Table Of Content

VOL. 83, NO. 5, DECEMBER 2010 Index to Volume 83 AUTHORS Dorée, Suzanne, see Arett, Danielle Franks, John, Cantor’s Other Proofs that R Is Abrams, Gene and Jessica K. Sklar, The Uncountable, 283-289 Graph Menagerie: Abstract Algebra and Frayer, Christopher, More Polynomial Root the Mad Veterinarian, 168—179 Squeezing, 218-221 Adkins, William A. and Mark G. Davidson, Gelman, Andrew and Nate Silver, What Do Putzer’s Algorithm for e“' via the Laplace We Know at 7PM on Election Night? Transform, 267-275 258-266 Arcos, Carlos, Gary Brookfield, and Mike Goldstone, Richard, John McCabe, and Krebs, Mini-Sudokus and Groups, 111-122 Kathryn Weld, Ambiguous Groups and Arett, Danielle and Suzanne Dorée, Coloring Cayley Graphs—A Problem in and Counting on the Tower of Hanoi Distinguishing Opposites, 347-358 Graphs, 200-209; also 257, 266 Gomez-Calderon, Javier, see Bischof, Bryan Barnes, Julia and Lorelei Koss, The Ergodic Gover, Eugene, Monotonicity of Sequences Theory Carnival, 180-190 Approximating e* , 380-384 Benjamin, Arthur T., Bob Chen, and Griffiths, Martin, f(f(x)) = —x, Windmills Kimberly Kindred, Sums of Evenly Spaced and Beyond, \5—23 Binomial Coefficients, 370-373 Hajja, Mowaffaq, Another Morsel of Bennett, Curtis D., Blake Mellor, and Patrick Honsberger, 279-283 D. Shanahan, Drawing a Triangle on the Hirshon, Ron, How Fast Will We Lose? Thurston Model of Hyperbolic Space, 213-218 83-99 Holland, Finbarr, lim,,—5 0> °y_9(k/m)” Bischof, Bryan, Javier Gomez-Calderon, and = e/(e — 1), 51-54 Andrew Perriello, Integer-Coefficient Polynomials Have Prime-Rich Images, Holm, Michael, see Briggs, Joseph 55-57 Hudelson, Matt, Proof Without Words: The Bolker, Ethan D., Gergonne’s Card Trick, Alternating Harmonic Series Sums to \n2, Positional Notation, and Radix Sort, 46-49 294 Bradley, David M., Counting Ordered Pairs, Kheifets, Alexander and James Propp, A 302 Counterexample to Integration by Parts, Briggs, Joseph, Kathryn Dabbs, Michael Holm, Joan Lubben, Richard Rebarber, Kindred, Kimberly, see Benjamin, Arthur T. Brigitte Tenhumberg, and Daniel Kocik, Jerzy, Golden Window, 384-390 Riser-Espinoza, Structured Population Kodokostas, Dimitrios, Triangle Equalizers, Dynamics: An Introduction to Integral 141-146 Modeling, 243-257 Koss, Lorelei, see Barnes, Julia Brookfield, Gary, see Arcos, Carlos Krebs, Mike, see Arcos, Carlos Brookfield, Gary, Yet Another Elementary Solution of the Brachistochrone Problem, Lamphere, Robert L., Solving the 59-63 Noneuclidean Uniform Circular Motion Problem by Newton’s Impact Method, Carmichael, Jennifer, Keith Schloeman, and 366-369 Michael B. Ward, Cosets and Cayley-Sudoku Tables, 130-139 and Lih, Ko-Wei, A Remarkable Euler Square 147-148 before Euler, 163-167 Chen, Bob, see Benjamin, Arthur T. Lubben, Joan, see Briggs, Joseph Coll, Vincent and Jeff Dodd, Which Surfaces McCabe, John, see Goldstone, Richard of Revolution Core Like a Sphere? Mellor, Blake, see Bennett, Curtis D. 191-199 Melman, Aaron, Gershgorin Disk Fragments, Dabbs, Kathryn, see Briggs, Joseph 123-129 Davidson, Mark G., see Adkins, William A. Morrison, Kent E., The Multiplication Game, Dodd, Jeff, see Coll, Vincent 100-109 404 MATHEMATICS MAGAZINE Nicodemi, Olympia, Galileo and Oresme: Cantor’s Other Proofs that R Is Uncountable, Who Is Modern? Who Is Medieval? 