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5Let’s just chat for a minute why it’s √1
 2. 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 = √b2+-c2. Since b = c, then a =  ---
√2b2. As we said a couple of paragraphs earlier, the radius of the circle (and therefore the length of the hypotenuse) is 1. Therefore √---
 2b2 = 1. Therefore √-
 2√--
 b2 = 1. Therefore √ --
  b2 = 1∕√-
 2. Therefore b = 1∕√ -
  2.