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    Journal: The American Mathematical Monthly

    Volume 109, Issue 9

    785 -- 795Ulrich Daepp, Pamela Gorkin, Raymond Mortini. Ellipses and Finite Blaschke Products
    796 -- 805Daniel Isaksen. A Cohomological Viewpoint on Elementary School Arithmetic
    806 -- 817Bennett Eisenberg, Rosemary Sullivan. The Fundamental Theorem of Calculus in Two Dimensions
    818 -- 826Iwan Praton. Cutting Polyominos into Equal-Area Triangles
    827 -- 839Leonard F. Klosinski, Gerald L. Alexanderson, Loren C. Larson. The Sixty-Second William Lowell Putnam Mathematical Competition
    840 -- 843Chun-Hung Hsu, Ming-Chia Li. Transitivity Implies Period Six: A Simple Proof
    843 -- 845N. J. Wildberger. A New Proof of Cavalieri's Quadrature Formula
    845 -- 850Yingying Li. On Euler's Constant-Calculating Sums by Integrals
    850 -- 853Alf van der Poorten. Life on the Edge
    854 -- 0Razvan A. Satnoianu. Problem 10970
    854 -- 0Leslie D. Servi. Problem 10973
    854 -- 0C. P. Rupert. Problem 10971
    854 -- 855Syrous Marivani. Problem 10974
    854 -- 0Tim Ferguson, Lenny Jones. Problem 10972
    855 -- 0Vitaly I. Voloshin. Problem 10976
    855 -- 0Emeric Deutsch. Problem 10975
    855 -- 856Howard M. Taylor, Richard A. Groeneveld, John Stufken, John G. Kemeny, James Laurie Snell, Anthony W. Knapp. A Careless Walk toward Zero: 10788
    856 -- 857David Beckwith, et al.. Additive Atoms: 10828
    857 -- 858Anna Dyubina, Stephen M. Gagola Jr.. A Group That Is Not Finitely Generated: 10835
    858 -- 0Erwin Just, Charles Lanski. Consequences of a Relation on a Ring: 10841
    858 -- 859Bruce Reznick, Li Zhou, et al.. Nondivisibility of Binomial Coefficients: 10842
    859 -- 860David Beckwith, Li Zhou, David Callan. A Property of the Binary Sum of a Family of Sets: 10865
    860 -- 861Ovidiu Furdui, Albert Nijenhuis. A Square Property: 10904
    860 -- 0Ricardo Martini, Gerhard F. Post, Gerald Leibowitz. An Inequality of Hardy: 10899

    Volume 109, Issue 8

    689 -- 703Scott Bailey, Theodore Kim, Robert S. Strichartz. Inside the Lévy Dragon
    704 -- 728Anthony Philippakis. The Orthic Triangle and the O.K. Quadrilateral
    729 -- 740Fernando Rodriguez-Villegas, Lorenzo Sadun, José Felipe Voloch. Blet: A Mathematical Puzzle
    741 -- 745Mark Levene, George Loizou. Kemeny's Constant and the Random Surfer
    746 -- 749Daniel J. Velleman. Partial Fractions, Binomial Coefficients, and the Integral of an Odd Power of sec θ
    750 -- 752Per E. Manne, Steven R. Finch. A Solution to the Bent Wire Problem
    753 -- 754Brunero Liseo. A Probabilistic Derivation of Dirichlet Integrals
    755 -- 756Roberto Sánchez-Peregrino. A Note on a Closed Formula for Poly-Bernoulli Numbers
    756 -- 758Harold Parks, Dean C. Wills. An Elementary Calculation of the Dihedral Angle of the Regular n-Simplex
    759 -- 0John Melville. Problem 10965
    759 -- 760Stephen C. Locke. Problem 10968
    759 -- 0Jean-Marie De Koninck. Problem 10966
    759 -- 0Douglas B. West. Problem 10967
    759 -- 0Paul Deiermann. Problem 10963
    759 -- 0H. A. ShahAli. Problem 10964
    760 -- 761M. Mirzavaziri, et al.. Least Number with Exactly m Divisors: 10820
    760 -- 0Richard Stanley. Problem 10969
    760 -- 0Ovidiu Furdui. Problem 10950
    761 -- 762George E. Andrews, Karl David, S. J. Bernau, Marty Getz, Dixon Jones. Periodicity under Shift and Complement: 10823
    762 -- 763Carl Miller, Donald E. Knuth. A Fibonacci-Lucas Extremum: 10825
    763 -- 764Sung-Soo Kim, Richard Johnsonbaugh, Ronald E. Prather, Donald E. Knuth. Min-Plus Matrix Multiplication: 10834
    763 -- 0Walther Janous, Rolf Richberg, Raul A. Simon. A Totient Sum: 10829
    764 -- 765Razvan A. Satnoianu, O. P. Lossers. The Minimum Median: 10880
    765 -- 766Klaus Huber, O. P. Lossers, Norbert Ortner, A. Serret. Cassini's Length: 10889
    774 -- 776Bruce P. Palka. Editor's Endnotes

