VOL. 66, NO. 5, DECEMBER 1993 349 AUTHORS Conjecture, 44-45. Gluchoff, Alan D., Complex Power Series—a Vector Field Visualization, 189-191. Alexander, J.C., Symbolic Dynamics of the Sequence of Graham, Ron, see Chung, Dean. Pedal Triangles, The, 147-158. Grassl, Richard M., Euler Numbers and Skew-Hooks, Auslander, Joel, Arthur T. Benjamin, and Daniel 181-188. Shawcross Wilkerson, Optimal Leapfrogging, 14- Guy, Richard K., There Are Three Times as Many 19. Obtuse-Angled Triangles as There Are Acute-Angled Ayoub, Ayoub B., The Central Conic Sections Ones, 175-179. Revisited, 322-325. Hamilton, Wallace, see Shapiro, Lou. Bailey, Herb R., and Roger G. Lautzenheiser, A Hodges, Laurent, A Lesser-Known Goldbach Curious Sequence, 34-35. Conjecture, 45-47. Baker, John A., Coordinate Systems and Primitive Hoehn, Larry, A Menelaus-Type Theorem for the Maps, 236-237. Pentagram, 121-123. Bandy, C., Using Complex Solutions to Aid in Hull, David M., How Many Mating Units Are Graphing, 125. Needed to Have a Positive Probability of Survival?, Bartelt, Martin W., and John J. Swetits, An Elementary 28-33. Extension of Tietze’s Theorem, 330-331. Hurd, Spencer P., and David A. Trautman, The Beekman, Richard M., Proof without Words: Area Knight’s Tour on the 15-Puzzle, 159-166. under a Cycloid Cusp, 39. Hutchinson, Joan P., Coloring Maps, Maps of Empires, Bell, Denis, On the Limitations of a Well-Known and Maps of the Moon, 211-226. Integration Technique, 243-244. Jackson, Kelly, Francis Masat, and Robert Mitchell, Benjamin, Arthur T., see Auslander, Joel. Extensions of a Sums-of-Squares Problem, 41-43. Benson, Clark, and Franklin Lowenthal, The Marriage Johnson, B.R., see Davidson, R.R. Lemma for Polygamists, 238-242. Jones, Gareth A., 6/17, 290-298. Bencze, Mihaly, and Norman Schaumberger, A New Jones, Martin L., A Problem of Selection of Points from Proof of the Arithmetic-Geometric Mean Inequality, the Unit Interval, 116-120. 245. Kleiner, I., and A. Shenitzer, Mathematical Building Blecksmith, Richard and Charles Nicol, Monotonic Blocks, 3-13. Numbers, 257-262. Kroopnick, Allan, A Surprising Application of the Bloom, David M., An Old Algorithm for the Sums of Integral j£1 -Fix)d e to Revenue Projection, 254-256. Integer Powers, 304-305. Kung, Sidney H., Proof without Words: Area and Boas, Ralph P., Naming Things, 43. the Projection Theorem of a Right Triangle, 13. Bollinger, Richard C., Extended Pascal Triangles, 87- Lautzenheiser, Roger G., see Bailey, Herb R. 94. Lowenthal, Franklin, see Benson, Clark. Cairns, Grant, Margaret McIntyre, and John Strantzen, Machover, Maurice, Fractal Basin Street Blues, 226. Geometric Proof of Some Recent Results of Yang Lu, Malm, Donald E.G., A Graph of Primes, 317-320. 263-265. Marino, Giuseppe, and Paolamaria Pietramala, Chung, Dean, Ron Graham, and Herbert Taylor, Unconventional Orthonormal Basis Provides an Graceful Configurations in the Plane, 96-104. Unexpected Counterexample, 309-311. Clarke, Robert J., and Marta Sved, Derangements and Markham, Elizabeth M., Proof without Words: Bell Numbers, 299-303. Geometric Series, 242. Cross, James T., Jn the Gaussian Integers, a‘ +p* *y', Masat, Francis, see Jackson, Kelly. 