24-32 by John Franks, 283-289 Parker, Edward, A Property Characterizing Coloring and Counting on the Tower of the Catenary, 63-64 Hanoi Graphs, by Danielle Arett and Perriello, Andrew, see Bischof, Bryan Suzanne Dorée, 200-209; also 257, 266 Pippenger, Nicholas, The Hypercube of Cosets and Cayley-Sudoku Tables, by Jennifer Resistors, Asymptotic Expansions, and Carmichael, Keith Schloeman, and Preferential Arrangements, 331-346 Michael B. Ward, 130-139 and 147-148 Plaza, Angel, Proof Without Words: Counterexample to Integration by Parts, A, by Mengoli’s Series, 140 Alexander Kheifets and James Propp, Pratt, Rob, Proof Without Words: A Tangent 222-225 Inequality, 110 Counting Ordered Pairs, by David M. Propp, James, see Kheifets, Alexander Bradley, 302 Pudwell, Lara K., Stacking Blocks and Differential Equations—Not Just a Bag of Counting Permutations, 297—302 Tricks! by Shirley Llamado Yap, 3-14 Rebarber, Richard, see Briggs, Joseph Drawing a Triangle on the Thurston Model of Riser-Espinoza, Daniel, see Briggs, Joseph Hyperbolic Space, by Curtis D. Bennett, Ross, Kenneth A., Repeating Decimals: A Blake Mellor, and Patrick D. Shanahan, Period Piece, 33-45 83-99 Schloeman, Keith, see Carmichael, Jennifer Ergodic Theory Carnival, The, by Julia Shanahan, Patrick D., see Bennett, Curtis D. Barnes and Lorelei Koss, 180-190 Siehler, Jacob A., How Long Until a Random t(f(x)) = —x, Windmills and Beyond, by Martin Griffiths, 15—23 Sequence Decreases? 374-379 Silver, Nate, see Gelman, Andrew Galileo and Oresme: Who Is Modern? Who Is Medieval? by Olympia Nicodemi, 24—32 Sklar, Jessica K., see Abrams, Gene Spivey, Michael Z., Letter to the Editor, Geometry of the Snail Ball, The, by Stan 54-55 Wagon, 276-279 Sury, B., Nothing Lucky About 13, 289-293 Gergonne’s Card Trick, Positional Notation, Swanson, Christopher N., Probability in Look and Radix Sort, by Ethan D. Bolker, 46-49 Up and Scream, 359-366 Gershgorin Disk Fragments, by Aaron Tenhumberg, Brigitte, see Briggs, Joseph Melman, 123-129 Unal, Hasan, Proof Without Words: Sums of GM-AM Ratio, A, by Conway Xu, 49-50 Octagonal Numbers, 58 Golden Window, by Jerzy Kocik, 384-390 Wagon, Stan, The Geometry of the Snail Ball, Graph Menagerie: Abstract Algebra and the 276-279 Mad Veterinarian, The, by Gene Abrams Ward, Michael B., see Carmichael, Jennifer and Jessica K. Sklar, 168-179 Weld, Kathryn, see Goldstone, Richard How Fast Will We Lose? by Ron Hirshon, Will, Todd G., When is n* a Sum of k 213-218 Squares? 210-213 How Long Until a Random Sequence Xu, Conway, A GM-AM Ratio, 49-50 Decreases? by Jacob A. Siehler, 374-379 Yap, Shirley Llamado, Differential Hypercube of Resistors, Asymptotic Equations—Not Just a Bag of Tricks! 