You could try it directly in front of the moon to

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the ping pong ball (say) at just the right distance that it looks to you exactly the same size as the moon. You could try it directly in front of the moon, to just block it, or side by side with the moon, whatever works best for you. Now, measure the distance from your eye to the ball, and measure the diameter of the ball. Given that the moon is 230,000 miles away, figure out the moon's diameter. What is the angular size of the moon? That is, if you take two pencils, point one at the bottom of the moon, and one at the top, as seen from here, what is the angle between them? You can answer in degrees or radians. (One radian is the angle of a piece of pie having the curved side the same length as the straight sides.) 3. You set up base camp on a bear hunting expedition. You travel exactly twenty miles south, rest for a meal, then go twenty miles east, where you shoot a bear. Now you go twenty miles north and you are back at your base camp. What color was the bear? Give your reasoning. 4. Plato defined a regular solid as one with every edge the same length, and the same number of edges meeting at each vertex. Explain in your own words (but with diagrams) why there can only be five such solids. 5. Prove that the square root of three cannot be expressed as a ratio of whole numbers. (Hint: remember that any whole number can be expressed as a product of prime factors. The proof of the square root of two was all about odd and even numbers, this time concentrate of factors of 3, not 2.)
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  • Spring '08
  • Fowler
  • Work, ping pong ball

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