105-108. Mcintyre, Margaret, see Cairns, Grant. Davidson, R.R., and B.R. Johnson, Interchanging Miller, William A., Proof without Words: Sum of Parameters of the Hypergeometric Distribution, Pentagonal Numbers, 325. 328-329. Mitchell, Robert, see Jackson, Kelly. Dence, Thomas P., Proof without Words, 179. Nair, N. Gopalakrishnan, Proof without Words: kth Dotson, William, Frederick Norwood, and Charlies Poweorf a Natural Numbern as the Sum ofn Taylor, Fiber Optics and Fibonacci, 167-174. Consecutive Odd Numbers (k=2,3,...), 329. Eckert, Ernest J., Constructions without Words, 113. Nelsen, Roger B., Proof without Words: Aristarchus’ Euler, Houston, Mathematical Ballroom Dancing, 321. Inequalities, 65. Fine, Benjamin, Classification of Finite Rings of Order Nelsen, Roger B., Proof without Words: Diophantus of p’, 248-252. Alexandria's “Sum of Squares" Identity, 180. Fulda, Joseph S., Exclusive Disjunction and the Nelsen, Roger B., Proof without Words: Every Cube Is Biconditional: An Even-Odd Relationship, 124. the Sum of Consecutive Odd Numbers, 316. Gallian, Joseph A., On the Converse of Lagrange’s Nicol, Charles, see Blecksmith, Richard. Theorem, 23. Norwood, Frederick, see Dotson, William. Gauld, David, Did the Young Volterra Know About Pfiefer, Richard E. and Cathleen Van Hook, Circles, Cantor?, 246-247. Vectors, and Line Algebra, 75-86. Gerstein, Larry J., A Reformulation of the Goldbach Pietramala, Paolamaria, see Marino, George. 350 MATHEMATICS MAGAZINE Reznick, Bruce, A Set is a Set, 95. Derangements and Bell Numbers, Roberta J. Clarke Richards, Kendall, Comparing Comparisons: Infinite |a nd Marta Sved, 299-303. Sums vs. Partial Sums, 326-327. Did the Young Volterra Know About Cantor?, David Schneebeli, H.R., Pythagoras—Space Traveller with q Gauld, 246-247. One-Way Ticket, 283-289. Elementary Extension of Tietze’s Theorem, An, Martin Selkirk, Keith, Rational Triangles, 24-27. W. Bartelt and John J. Swetits, 330-331. Shapiro, Lou, and Wallace Hamilton, The Catalan _—E yler Numbers and Skew-Hooks, Richard M. Grassi, Numbers Visit the Worid Series, 20-22. 181-188. Shenitzer, A., see Kleiner, I. Exclusive Disjunction and the Biconditional: An Even- Sherman, B.F., The Fourth Side of a Triangle, Odd Relationship, Joseph S. Fulda, 124. 333-337. Extended Pascal Triangles, Richard C. Bollinger, 87- Sinkhorn, Richard, The Range of the Adjugate Map, 94, 109-113. Extensions of a Sums-of-Squares Problem, Kelly Skrbina, David A., Conversion of Sequences from Jackson, Francis Masat, and Robert Mitchell, Deductive to Inductive Form, 312-313. 41-43. Smiley, Leonard M., A Quick Solution of Triangle Fiber Optics and Fibonacci, William Dotson, Frederick Counting, 40. Norwood, and Charles Taylor, 167-174. Stanton, Robert O., The Remarkable Number 648, Fourth Side of a Triangle, The, B.F. Sherman, 333. 48-55. Fractal Basin Street Blues, Maurice Machover, 226. Stephany, Timothy, Taxis, 305. Geometric Proofs of Some Recent Results of Yang Lu, Strantzen, John, see Cairns, Grant. Grant Cairns, Margaret McIntyre, and John Sullivan, Donald, The Square Roots of 2x 2 Matrices, Strantzen, 263-265. 