with the dot on the edge, one side is a line dropping straight down from
the dot, and the third side is a horizontal line extending to the right from the centre. Since the
angle of rotation is 45^{∘}, the triangle is isoceles, meaning that the two short sides are of equal
length. We also know from Section 1.2 that a = . Since b = c, then a = . As
we said a couple of paragraphs earlier, the radius of the circle (and therefore the length of the
hypotenuse) is 1. Therefore = 1. Therefore = 1. Therefore = 1∕. Therefore
b = 1∕.