Table Of Content

NEWS AND LETTERS Acknowledgments In addition to our Associate Editors, the following referees have assisted the MAGAZINE during the past year. We thank them for their time and care. Allman, Elizabeth S., University of Southern Case, Jeremy S., Taylor University, Upland, Maine, Falmouth, ME IN Andrews, Peter G., Eastern Illinois Univer- Chakerian, G. Don, University of California, sity, Charleston, IL Davis, Davis, CA Appleby, Glenn D., Santa Clara University, Culp-Ressler, Wendell, Franklin & Marshall Santa Clara, CA College, Lancaster, PA Axler, Sheldon, San Francisco State Univer- DeTemple, Duane W., Washington State Uni- sity, San Francisco, CA versity, Pullman, WA Axtell, Michael C., Wabash College, Craw- Dodge, Clayton W., University of Maine, fordsville, IN Orono, ME Barbeau, Jr., Edward J., University of Drobot, Vladimir, San Jose State University, Toronto, Toronto, Canada San Jose, CA Barksdale, Jr., James B., Western Kentucky Dunne, Edward G., American Mathematical University, Bowling Green, KY Society, Providence, RI Bauer, Craig P., Northwestern State Univer- Eisenberg, Bennett, Lehigh University, sity, Natchitoches, LA Bethelem, PA Baxley, John V., Wake Forest University, Elderkin, Richard H., Pomona College, Winston-Salem, NC Claremont, CA Beals, Richard W., Yale University, New Emert, John W., Ball State University, Haven, CT Muncie, IN Beauregard, Raymond A., University of Ensley, Douglas E., Shippensburg University, Rhode Island, Kingston, RI Shippensburg, PA Beezer Robert A., University of Puget Feroe, John A., Vassar College, Poughkeep- Sound, Tacoma, WA sie, NY Bergum, Gerald E., South Dakota State Uni- Firey, William, Corvallis, OR versity, Brookings, SD Fisher, Evan, Lafayette College, Easton, PA Berndt, Bruce C., University of Illinois, Ur- Fisher, J. Chris, University of Regina, Regina, bana, IL Canada Borwein, Jonathan M., Simon Fraser Univer- Fleron, Julian F, Westfield State College, sity, Burnaby, Canada Westfield, MA Brawner, James N., Armstrong Atlantic State Flint, Donna L., South Dakota State Univer- University, Savannah, GA sity, Brookings, SD Brown, Peter, University of New South Wales, Foster, Lorraine L. T., California State Uni- Sydney, Australia versity, Northridge, Northridge, CA Bullington, Grady D., University of Wiscon- Frantz, Marc, Indiana University, Blooming- sin, Oshkosh, Oshkosh, WI ton, IN Burton, David M., University of New Hamp- Fredricks, Gregory A., Lewis & Clark Col- shire, Durham, NH lege, Portland, OR Callan, C. David, University of Wisconsin, Fung, Maria G., University of Wisconsin- Madison, WI Stout, Menomonie, WI Cammack, Larry A., Central Missouri State Gallian, Joseph A., University of Minnesota— University, Warrensburg, MO Duluth, Duluth, MN 412 NEWS AND LETTERS Acknowledgments In addition to our Associate Editors, the following referees have assisted the MAGAZINE during the past year. We thank them for their time and care. Allman, Elizabeth S., University of Southern Case, Jeremy S., Taylor University, Upland, Maine, Falmouth, ME IN Andrews, Peter G., Eastern Illinois Univer- Chakerian, G. Don, University of California, sity, Charleston, IL Davis, Davis, CA Appleby, Glenn D., Santa Clara University, Culp-Ressler, Wendell, Franklin & Marshall Santa Clara, CA College, Lancaster, PA Axler, Sheldon, San Francisco State Univer- DeTemple, Duane W., Washington