3-14 Expansions, and Preferential Zhang, Cheng, Period Three Begins, 295-297 Arrangements, The, by Nicholas Pippenger, 331-346 Integer-Coefficient Polynomials Have TITLES Prime-Rich Images, by Bryan Bischof, Ambiguous Groups and Cayley Graphs—A Javier Gomez-Calderon, and Andrew Perriello, 55-57 Problem in Distinguishing Opposites, by Richard Goldstone, John McCabe, and Letter to the Editor, by Michael Z. Spivey, Kathryn Weld, 347-358 54-55 Another Morsel of Honsberger, by Mowaffaq liMm— oo reo (k/m)”™ = e/(e — 1), by Hajja, 279-283 Finbarr Holland, 51-54 VOL. 83, NO. 5, DECEMBER 2010 405 Mini-Sudokus and Groups, by Carlos Arcos, Which Surfaces of Revolution Core Like a Gary Brookfield, and Mike Krebs, 111-122 Sphere? by Vincent Coll and Jeff Dodd, Monotonicity of Sequences Approximating e*, 191-199 by Eugene Gover, 380-384 Yet Another Elementary Solution of the More Polynomial Root Squeezing, by Brachistochrone Problem, by Gary Christopher Frayer, 218-221 Brookfield, 59-63 Multiplication Game, The, by Kent E. PROBLEMS Morrison, 100-109 Nothing Lucky About 13, by B. Sury, 289-293 The letters P, Q, and S refer to Proposals, Period Three Begins, by Cheng Zhang, Quickies, and Solutions, respecitvely; page 295-297 numbers appear in parentheses. For example, P1848 (226) refers to Proposal 1848, which Probability in Look Up and Scream, by Christopher N. Swanson, 359-366 appears on page 226. Proof Without Words: A Tangent Inequality, February: P1836-—1840 and (corrected)P1834; by Rob Pratt, 110 Q997-998; S1811-1815 Proof Without Words: Mengoli’s Series, by April: P1841—1843; Q999-1000; Angel Plaza, 140 $1816—1820 Proof Without Words: Sums of Octagonal June: P1846—1850; Q1001-—1002; Numbers, by Hasan Unal, 58 $1821-1825 Proof Without Words: The Alternating October: P1851—1855; Q1003—1004; Harmonic Series Sums to \n2, by Matt S$1826—-1830 Hudelson, 294 December: P1856—1860; Q1005—1006; Property Characterizing the Catenary, A, by $1831-1833 and $1835 Edward Parker, 63-64 Solution $1834 will appear in February, 2011. Putzer’s Algorithm for e“' t via the Laplace Transform, by William A. Adkins and Bailey, Herb, $1814 (69), P1848 (226) Mark G. Davidson, 267-275 Bataille, Michel, $1821 (227) Remarkable Euler Square before Euler, A, by Bell, Howard E., $1825 (232) Ko-Wei Lih, 163-167 Benjamin, Philip, $1816 (150) Repeating Decimals: A Period Piece, by Botsko, Michael W., Q1000 (150), Q1002 Kenneth A. Ross, 33-45 (227), P1853 (303), Q1005 (392) Solving the Noneuclidean Uniform Circular Burdick, Bruce S., $1819 (152) Motion Problem by Newton’s Impact Byrd, Stan and Ossama A. Saleh, $1828 (306) Method, by Robert L. Lamphere, 366-369 Calcaterra, Robert, $1815 (69) Stacking Blocks and Counting Permutations, Cheng, Eddie and Jerrold W. Grossman, by Lara K. Pudwell, 297-302 P1846 (226) Structured Population Dynamics: An Donnantouni, Marcos and José H. Nieto, Introduction to Integral Modeling, by $1817 (151) Joseph Briggs, Kathryn Dabbs, Michael Doucette, Robert