Allow me to start you on a journey in Golygon City. You can take a similar trip in Manhattan, Tokyo, or almost any large city whose streets form a grid of squares. Here are your directions. Stroll down a city block, and at the end turn left or right. Walk two more blocks, turn left or right, then walk another three blocks, turn once more, and so on. Each time you turn, you must walk straight one block farther than before. If after a number of turns you arrive at your starting point, you have traced a golygon, as shown in Figure 7.32. A golygon consists of straight-line segments that have lengths (measured in miles, meters, or whatever unit you prefer) of one, two, three, and so on. Draw some golygons. Can you make a conjecture about golygons?

Figure 7.32

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