What of the chain? Its position, defined by C , begins at 0 and reaches 1 when its next link moves forward to the fatal position, then 2 and so on. The chain must move in synch with the teeth on the sprocket at the center of the rear wheel, and that sprocket has n teeth, and so after a complete revolution of the rear wheel, when [theta] = 0 again, C = n . After a second complete revolution of the rear wheel, once again [theta] = 0 but now C = 2 n . The next time it’s C = 3 n and so on. But remember that the chain is not an infinite linear thing, but a loop having only l positions; at C = l it loops back around to C = 0 and repeats the cycle. So when calculating the value of C it is necessary to do modular arithmetic—that is, if the chain has a hundred links ( l = 100) and the total number of links that have moved by is 135, then the value of C is not 135 but 35. Whenever you get a number greater than or equal to l you just repeatedly subtract l until you get a number less than l . This operation is written, by mathematicians, as mod l . So the successive values of C , each time the rear wheel spins around to [theta] = 0, are