302 HW 11 - Golden Rectangle so if we start with the small...

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M302 HOMEWORK #11 Dr. Schurle Assignment: page 244, #1, 3, 8, 9, 12, 16, 20 Grade the following for 2 points each, then give all or part of the remaining two points depending on how much work they've done on the other problems. #3. 5/3 = 1.66667 11/8.5 = 1.29412 14/11 = 1.27273 and 17/11 = 1.54545 while the Golden Ration is about 1.61803. The 3 by 5 inch index card has ratio closest to the Golden Ratio. #9. Yes. The folding has cut the lengths of the longest and shortest sides each in half, so the ratio remains the same, and so will still be the Golden Ratio. #12. Yes. If we repeat the process we will continue to get Golden Rectangles. [Explanation is not asked for in this problem, but this is just the reverse of the process in which we cut a large square from a Golden Rectangle and got another
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Unformatted text preview: Golden Rectangle, so if we start with the small one and reverse the process, we'll get the large one. Or, if we start with base b and height h , then b h =∅ , the Golden Ratio. When we add the square, the long side is b + h and the short side is b, and then b h h = b h 1 b h = ∅ 1 ∅ = 1 1 ∅ and we know that ∅= 1 1 ∅ so again the ratio is Golden.] #16. The area of G is bh . The dimensions G' are h and b – h so G' has area h(b – h) . So the ratio is h b − h bh = b − h b = b h − 1 b h = ∅− 1 ∅ because G is Golden. The answer does NOT depend on b or h . Surprise is in the eye of the beholder!...
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This note was uploaded on 03/19/2008 for the course M 302 taught by Professor Irwin during the Spring '08 term at University of Texas.

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