State Uni- sity, San Francisco, CA versity, Pullman, WA Axtell, Michael C., Wabash College, Craw- Dodge, Clayton W., University of Maine, fordsville, IN Orono, ME Barbeau, Jr., Edward J., University of Drobot, Vladimir, San Jose State University, Toronto, Toronto, Canada San Jose, CA Barksdale, Jr., James B., Western Kentucky Dunne, Edward G., American Mathematical University, Bowling Green, KY Society, Providence, RI Bauer, Craig P., Northwestern State Univer- Eisenberg, Bennett, Lehigh University, sity, Natchitoches, LA Bethelem, PA Baxley, John V., Wake Forest University, Elderkin, Richard H., Pomona College, Winston-Salem, NC Claremont, CA Beals, Richard W., Yale University, New Emert, John W., Ball State University, Haven, CT Muncie, IN Beauregard, Raymond A., University of Ensley, Douglas E., Shippensburg University, Rhode Island, Kingston, RI Shippensburg, PA Beezer Robert A., University of Puget Feroe, John A., Vassar College, Poughkeep- Sound, Tacoma, WA sie, NY Bergum, Gerald E., South Dakota State Uni- Firey, William, Corvallis, OR versity, Brookings, SD Fisher, Evan, Lafayette College, Easton, PA Berndt, Bruce C., University of Illinois, Ur- Fisher, J. Chris, University of Regina, Regina, bana, IL Canada Borwein, Jonathan M., Simon Fraser Univer- Fleron, Julian F, Westfield State College, sity, Burnaby, Canada Westfield, MA Brawner, James N., Armstrong Atlantic State Flint, Donna L., South Dakota State Univer- University, Savannah, GA sity, Brookings, SD Brown, Peter, University of New South Wales, Foster, Lorraine L. T., California State Uni- Sydney, Australia versity, Northridge, Northridge, CA Bullington, Grady D., University of Wiscon- Frantz, Marc, Indiana University, Blooming- sin, Oshkosh, Oshkosh, WI ton, IN Burton, David M., University of New Hamp- Fredricks, Gregory A., Lewis & Clark Col- shire, Durham, NH lege, Portland, OR Callan, C. David, University of Wisconsin, Fung, Maria G., University of Wisconsin- Madison, WI Stout, Menomonie, WI Cammack, Larry A., Central Missouri State Gallian, Joseph A., University of Minnesota— University, Warrensburg, MO Duluth, Duluth, MN 412 VOL. 74, NO. 5, DECEMBER 2001 2 Ghahramani, Saeed, Western New England Larson, Loren C., St. Olaf College, North- College, Springfield, MA field, MN Gillman, Leonard, University of Texas at Lautzenheiser, Roger G., Rose-Hulman Insti- Austin, Austin, TX tute of Technology, Terre Haute, IN Gluchoff, Alan Daniel, Villanova University, Lo Bello, Anthony J., Allegheny College, Downingtown, PA Meadville, PA Loud, Warren S., Minneapolis, MN Grabiner, Judith V., Pitzer College, Clare- mont, CA Lynch, Mark, Millsaps College, Jackson, MS Green, Euline I., Abilene Christian Univer- Mackin, Gail, Northern Kentucky University, sity, Abilene, TX Highland Heights, KY Grosshans, Frank D., West Chester Univer- Mackiw, George B., Loyola College in Mary- sity of Pennsylvania, Baltimore, MD land, Baltimore, MD Guichard, David R., Whitman College, Walla Martin, Greg, The University of British Walla, WA Columbia, Vancouver, Canada Guy, Richard K., University of Calgary, Cal- McCleary, John H., Vassar College, Pough- gary, Canada keepsie, NY Harborth, Heiko, Tech University Carolo- McDermot, Richard F., Allegheny College, Meadville, PA . Wilhelmina, Braunschweig, Germany Hayashi, Elmer K., Wake Forest University, McGuire, Linda E., Muhlenberg College, Al- Winston-Salem, NC