    Volume 109, Issue 7

    585 -- 594Bob Witte. The 2001 James R. C. Leitzel Lecture: What I Have Learned from the Mathematics Community
    595 -- 611Robert F. Brown, Jack E. Girolo. Isolating Fixed Points
    612 -- 622James T. Smith. Thomsen's Equation
    623 -- 638John McCleary. Trigonometries
    639 -- 649Ezra Brown, Bruce T. Myers. Elliptic Curves from Mordell to Diophantus and Back
    650 -- 655Robert L. Lamphere. Solution of the Direct Problem of Uniform Circular Motion in Non-Euclidean Geometry
    655 -- 657M. J. Jamieson. Fibonacci Numbers and Cotangent Sequences
    657 -- 659Iosif Pinelis. An Equidistribution Phenomenon: Is There a Principle behind It?
    660 -- 661P. G. Walsh. On a Question of Kaplansky
    661 -- 663Judy A. Holdener. A Theorem of Touchard on the Form of Odd Perfect Numbers
    664 -- 0John McCarthy. Problem 10956
    664 -- 0Victor Alexandrov. Problem 10957
    664 -- 0Robin Chapman. Problem 10958
    665 -- 0Brian Conrad. Problem 10961
    665 -- 0Oliver Eng. Problem 10960
    665 -- 0George Lamb. Problem 10959
    665 -- 0Mihály Bencze. Problem 10962
    665 -- 666Alberto Facchini, Francesco Barioli, Robin Chapman, Ron Martin Carroll. Nonsingular Sums of Matrices: 10784
    666 -- 667George E. Andrews, Robin J. Chapman. A Sparse Determinant: 10831
    667 -- 668Sung-Soo Kim, Richard Johnsonbaugh, Ronald E. Prather, Donald E. Knuth. Min-Plus Matrix Multiplication: 10834
    668 -- 669Ernesto Bruno Cossi, Robin Chapman. Points on a Sphere: 10855
    669 -- 0Jerry Kazdan, Herbert S. Wilf, Darryl K. Nester. Waiting for the Bus: 10866
    669 -- 670Wu Wei Chao, Li Zhou. Parallelogram Circumcenters: 10874
    670 -- 0Erwin Just, Norman Schaumberger, Paul Budney. A Little Convexity: 10882
    670 -- 671Zafar Ahmed, Knut Dale, George Lamb. Definitely an Integral: 10884

    Volume 109, Issue 6

    497 -- 516Elena Anne Marchisotto. The Theorem of Pappus: A Bridge between Algebra and Geometry
    517 -- 524Carrie E. Finch, Lenny Jones. A Curious Connection between Fermat Numbers and Finite Groups
    525 -- 533Tom M. Apostol, Mamikon A. Mnatsakanian. Subtangents - An Aid to Visual Calculus
    534 -- 543Jeffrey C. Lagarias. An Elementary Problem Equivalent to the Riemann Hypothesis
    544 -- 553Leonard Gillman. Two Classical Surprises Concerning the Axiom of Choice and the Continuum Hypothesis
    554 -- 559G. E. Hardy, M. V. Subbarao. A Modified Problem of Pillai and Some Related Questions
    559 -- 564Michael Nyblom. Some Curious Sequences Involving Floor and Ceiling Functions
    565 -- 568Timothy G. Feeman, Osvaldo Marrero. The Right-Hand Derivative of an Integral
    569 -- 0Ovidiu Furdui. Problem 10950
    569 -- 0Jeffrey C. Lagarias. Problem 10949
    569 -- 0David Callan. Problem 10952
    569 -- 0Sung-Soo Kim. Problem 10951
    570 -- 571Doru Caragea, Viviana Ene, Dean Alvis, Nasha Komanda. A Millennial Polynomial Problem: 10802
    570 -- 0Erwin Just, Norman Schaumberger. Problem 10954
    570 -- 0Leroy Quet. Problem 10953
    570 -- 0Razvan A. Satnoianu. Problem 10955
    571 -- 572Fred Richman, et al.. Subspaces of the Vector Space of 2-by-2 Matrices: 10813
    572 -- 573Stevo Stevic, Alain Tissier. The Limit of a Sequence: 10853
    573 -- 574Harold G. Diamond, Alain Tissier. Truncated Series Ratios Alternating about tanh x: 10857
    574 -- 0Calin Popescu, Xiaoshen Wang, Thomas McMillan. Compact Subsets Countable: 10864
    575 -- 576Oscar Ciaurri Ramirez, Daniele Donini. Sum of an Infinite Series: 10867