L., $1829 (308) Holm, Joan Lubben, Richard Rebarber, Brigitte Tenhumberg, and Daniel Edelman, Alan and Daniel Edelman, Q1004 Riser-Espinoza, 243-257 (305) Edelman, Daniel and Alan Edelman, Q1004 Sums of Evenly Spaced Binomial Coefficients, by Arthur T. Benjamin, Bob Chen, (305) Kimberly Kindred, 370-373 Efthimiou, Costas, P1838 (65) Triangle Equalizers, by Dimitrios Furdui, Ovidiu, Q998 (66), P1849 (227) Kodokostas, 141-146 G.R.A.20 Problems Group, $1811 (66) What Do We Know at 7PM on Election Getling, David, $1821 (228) Night? by Andrew Gelman and Nate Goldenberg, Michael and Mark Kaplan, Silver, 258-266 P1855 (304) When is n* a Sum ofk Squares? by Todd G. Gologan, Radu and Cezar Lupu, P1852 (303) Will, 210-213 Grossman, Jerrold W., $1831 (392) 406 MATHEMATICS MAGAZINE Grossman, Jerrold W. and Eddie Cheng, Northwestern University Math Problem P1846 (226) Solving Group, $1832 (393) Hajja, Mowaffaq, Q1006 (392) Pité, Eric, Q997 (66), P1851 (303) lordache, Bianca-Teodora, P1842 (149) Pohoata, Cosmin, P1834 (66), $1820 (153) Kaplan, Mark and Michael Goldenberg, Roelants, Herman, Q1001 (227), P1858 (391) P1855 (304) Russell, Robert A., P1839 (65) Khoury, Michael Cap, $1826 (305) Saleh, Ossama A. and Stan Byrd, $1828 (306) Kim, Young Ho, $1813 (68) ShahAli, H. A., P1841 (149), P1856 (391) Kouba, Omran, $1822 (229), $1830 (309), Singer, Nicholas C., $1830 (309) $1835 (396) Smith, Steven D. and Rick Mabry, $1833 Krasniqi, Valmir, P1859 (392) (394) Le, Tuan, P1840 (65) Stadler, Albert, $1812 (67) Ligouras, Panagiote, P1847 (226) Stephens, Richard, P1850 (227) Lupu, Cezar and Radu Gologan, P1852 (303) Suppa, Ercole, $1829 (308) Lupu, Cezar and Tudorel Lupu, P1857 (391) Tetiva, Marian, P1844 (150), P1854 (304), Lupu, Tudorel and Cezar Lupu, P1857 (391) P1860 (392) Mabry, Rick, Q1003 (305) Thong, Duong Viet, P1837 (65) Mabry, Rick and Steven D. Smith, $1833 Trautman, Dave, $1824 (231) (394) Wolterman, Michael, P1836 (65), $1826 Martin, Reiner, $1827 (305) (304) Nieto, José H., P1843 (149), $1823 (230) Wong, Albert F. S., P1845 (150) Nieto, José H. and Marcos Donnantouni, Woodcock, Timothy, $1818 (152) $1817 (151) Zeng, Hongbiao, Q999 (150) To appear in College Mathematics Journal, January 2011 Articles Chutes and Ladders for the Impatient, by Leslie A. Cheteyan, Stewart Hengeveld, and Michael A. Jones Probability 1/e, by Reginald Koo and Martin L. Jones The Band Around a Convex Body, by David Swanson Two-Person Pie-Cutting: The Fairest Cuts, by Julius B. Barbanel and Steven J. Brams Augustus De Morgan: Champion of Hamilton, Boole, Gompertz, and Ramchundra, by Charlotte Simmons Computing Determinants by Double-Crossing, by Deanna Leggett, John Perry, and Eve Torrence Boundary Conditions, by Ursula Whitcher Classroom Capsules An Elementary Treatment of General Inner Products, by Jack E. Graver Cantor Groups, by Ben Mathes Book Review The Monty Hall Problem: The Remarkable Story of Math’s Most Contentious Brain Teaser by Jason Rosenhouse, reviewed by Edward J. Barbeau