314-316. Graceful Configurations in the Plane, Dean Chung, Ron Sved, Marta, see Clarke, Robert J. Graham, and Herbert Taylor, 96-104. Swetits, John J., see Bartelt, Martin W. Graph of Primes, A, Donald E.G. Malm, 317-320. Szabé, Sindor, On Finite Abelian Groups and Parailel How Many Mating Units Are Needed to Have a Edges on Polygons, 36-39. Positive Probability of Survival?, David Hull, 28-33. Taylor, Charies, see Dotson, William. In the Gaussian Integers,a‘+p»*y ; James T. Cross, Taylor, Herbert, see Chung, Dean. 105-108. Thurston, Hugh, On Tangents, 227-235. Interchanging Parameters of the Hypergeometric Trautman, David A., see Hurd, Spencer T. Distribution, R.R. Davidson and B.R. Johnson, Tugger, Roberta T., Subgroups and the Partitioning 328-329. Property, 114-115. Knight’s Tour on the 15-Puzzle, The, Spencer P. Hurd Van Hook, Cathleen, see Pfiefer, Richard E. and David A. Trautman, 159-166. Wilkerson, Daniel Shawcross, see Auslander, Joel. _L esser-Known Goldbach Conjecture, A, Laurent Wolsson, Kenneth, A Relation Between the Jacobian Hodges, 45-47. and Certain Generalized Wronskians, 253-254. Marriage Lemma for Polygamists, The, Clark Benson Wong, Roman, The Prisoner’s Dilemma, 306-309. and Franklin Lowenthal, 238-242. Mathematical Ballroom Dancing, Houston Euler, 321. TITLES Mathematical Building Blocks, /. Kleiner and A. Shenitzer, 3-13. Catalan Numbers Visit the World Series, The, Lou — Menelaus-Type Theorem for the Pentagram, A, Larry Shapiro and Wallace Hamilton, 20-22. Hoehn, 121-123. Central Conic Sections Revisited, The, Ayoub B. Monotonic Numbers, Richard Blecksmith and Charles Ayoub, 322-325. Nicol, 257-262. Circles, Vectors, and Linear Algebra, Richard E. Naming Things, Ralph P. Boas, 43. Pfiefer and Cathleen Van Hook, 75-86. New Proof of the Arithmetic-Geometric Mean Classification of Finite Rings of Order p?, Benjamin Inequality, A, Mihdly Bencze and Norman Fine, 248-252. Schaumberger, 245. Coloring Ordinary Maps, Maps of Empires, and Maps Qjd Algorithm for the Sums of Integer Powers, An, of the Moon, Joan P. Hutchinson, 211-225. David M. Bloom, 304-305. Comparing Comparisons: Infinite Sums vs. Partial Qn Finite Abelian Groups and Parallel Edges on Sums, Kendall Richards, 326-327. Polygons, Sdndor Szabé, 36-39. Complex Power Series~a Vector Field Visualization, Op Tangents, Hugh Thurston, 227-235. Alan D. Gluchoff, 189-191. On the Converse of Lagrange’s Theorem, Joseph A. Constructions without Words, Ernest J. Eckert, 113. Gallian, 23. Conversion of Sequences from Deductive to Inductive On the Limitations of a Well-Known Integration Form, David F. Skrbina, 312-313. Technique, Denis Bell, 243-244. Coordinate Systems and Primitive Maps, John A. Optimal Leapfrogging, Joel Auslander, Arthur T. Baker, 236-237. Benjamin, and Daniel Shawcross Wilkerson, 14-19. Curious Sequence, A, Herb R. Bailey and Roger G. Prisoner’s Dilemma, The, Roman Wong, 306-309. Lauzenheiser, 34-35. VOL. 66, NO. 5, DECEMBER 1993 351 Problem of Selection of Points from the Unit Interval, February: P1413-1417; Q800-801; $1388-1392. A, Martin L. Jones, 116-120. April: P1418-1422; Q802-804; $1393-1397. Proof without Words, Thomas P. Dence, 179. June: P1423-1427; Q805-807; $1398-1402. Proof without Words: Area and Projection Theorem October: P1428-1432; Q808-810; $1403-1407. of a Right Triangle, Sidney H. Kung, 13. December: P1433-1437; Q811-813; $1408-1412. Proof without Words: Area under a Cycloid Cusp, Richard M. Beekman, 39. Andreoli, Michael, $139711(133). Proof without Words: Aristarchus’ Inequalities, Apostol, Tom M., $13911(62). Roger B. Nelsen, 65. Barnouin, Pierre, Q803(127). Proof without Words: Diophantus of Alexandria’s "Sum Barrett, David Jonathan, $1407(271). of Squares” Identity, Roger B. Nelsen, 180. Binz, J.C., P1424(192). Proof without Words: Every Cube Is the Sum of Bloom, D.M., $1403(268). Consecutive Odd Numbers, Roger B. Nelsen, 316. Bonomo, John, Q801(57). Proof without Words: Geometric Series, Elizabeth M. Borchers, Brian, $1400(198). Markham, 242. Bulman-Fleming, Syd, and Edward T.H. Wang, Proof without Words: kth Power of a Natural Number P1434(338). n as the Sum of n Consecutive Odd Numbers Callan, David, $1388b(58). (k=2,3,...), N. Gopalakrishnan Nair, 329 ___» P1422(127). Proof without Words: Sum of Pentagonal Numbers, ___» $1406(270). William A. Miller, 325. __.» $14101G41). Pythagoras—Space Traveller with a One-Way Ticket, Campbell-Wright, Randall K., P1436(339). H.R. Schneebeli, 283-289. Cheng, Benny N., Q811(339). Quick Solution of Triangle Counting, A, Leonard M. Con Amore Problem Group, $1401(198). Smiley, 40. __» $14101341). Range of the Adjugate Map, The, Richard Sinkhorn, Demir, Hiiseyin, $1405(269). 109-113. Diao, Yuanan, P1437(339). Rational Triangles, Keith Selkirk, 24-27. Dodd, Fred, $13901(61). Reformation of the Goldbach Conjecture, A, Larry Doster, David, P1430(266). J. Gerstein, 44. Doucette, Robert L., $13991(196). Relation Between the Jacobian and Certain Generalized ___» $1408(340). Wronskians, A, Kenneth Wolsson, 253-254. Duncan, John, and Mihalis Maliakas, P1415(56). Remarkable Number 648, The, Robert O. Stanton, Fukuta, Jiro, P1421(126). 48-55. —__» P1426(192). Set is a Set, A, Bruce Reznick, 95. ___» PP1431(266). 6/x*, Gareth A. Jones, 290-298. Gan, Wee Liang, P1429(266). Square Roots of 2 x 2 Matrices, The, Donaid Sullivan, Gessel, Ira, $1392(63). 314-316. Goffinet, Daniel, and Patrick Goffinet, Q810(268). Subgroups and the Partitioning Property, Roberta T. Goffinet, Patrick, see Goffinet, Daniel. Tugger, 114-115. Hentzel, Irvin Roy, and Richard H. Sprague, Surprising Application of the Integral /(1 -Ax)d e P1418(126). to Revenue Projection, Allan Kroopnick, 254-256. Heuver, John G., $13951(130). Symbolic Dynamics of the Sequence of Pedal High, Robert, $139011(61). Triangles, The, J.C. Alexander, 147-158. Holzsager, Richard, $13981(194). Taxis, Timothy Stephany, 305. Kapudere, Serif, $139611(132). There Are Three Times as Many Obtuse-Angled Killingbergtro, Hans Georg Horten, and Ivar Skau, Triangles as There Are Acute-Angled Ones, Richard $14111(342). K. Guy, 175-179. Kitchen, Edward, Q813(339). Unconventional Orthonormal Basis Provides an Klamkin, Murray, CQ791(65). Unexpected Counterexample, Giuseppe Marino and _—_» Q802(127). Paolamaria Pietramala, 309-311. —_» Q805(193). Using Complex Solutions to Aid in Graphing, C. ___» P1428(266). Bandy, 125. ——» Q809(267). __.» P1437(339). PROBLEMS —___» Q812(339). Klee, Victor, P1413(56). P, S, Q, and C refers to Proposals, Solutions, Ladas, Gerry, Q806(193). Quickies, and Comments, respectively. Page numbers __, $139811(194). are given in parentheses. Thus, P1338(S6) refers to Lau, Kee-Wai, $14121(43). proposal number 1338, which appears on page 56. Li, Wenbo V., Q808(267). Litchfield, Kay P., $1388a(58).