    Volume 109, Issue 5

    409 -- 442Jason Cantarella, Dennis DeTurck, Herman Gluck. Vector Calculus and the Topology of Domains in 3-Space
    443 -- 451Shay Gueron, Ran Tessler. The Fermat-Steiner Problem
    452 -- 458M. Ram Murty. Prime Numbers and Irreducible Polynomials
    459 -- 462Alf van der Poorten, Gerhard J. Woeginger. Squares from Products of Consecutive Integers
    463 -- 465Jeff Brooks, Satha Push. The Cycloidal Pendulum
    466 -- 471Paulo Viana, Paula M. Veloso. Galois Theory of Reciprocal Polynomials
    471 -- 473Mira Bhargava. When Is a Group the Union of Proper Normal Subgroups?
    473 -- 474Gregory F. Bachelis. A Short Proof of Hall's Theorem on SDRs
    475 -- 0Walther Janous. Problem 10942
    475 -- 476Slavko Simic. Problem 10945
    475 -- 0Marcin Mazur. Problem 10944
    475 -- 0Calin Popescu. Problem 10943
    476 -- 0Stevo Stevic. Problem 10946
    476 -- 477Antal Fekete, Johann Cigler. Stirling and Bell and Binomial, Oh My!: 10805
    476 -- 0. Problem 10947
    476 -- 0Peter Walker. Problem 10948
    477 -- 478David Beckwith, Karl David. An Identity for Partitions of Integers: 10809
    478 -- 0Phil Tracy, et al.. The Distance between the Endpoints of a Longest Path: 10811
    478 -- 479Emeric Deutsch, Wen-Jin Woan. Special Motzkin Paths: 10816
    479 -- 480Cezar Joita, Robin Chapman. The Functional Equation f g = f: 10818
    480 -- 481Olaf Krafft, Gabriela Stanica, Pantelimon Stanica. A Binomial Coefficient Estimate: 10819
    481 -- 482Ho-Joo Lee, Marc A. P. Bernstein. Brocard Angle 30 Degrees: 10824
    482 -- 0Ulrich Abel, Douglas B. Tyler. Reminiscent of Gibbs: 10827

    Volume 109, Issue 4

    321 -- 337Alan D. Taylor. The Manipulability of Voting Systems
    338 -- 361Jeffrey C. Lagarias, Colin L. Mallows, Allan R. Wilks. Beyond the Descartes Circle Theorem
    362 -- 370Shay Gueron. Two Applications of the Generalized Ptolemy Theorem
    371 -- 377Rita Aggarwala, Michael P. Lamoureux. Inverting the Pascal Matrix Plus One
    378 -- 380Liu Wen. A Nowhere Differentiable Continuous Function Constructed by Infinite Products
    380 -- 383Johannes Huisman. Rino's Flight around the World in Circles
    383 -- 388Casey Mann. A Tile with Surround Number 2
    388 -- 390Reinhard Michel. On Stirling's Formula
    390 -- 391Andrea Vietri. An Inductive Proof of a Known Result about ψ(x)
    392 -- 0Zhibing Chen. Problem 10935
    392 -- 0Andor Lukács, Szilárd András. Problem 10936
    392 -- 0Aleksandar Ivic. Problem 10939
    392 -- 0Jean-Pierre Grivaux. Problem 10938
    392 -- 0David G. Wagner. Problem 10937
    393 -- 394Paul Bateman, Jeffrey Kalb, Allen Stenger. A Limit Involving Least Common Multiples: 10797
    393 -- 0Jeffrey C. Lagarias. Problem 10941
    393 -- 0Yves Nievergelt. Problem 10940
    394 -- 395Paul R. Pudaite, Owen D. Byer, Deirdre Longacher Smeltzer. A Gambler Urns His Money: 10801
    395 -- 396Stephen G. Penrice, et al.. Expected Rank in an NBA Draft Lottery: 10803
    396 -- 397Floor van Lamoen. Circumcenters on a Circle: 10830
    397 -- 398Florian S. Pârvânescu, Roy Barbara. When ABC Is Equilateral: 10838
    398 -- 399Jiansheng Yang, ShuLin Zhou, O. P. Lossers. An Elaborate Uniform Convergence: 10840