lentown, PA Meda, Gowri, Pacific University, Forest Hirschhorn, Michael D., University of New South Wales, Sydney, Australia Grove, OR Merrill, Kathy D., Colorado College, Col- Hoffman, Frederick, Florida Atlantic Univer- orado Springs, CO sity, Boca Raton, FL Michaels, John G., State University of New Howard, Fredric T., Wake Forest University, York at Brockport, Brockport, NY Winston-Salem, NC Mills, Mark A., Central College, Pella, IA Isaac, Richard, Herbert H. Lehman College CUNY, Bronx, NY Moore, Thomas L., Grinnell College, Grin- nell, IA Jafari, Farhad, University of Wyoming, Morics, Steven W., University of Redlands, Laramie, WY Redlands, CA Janke, Steven J., Colorado College, Colorado Needham, Tristan, University of San Fran- Springs, CO cisce, San Francisco, CA Jepsen, Charles H., Grinnell College, Grin- Neidinger, Richard D., Davidson College, nell, IA Davidson, NC Johnson, Diane L., Humboidt State Univer- Nelsen, Roger B., Lewis and Clark College, sity, Arcata, CA Portland, OR Johnson, Warren P., University of Wisconsin— Nicodemi, Olympia E., State University of Madison, Madison, WI New York, Geneseo, NY Jones, Michael A., Montclair State Univer- Oakley, Patricia A., Goshen College, Goshen, sity, Upper Montclair, NJ IN Jordan, James H., Washington State Univer- Ostrov, Daniel N., Santa Clara University, sity, Pullman, WA Santa Clara, CA Kerckhove, Michael G., University of Rich- Otero, Daniel E., Xavier University, Cincin- mond, Richmond, VA nati, OH Kiltinen, John O., Northern Michigan Uni- Park, Efton L., Texas Christian University, versity, Marquette, MI Ft. Worth, TX Kimberling, Clark, University of Evansville, Pedersen, Jean J., Santa Clara University, Evansville, IN Santa Clara, CA Kuzmanovich, James J., Wake Forest Univer- Perline, Ronald K., Drexel University, sity, Winston-Salem, NC Philadelphia, PA Larson, Dean S., Gonzaga University, Pfiefer, Richard E., San Jose State University, Spokane, WA San Jose, CA 414 MATHEMATICS MAGAZINE Pinsky, Mark A., Northwestern University, Sherman, Gary, Rose-Hulman Institute of Evanston, IL Technology, Terre Haute, IN Ratliff, Thomas C., Wheaton College, Nor- Shifrin, Theodore, University of Georgia, ton, MA Athens, GA Rodger, Chris, Auburn University, Mont- Simoson, Andrew J., King College, Bristel, gomery, AL TN Ross, Kenneth A., University of Oregon, Eu- Sloughter, Daniel C., Furman University, gene, OR Greenville, SC Ross, Peter, Santa Clara University, Santa Smolarski, S. J., Dennis C., Santa Clara Uni- Clara, CA versity, Santa Clara, CA Roth, Richard L., University of Colorado, Snell, J. Laurie, Dartmouth College, Boulder, CO Hanover, NH Roy, Ranjan, Beloit College. Beloit, WI Solheid, Ernie S., California State University, Fullerton, Fullerton, CA Sadek, Jawad, Northwest Missouri State Uni- versity, Maryville, MO Stone, Alexander P., University of New Mex- ico, Albuquerque, NM Samuels, Stephen M., Purdue University, Szabo, Tamas, Weber State University, Og- West Lafayette, IN den, UT Sander, Evelyn, George Mason University, Townsend, Douglas W., Indiana University- Fairfax, VA Purdue University at Fort Wayne, Ft. Wayne, Saunders, Sam C., Scientific Consulting Ser- IN vices, Inc, Kirkland, WA Towse, Chris, Scripps College, Claremont, Saxe, Karen, Macalester College, St. Paul, CA MN Tucker, Thomas W., Colgate University, Schumer, Peter D., Middlebury College, Mid- Hamilton, NY