Spring 2001

The Bailey Challenge

The problems for this issue are not new. They were considered by Pappus of Alexandria in the first half of the fourth century. One is on geometry from book V of his treatise Mathematical Collection and the other on mechanics from book VIII. He introduces the geometry problem with the statement "It is of course to men that God has given the most perfect notion of wisdom in general and mathematical science in particular, but partial share in these things he allotted to some of the unreasoning animals as well." Then he follows with what I will call problem 1.

Problem 1. "There being three figures which themselves can fill up a space round a point, viz. the triangle, the square and the hexagon, the bees have wisely selected for their structure that which contains most angles, suspecting indeed that it could hold more honey than either of the other two." Your problem is to explain the first underlined phrase and to explain and prove the second. As a starter, show that you could not tile a bathroom floor with small tiles that are regular pentagons.

Problem 2. A 3" by 5" rectangular piece of cardboard ABCD is to have one corner clipped off by cutting along BQ as shown. Find where the point Q should be located so that when the rectangle is hung by a string attached at Q , the side AB will be horizontal. The true engineer will want to test their solution in the 'lab'. Hint: As you learned in Calculus and again in Statics, the distance from the base of a thin triangle to its center of gravity is equal to one third of the altitude to that base.

The solvers of the Winter problems follow. Bob Burger used a recursive method and an up-to-date programming language called Scheme. He found that there are 53,995,291 ways to make change for a $20. You may be interested in some of these if you decide to take up clerking in your senior years. The answer for changing $1 is 292 ( 293 if you include dollar for dollar).

A less up-to-date method for solving the area problem was submitted by our senior solver, Bill Barrick '41. He used a polar planer planimeter (Am. Steam Gauge Co.) and traced the perimeter to find the area. The instrument is so old that my spell check does not include it. You might figure out how to design such an instrument. The answer to the area problem using methods of Euclid (300 B.C.) is .

Send your solutions to Herb.Bailey@rose-hulman.edu or to Herb Bailey, Math. Dept., Rose-Hulman, 5500 Wabash Ave., Terre Haute IN 47803.

Solvers from our last problem

Alumni: B. Barrick, 1941; R. Mott, 1943; T. Blickwedel, 1946; J. Hurt, 1948; A. Schairbaum, 1949; C. Cook, 1949; A. Junker, 1950; J. Lambermont, 1951; C. Hirschfield, 1954; J. Chinn, 1956; C. Cooper, 1956; H Brown, 1957; R. Reeves, 1959; D. Bailey, 1959; R. Archer, 1961; J. Tindall, 1961; J. Snyder, 1962; D. Todd, 1962; N.Hannum, 1962; E. Blahut, 1963; J. Sauser, 1964; R. Kevorkian, 1966; R. Bloch, 1968; R. Lowe, 1969; M. Ring, 1970; J. Born, 1970; A. Mahler, 1971; J. Havener, 1973; P. Chilson, 1974; J. Schroeder, 1976; J. Matthews, 1977; D. Zona, 1977; S. Warner, 1978; M. Clouser, 1979; J. Slupesky, 1979; S. Felix, 1982; G. D'Orazio, 1985; C. Hastings, 1986; M. Nigrovic, 1987; M. Lancaster, 1987; J. Jachim, 1989; C. Abdnour, 1989; E. Forster, 1990; B. Steele, 1990; D. Devore, 1991; B. Cox, 1991; B. Burger, 1991; R. Aronen, 1991; J. Waldby, 1994; J. Skeel, 1996; E. Hayes, 1997; R. Smeltzer, 1998; C. Hartmann, 1998; M. Pilcher, 1998; R. Loftus, 1998; J. Horen, 1999; A. Primozich, 2000; G. Lara, 2000; J. Briggs, 2001; C. Lehman, 2005; and E. Tollefson, 2005.

Friends: P. Hines, W. Talbot, C. Brown, D. Templeton, R. Templeton, M. Carr, N. Flatter, L. Gaintner, and C. Linden.