    Volume 109, Issue 3

    217 -- 234Warren P. Johnson. The Curious History of Faà di Bruno's Formula
    235 -- 245Wladimir de Azevedo Pribitkin. Laplace's Integral, the Gamma Function, and beyond
    246 -- 257Sam Northshield. Associativity of the Secant Method
    258 -- 272Aimee S. A. Johnson, Kathleen Madden. Renewal Systems, Sharp-Eyed Snakes, and Shifts of Finite Type
    273 -- 277Warren P. Johnson. Combinatorics of Higher Derivatives of Inverses
    277 -- 278Christian Radoux. The Hankel Determinant of Exponential Polynomials: A Very Short Proof and a New Result Concerning Euler Numbers
    279 -- 284Karl Dilcher, Kurt Girstmair. Dedekind Sums and Uniform Distributions
    285 -- 0Robbert Fokkink. 3 Has No Root
    286 -- 297John Stillwell. The Continuum Problem
    298 -- 0Paul Schweitzer. Problem 10930
    298 -- 0Robert DiSario. Problem 10931
    298 -- 299Christian Bey, Jerrold R. Griggs. Problem 10932
    298 -- 0Christopher J. Hillar. Problem 10928
    298 -- 0Lajos Csete. Problem 10929
    299 -- 0Paul Lescott. Problem 10933
    299 -- 0Vasile Mihai. Problem 10934
    299 -- 0Hadi Salmasian, et al.. Minimizing the Sum of Negative Powers of Orders of Group Elements: 10775
    300 -- 0Yongge Tian, David W. Carter. Squashing a Matrix by Adding an Imaginary Part: 10776
    300 -- 301Leonard Smiley, Helmut Prodinger, Robin Chapman, et al.. A Tree-Counting Identity: 10781
    301 -- 302Douglas Iannucci, O. P. Lossers, et al.. Divisibility Involving Random Sets of Integers: 10782
    302 -- 304Emeric Deutsch, John Henry Steelman, David Callan. A Recursively Defined Sequence of Functions: 10785
    304 -- 305Douglas E. Iannucci, Kee-Wai Lau. Triperfect Numbers: 10800
    305 -- 0Wu Wei Chao, Geoffrey A. Kandall. The Median Meets the Circle of Appolonius: 10862
    313 -- 314Bruce P. Palka. Editor's Endnotes

    Volume 109, Issue 2

    105 -- 120Eleanor Robson. Words and Pictures: New Light on Plimpton 322
    121 -- 139Audrey A. Terras. Finite Quantum Chaos
    140 -- 150Aaron Abrams, Robert Ghrist. Finding Topology in a Factory: Configuration Spaces
    151 -- 164Arthur Baragar. Constructions Using a Compass and Twice-Notched Straightedge
    165 -- 172Frank Morgan, Roger Bolton. Hexagonal Economic Regions Solve the Location Problem
    173 -- 186James Kuzmanovich, Andrey Pavlichenkov. Finite Groups of Matrices Whose Entries Are Integers
    187 -- 188Liu Zheng. An Elementary Proof for Two Basic Alternating Series
    188 -- 192Robert A. Agnew. On the TEAM Approach to Investing
    192 -- 194Craig Huneke. The Friendship Theorem
    194 -- 196Claude-Alain Faure. A Short Proof of Lebesgue's Density Theorem
    196 -- 200Josef Hofbauer. 2/6 and Related Identities
    201 -- 0Amol J. Sasane. Problem 10924
    201 -- 202David Callan. Problem 10925
    201 -- 0Stephen B. Gray. Problem 10923
    201 -- 0David M. Bloom. Problem 10921
    201 -- 0Mizan R. Khan. Problem 10922
    202 -- 203Jean Anglesio, Reiner Martin. Continued Fractions for Some Quadratic Surds: 10773
    202 -- 0Harold G. Diamond. Problem 10926
    202 -- 0Jeffrey C. Lagarias, Eric M. Rains, Neil J. A. Sloane. Problem 10927
    203 -- 204Catalin Zara, Zachary Franco, T. S. Michael, Todor E. Milev. A High-Powered Fibonacci Identity: 10774
    204 -- 205Paul Bateman, Dennis Eichhorn, Robin Chapman. Grouping k-Tuples of Integers by the Sum of Their Squares: 10778
    205 -- 206Robin Chapman, M. A. Prasad. An Expression for Even-Indexed Bernuoulli Numbers: 10789
    206 -- 207Florian Luca, Nasha Komanda. A Number and Its Totient Are Not Amicable: 10793
    207 -- 208David S. Hough, Rodica Simion, Ali Ekber Gürel. Divisors of Generalized Catalan Numbers: 10794
    208 -- 0Calin Popescu, Roy Barbara, Omran Kouba. A Sum Related to Quadratic Residues: 10852