dlebury, VT Whitehead, Tamsen, Santa Clara University, Scott, Richard A., Santa Clara University, San Jose, CA Santa Clara, CA Worner, Tamara S., Wayne State College, Shahriari, Shahriar, Pomona College, Clare- Wayne, NE mont, CA Zeleke, Melkamu, William Patterson Univer- Shell, Amy E., United States Military sity, Wayne, NJ Academy, West Point, NY Zullo, Holly S., Carroll College, Helena, MT Index to Volume 74 AUTHORS Bosman, Reinier J. C., see Dunbar, Steven R. Burm, Jacqueline; Fishback, Paul E., Period- Avidon, Michael Richard; Mabry, Richard 3 Orbits via Sylvester’s Theorem and Resul- D.; Sisson, Paul D., Enumerating Row Ar- tants, 47-51 rangements of Three Species, 130-134 Bush, Nancy-Elizabeth; Isihara, Paul A., The Bak, Joseph, The Anxious Gambler’s Ruin, Cwatset of aG raph, 41-47 182-193 Callan, C. David, Permutations and Coin- Beauregard, Raymond A.; Suryanarayan, E. Tossing Sequences, 55-57 R., Pythagorean Boxes, 223-227 Carroll, Maureen T.; Jones, Michael A.; Blachman, Nelson M.; Kilgour, D. Marc, Rykken, Elyn K., The Wallet Paradox Re- Elusive Optimality in the Box Problem, \7\- visited, 378-383 181 Chakerian, G. Don, Central Force Laws, Bliss, A.; Haas, S.; Rouse, Jeremy; Thatte, Hodographs, and Polar Reciprocals, 3-18 G., Math Bite: Four Constants in Four 4s, Chamberland, Marc A., Proof Without 2i2 Words: Look Ma, No Substitution! 55 VOL. 74, NO. 5, DECEMBER 2001 Dimitri¢, Radoslav M., Using Less Calcu- Kilgour, D. Marc, see Blachman, Nelson M. lus in Teaching Calculus: An Historical Ap- Kocik, Jerzy, Proof Without Words: Simp- proach, 201-211 son’s Paradox, 399 Dresden, Gregory P. B., Two Irrational Num- Koo, Reginald, see Jones, Martin L. bers That Give the Last Non-Zero Digits of Kosinski, Antoni A., Cramer’s Rule Is Due to n! and n", 316-320 Cramer, 310-312 Dunbar, Steven R.; Bosman, Reinier J. C.; Kubelka, Richard P., Means to an End, 141- Nooij, Sander E. M., The Track of a Bicycle 145 Back Tire, 273-287 Kung, Sidney H., Proof Without Words: The Edwards, B. Carter; Shurman, Jerry, Folding Weierstrass Substitution, 393 Quartic Roots, 19-25 Lampret, Vito, The Euler-Maclaurin and Ellermeyer, Sean F.; Robinson, David, /nte- Taylor Formulas: Twin, Elementary Deriva- grals of Periodic Functions, 393-396 tions, 109-122 England, William T.; Miller, T. Len, Volumes Lanski, Charles P., A Characterization of In- and Cross Sectional Areas, 288—295 finite Cyclic Groups, 61-65 Ferlini, Vincent J., Proof Without Words: Lotto, Benjamin A., see Feroe, John A. Logarithm of a Number and Its Reciprocal, 59 Lenard, Andrew, An Application of the Mar- riage Lemma, 234-238 Feroe, John A.; Lotto, Benjamin A.; Stein- horn, Charles L., Boxlike Domains in the Mabry, Richard D., see Avidon, Michael Complex Plane, 388-392 Richard Fishback, Paul E., see Burm, Jacqueline Margolius, Barbara H., Avoiding Your Spouse at a Bridge Party, 33-41; Letter to the Edi- Frantz, Marc, Visualizing Leibniz’s Rule, tor, 368 143-145 Martin-Sanchez, Oscar; Pareja-Flores, Gallian, Joseph A., The Classification of Groups of Order 2 p, 60-61 Cristobal, Two Reflected Analyses of Lights Out, 295-304 Gauchman, Hillel, A Special Case of Dirich- let’s Theorem on Primes in an Arithmetic McKinzie, Mark; Tuckey, Curtis, Higher Progression, 397-399 Trigonometry, Hyperreal Numbers, and Eu- ler’s Analysis of Infinities, 339-368 Giblin, Peter J., Zigzags, 259-272 