Summer 2008
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Summer 2008 |
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Bailey Challenge Please excuse any mistakes in my tally of the spring solvers. I blame all errors on my aging brain and the large number of solvers. The solver numbers for the three recent issues were 47, 110, and 204. I hope to repair my brain, add staff or find very hard problems. The Pythagorean Theorem (a2 + b2 = c2) was known to the Babylonians about 1500 B.C. and first proved about 500 B.C. by Pythagoras. President Garfield had his proof published in 1876 in the Journal of Education. Problem 1 is your chance to prove it. Problem 1
Use the figure (right) as shown to prove the Pythagorean Theorem. My wife tells me that this figure is the 'windmill' quilt block.
Problem 2 Let ABCD be a rectangular card with AB = DC = 5 inches and AD = BC = 3 inches. Let H be the point on the card that is one inch from each of the sides AB and AD. The card is vertical with AB initially resting on a table top PQ. The card “rolls” along the table with the first rotation clockwise around vertex B until C contacts the table. The second rotation is then around the new location of C, etc. After the fourth and last rotation the card has returned to its original orientation. Find the total path length traveled by H during these four rotations. Also find the area below this path and above the tabletop. No matter if you have forgotten integration techniques, you don’t need them.
Send your solutions to Herb.Bailey@rose-hulman.edu or to Herb Bailey, Math. Dept., Rose-Hulman, 5500 Wabash Ave., Terre Haute IN 47803. Please include your class year if you are an alum. Solution for previous issue 29786 850 850 ----- 31486 A solution of the addition problem forty + ten + ten = sixty is shown. I was pleased and surprised that so many of you had the time and patience to show that this solution is unique. |
