Winter 1997
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Winter 1997 |
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by Herb Bailey, professor emeritus of mathematics
Two of my many retirement hobbies are blowing soap bubbles (with or without the help of my grandchildren) and checking the racing forms (without). Problem 1: How many different finishes are possible for a race with four horses competing? Hints: An example finish could be: C first, B and D tie for second and A last. The answer is a positive integer between 40 and 90. Problem 2: A soap bubble has two compartments. The base is a sphere with a segment sliced off the top, the second compartment is a hemisphere whose base is the circle which was made when the segment was cut from the original sphere (see figure). What is the maximum height of the two-compartment bubble if the diameter of the original sphere is one? Hint: You may need to remember that the maximum of a function is where its derivative is zero (usually). Problem 3: (Only for those who took Calc III seriously) Find the maximum height of a bubble with n compartments. Slicing a segment from the top hemisphere and adding a new hemisphere as in Problem 2 makes the additional compartments. Problem 3 is taken from a recent issue of The Mathematics Magazine. Reviewing the fall problems: There were 41 solutions to the fall '97 problems. In my work with fund drives, I know that is good to pit class against class. The class of 1943 (the year I entered Rose Poly) was the clear winner with 3 solvers out of a class of 115 graduates. None of these were sent via e-mail. What does this tell us? The answers to the fall problems are 1: 2424.7 square feet and 2: 36 days. Your new solutions and/or requests for fall solutions should be sent to: Herb Bailey, Box 185, Rose-Hulman, 5500 Wabash Ave., Terre Haute, IN, 47803 or e-mailto:herb.bailey@rose-hulman.edu Alumni solvers of the fall problems were: Dwight Heath ('43), William Soudriette ('43), R. C. Mott ('43), Bolivor Shagnasty ('64), Jeff Markwardt ('95), T. Jason Zigler ('94), Mark Bailey ('76), Donald Todd ('62), John Tindall ('61), Allan Mahler ('71), Scott O'Neil ('93), Edwin Bodine ('73) Cecil Cook ('49), Roger Bannister ('46), David Wahman ('96), Greg Heimann ('90), Brian Meister, Ric Antonini ('93), Charlie Cooper ('56), Bob Burger ('91), Joe Snyder ('62), J.G. Schroeder (`'76), Ben Hill ('90), Rich Priem (`'79), Chuck Hastings ('86), Jay Smith ('77), Bill Rinker ('51), Lee Mitchell ('49), Scott Blonigen ('86), Michael Walden ('86), Chris Abdnour ('89), Chris Sloffer ('89), Chuck Busenburg ('85), Jon Rhynard ('68), and Chuck Divine ('67). Others: James Jackson, George Miller, Dan Pate, Jason Garino, Roger Miller, Fred Payne, Neil Flatter, Bill Talbot, William Orr and Mike Rosene. — by Herb Bailey Professor Emeritus of Mathematics
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