Memory, Jasper D., The Wily Hunting of the Gomez, Jose A., Proof Without Words: Proof, 140; Dialog with Computer in the Pythagorean Theorem, \53 Proooff t he Four-Color Theorem, 313 Groetsch, Charles W., A Celestial Cubic, Michalek, Gary E., Writing Numbers in Base 145-152 3, the Hard Way, 51-54 Gudder, Stanley P.; Hagler, James N., Prob- Miller, T. Len, see Eng!and, William T abilities of Consecutive Integers in Lotto, 216-222 Missigman, Jennie; Weida, Richard A., An Easy Solution to Mini Lights Out, 57-59 Haas, S., see Bliss, A. Hagler, James N., see Gudder, Stanley P. Nelsen, Roger B., Letter to the Editor, 377 Hoehn, Larry P., Extriangles and Excevians, Neuwirth, Erich, Designing a _ Pleasing 384-388 Sound Mathematically, 91-98 Isihara, Paul A., see Bush, Nancy-Elizabeth Nooij, Sander E. M., see Dunbar, Steven R. Johnson, Warren P., A Simple Fact About Okuda, Shingo, Proof Without Words: The Eigenvectors That You Probably Don’t Triple-Angle Formulafso r Sine and Cosine, Know, 227-230 135 Jones, Michael A., see Carroll, Maureen T. Osler, Thomas J., Cardan Polynomials and the Reduction of Radicals, 26-32 Jones, Martin L.; Koo, Reginald, The Disad- vantage of Too Much Success, 136-140 Pareja-Flores, Cristdbal, see Martin-Sanchez, Oscar Kanim, Katherine, Proof Without Words: How Did Archimedes Sum Squares in the Rispoli, Fred J., Counting Perfect Matchings Sand ?, 314-315 in Hexagonal Systems Associated with Ben- Khoury, Jr., Michael, Smullyan’s Vizier Prob- zenoids, 194-200 lem, 369-377 Robinson, David, see Ellermeyer, Sean F. 416 MATHEMATICS MAGAZINE Roth, Richard L., A History of Lagrange’s Celestial Cubic, A, by Charles W. Groetsch, Theorem on Groups, 99-108 145-152 Rouse, Jeremy, see Bliss, A. Central Force Laws, Hodographs, and Polar Rump, Christopher M., Strategies for Rolling Reciprocals, by G. Don Chakerian, 3-18 the Efron Dice, 212-216 Characterization of Infinite Cyclic Groups, Rykken, Elyn K., see Carroll, Maureen T. A, by Charles P. Lanski, 61-65 Shurman, Jerry, see Edwards, B. Carter Classification of Groups of Order 2 p, The, by Joseph A. Gallian, 60-61 Sisson, Paul, see Avidon, Michael Richard Steinhorn, Charles I., see Feroe, John A. Counting Perfect Matchings in Hexagonal Systems Associated with Benzenoids, by Suryanarayan, E. R., see Beauregard, Ray- Fred J. Rispoli, 194-200 mond A. Cramer’s Rule Is Due to Cramer, by Antoni Suzuki, Fukuzo,A n Equilateral Triangle with A. Kosinski, 310-312 Sides Through the Vertices of an Isosceles Cwatset of a Graph, The, by Nancy-Elizabeth Triangle, 304—310 Bush and Paul A. Isihara, 41-47 Tanton, James, Proof Without Words: Equi- Designing a Pleasing Sound Mathematically, lateral Triangle, 313 by Erich Neuwirth, 91-98 Thatte, G., see Bliss, A. Dialog with Computer in the Proof of the The VIEWPOINTS 2000 Group, Proof With- Four-Color Theorem, by Jasper D. Memory, out Words: Geometric Series, 320 313 Tuckey, Curtis, see McKinzie, Mark Disadvantage of Too Much Success, The, by Varilly, Anthony, Location of Incenters and Martin L. Jones and Reginald Koo, 136-140 Fermat Points in Variable Triangles, 123- Easy Solution to Mini Lights Out, An, by Jen- 129 nie Missigman and Richard A. Weida, 57- Wardlaw, William P., A Generalized General 59 Associative Law, 230-233 Elusive Optimality in the Box Problem, by Weida, Richard A., see Missigman, Jennie Nelson M. Blachman and D. Marc Kilgour, Wen, Liu, A Nowhere Differentiable Continu- 171-181 ous Function Constructed by Cantor Series, Enumerating Row Arrangements of Three 400-402 Species, by Michael Richard Avidon, Wu, Rex H., Proof Without Words: The Lav Richard D. Mabry, and Paul Sisson, 130- of Tangents, 161 134 Yang, Heng, see Yang, Hansheng Equilateral Triangle with Sides Through the Yang, Hansheng; Yang, Heng, The Vertices of an Isosceles Triangle, An, by Arithmetic-Geometric Mean Inequality and Fukuzo Suzuki, 304-310 the Constant e, 321-323 Euler-Maclaurin and Taylor Formulas, The: Twin, Elementary Derivations, by Vito TITLES Lampret, 109-122 Extriangles and Excevians, by Larry P. Anxious Gambler’s Ruin, The, by Joseph Hoehn, 384-388 Bak, 182-193 Folding Quartic Roots, by B. Carter Edwards Application of the Marriage Lemma, An, by and Jerry Shurman, 19-25 Andrew Lenard, 234-238 Generalized General Associative Law, A, by Arithmetic-Geometric Mean Inequality and William P. Wardlaw, 230-233 the Constant e, The, by Hansheng Yang and Higher Trigonometry, Hyperreal Numbers, Heng Yang, 321-323 and Euler’s Analysis of Infinities, by Mark Avoiding Your Spouse at a Bridge Party, by McKinzie and Curtis Tuckey, 339-368 Barbara H. Margolius, 33-41 History of Lagrange’s Theorem on Groups, Boxlike Domains in the Complex Plane, by A, by Richard L. Roth, 99-108 John A. Feroe, Benjamin A. Lotto, and Integrals of Periodic Functions, by Sean F. Charles I. Steinhorn, 388-392 Ellermeyer and David Robinson, 393-396 Cardan Polynomials and the Reduction of Letter to the Editor, by Barbara H. Mar- Radicals, by Thomas J. Osler, 26-32 golius, 368 VOL. 74, NO. 5, DECEMBER 2001 417 Letter to the Editor, by Roger B. Nelsen, 377 Strategies for Rolling the Efron Dice, by Location of Incenters and Fermat Points Christopher M. Rump, 212-216 in Variable Triangles, by Anthony Varilly, Track ofa Bicycle Back Tire, The, by Steven 123-129 R. Dunbar, Reinier J. C. Bosman, and Math Bite: Four Constants in Four 4s, by A. Sander E. M. Nooij, 273-287 Bliss, S. Haas, Jeremy Rouse, and G. Thatte, Two Irrational Numbers That Give the Last 272 Non-Zero Digits of n! and n" ,b y Gregory P. Means to an End, by Richard P. Kubelka, B. Dresden, 316-320 141-145 Two Reflected Analyses of Lights Out, by Nowhere Differentiable Continuous Function Oscar Martin-Sanchez and Cristobal Pareja- Constructed by Cantor Series, A, by Liu Flores, 295-304 Wen, 400-402 Using Less Calculus in Teaching Calculus: Period-3 Orbits via Sylvester’s Theorem and An Historical Approach, by Radoslav M. Resultants, by Jacqueline Burm and Paul E. Dimitri¢, 201-211 Fishback, 47-51 Visualizing Leibniz’s Rule, by Marc Frantz, Permutations and Coin-Tossing Sequences, 143-145 by C. David Callan, 55-57 Volumes and Cross Sectional Areas, by Probabilities of Consecutive Integers in William T. England and T. Len Miller, 288- Lotto, by Stanley P. Gudder and James N. 295 Hagler, 216-222 Wallet Paradox Revisited, The, by Maureen Proof Without Words: Equilateral Triangle, T. Carroll, Michael A. Jones, and Elyn K. by James Tanton, 313 Rykken, 378-383 Proof Without Words: Geometric Series, by Wily Hunting of the Proof, The, by Jasper D. The VIEWPOINTS Group, 320 Memory, 140 Proof Without Words: How Did Archimedes Writing Numbers in Base 3, the Hard Way, by Sum Squares in the Sand?, by Katherine Gary E. Michaiek, 51-54 Kanim, 314-315 Zigzags, by Peter J. Giblin, 259-272 Proof Without Words: Law of Tangents, The, by Rex H. Wu, 161 PROBLEMS Proof Without Words: Logarithm of a Num- ber and Its Reciprocal, by Vincent J. Ferlini, The letters P. Q, and S refer to Proposals, 59 Quickies, and Solutions, respectively; page Proof Without Words: Look Ma, No Substitu- numbers appear in parentheses. For ex- tion!, by Mare A. Chamberland, 55 ample, P1622(155) refers to Proposal 1622, which appears on page 155. Proof Without Words: Pythagorean Theorem, by Jose A. Gomez, 153 Proof Without Words: Simpson’s Paradox, by February: P1613—1617; Q907—908; S1589- Jerzy Kocik, 399 1593 Proof Without Words: The Triple-Angle For- April: P1618—1622; Q909-910; S1594—1598 mulas for Sine and Cosine, by Shingo Okuda, 135 June: P1623-1627; Q91 1-912; $1599-1602, 1577 Proof Without Words: The Weierstrass Sub- stitution, by Sidney H. Kung, 393 October: P1628—1632; Q913-914; S$1603- 1607 Pythagorean Boxes, by Raymond A. Beaure- gard and E. R. Suryanarayan, 223-227 December: P1633—1637; Q915-—916; S1608- 1612 Simple Fact About Eigenvectors That You Probably Don’t Know, A, by Warren P. John- Akhlaghi, Reza, $1599(241) son, 227-230 Bailey, Herb, $1594(155) Smullyan’s Vizier Problem, by Michael Barbara, Roy, $1610(405) Khoury, Jr., 369-377 Bencze, Mihaly, P1620(154), P1625(239) Special Case of Dirichlet’s Theorem on Primes in an Arithmetic Progression, A, by Carter, David, Q912(240) Hillel Gauchman, 397-399 Dale, Knut, $1606(329) 418 MATHEMATICS MAGAZINE Deshpande, M. N., P1615(67) Klamkin, Murray, Q910(155), P1624(239), Deutsch, Emeric, P1613(66), P1623(239), Q911(240), Q913(325), Q916(404) P1633(403), Q915(404) Knuth, Donald, P1621(154) Donini, Daniele, $1597(159), $1605(327) Korman, Philip, $1577(244) Doucette, Robert, §1603(325), $1612(408) Lau, Chi Hin, $1605(328) Dove, Kevin L., and Sumner, John S., Lau, Kee-Wai, S1590(68) $1609(405) Lee, Hojoo, P1626(240) Efthimiou, Costas, P1619(154) Martin, Reiner, $1607(330) Florin, Jon, $1593(70) Niculescu, Constantin P., P1634(403) Fukuta, Jiro, P1627(240) Nieto, José H., $1601(243) Gao, Peng, P1629(324) Quet, Leon, P1636(403) Gardner, Martin, Q907(67) Rey, Joaquin Gémez, Q909(155) Gelca, Razvan, P1628(324) Risteski, Ice B., $1599(241) Getz, Marty, and Jones, Dixon, $1598(160) Schaumberger, Norman, Q908(67) Ghalayini, Bassam B., and Tarabay, Ajaj A.., Schaumberger, Norman, and Just, Erwin $1611(407) P1616(67) Golomb, Michael, P1618(154), $1602(243) Sinefakopoulos, Achilleas, P1614(66) Gotz, Trenkler, P1622(155) Skau, Ivar, $1604(326) Hoehn, Larry, P1635(403) Sumner, John S., and Dove, Kevin L., Jahns, Kelly, Q914(325) $1609(405) Jones, Marty and Getz, Dixon, S1598(160) Stromquist, Walter, $1595(157) Just, Erwin, P1632(325), P1637(404) Tarabay, Ajaj A., and Ghalayini, Bassam B., Just, Erwin, and Schaumberger, Norman, $1611(407) P1616(67) Wardlaw, William, $1608(404) Kandall, Geoffrey A., P1630(324) Wee, Hoe-Teck, P1631(325) Kappus, Hans, $1589(68) Woltermann, Michael, $1600(242) Kidwell, Mark S1591(69) Yun, Zhang P1617(67) King, L. R., $1596(157) Zhou, Li, $1592(70), $1597(158) Thanks are also due to those who have refereed proposalfso r the Problems Column: Clifford Bergman, Alexander Burstein, Irvin Hentzel, Roger Maddux, and James Wilson of lowa State University, Ames, and Vania Mascioni of Western Washington University, Belling- ham. Letters to the Editor appear on pages 368 and 377.