    Volume 109, Issue 10

    873 -- 889Amy Shell-Gellasch. Mina Rees and the Funding of the Mathematical Sciences
    890 -- 899Mark Levi. Minimal Perimeter Triangles
    900 -- 908Tom M. Apostol, Mamikon A. Mnatsakanian. Tangents and Subtangents Used to Calculate Areas
    909 -- 915Richard Jerrard, John E. Wetzel. Equilateral Triangles and Triangles
    916 -- 918Manuel Benito, J. Javier Escribano. An Easy Proof of Hurwitz's Theorem
    918 -- 920Joshua Evan Greene. A New Short Proof of Kneser's Conjecture
    921 -- 0Jean-Pierre Grivaux. Problem 10978
    921 -- 0Carl Axness. Problem 10977
    921 -- 0Donald P. Minassian. Problem 10979
    921 -- 0Ye Zhong Hao. Problem 10980
    922 -- 0Bogdan Suceava. Problem 10983
    922 -- 0Nicholas Singer. Problem 10981
    922 -- 0Yuming Chen. Problem 10982
    922 -- 923Beresford N. Parlett, Olaf Krafft, Martin Schaefer. The Largest Eigenvalue of a Positive Definite Symmetric Matrix: 10839
    923 -- 0Sung-Soo Kim, Charles Diminnie, Roger Zarnowski. Intermediate Value Functions: 10861
    924 -- 925Szilárd András, Michael Reid. Arithmetic Means and Geometric Means: 10907
    925 -- 926Wu Wei Chao, Richard Stong, Doyle Henderson. A Functional Equation: 10908
    926 -- 927Támás Kalmán, O. P. Lossers. Isodynamic Points of a Triangle: 10909
    927 -- 928Stevo Stevic, Rade Todorovic, Peter M. Jarvis. nx mod 1: 10910
    928 -- 0. Errata: 10950
    928 -- 0. Errata: 10953
    928 -- 0. Errata: 10948
    928 -- 0. Errata: Squashing a Matrix by Adding an Imaginary Part: 10776
    928 -- 0. Errata: Triperfect Numbers: 10800
    928 -- 0. Errata: An Expression for Even-Indexed Bernuoulli Numbers: 10789
    933 -- 943. Volume Information

    Volume 109, Issue 1

    1 -- 12Robert Almgren. Financial Derivatives and Partial Differential Equations
    13 -- 20Richard Evan Schwartz. Lucy and Lily: A Game of Geometry and Number Theory
    21 -- 36J. A. C. Weideman. Numerical Integration of Periodic Functions: A Few Examples
    37 -- 45Victor L. Shapiro. Harmonic Functions in the Unit Disk
    46 -- 63Sérgio B. Volchan. What Is a Random Sequence?
    64 -- 70Paolo Roselli, Michel Willem. A Convexity Inequality
    70 -- 72William C. Waterhouse. Quadratic Polynomials and Unique Factorization
    72 -- 74Cristina M. Ballantine, Joel L. Roberts. A Simple Proof of Rolle's Theorem for Finite Fields
    74 -- 76Thomas Sellke. Yet Another Proof of the Radon-Nikodým Theorem
    77 -- 0Giovanni Falcone. Problem 10914
    77 -- 0C. P. Rupert. Problem 10915
    77 -- 0Jürgen Groß, Götz Trenkler. Problem 10917
    77 -- 0Gertrude Ehrlich. Problem 10916
    77 -- 0Matthias Beck. Problem 10918
    77 -- 78Michael Becker. Problem 10919
    78 -- 79Ciprian Demeter, Li Zhou. Another Collinearity Result for Triangles: 10845
    78 -- 0Nick MacKinnon, Stephen M. Gagola Jr.. Fibonacci Twin Primes: 10844
    78 -- 0André Kündgen, Radhika Ramamurthi. Problem 10920
    79 -- 80Józef H. Przytycki, Richard Stong. Shrinking Lattice Curves: 10846
    80 -- 0Robin Chapman, Kimmo Eriksson, Richard P. Stanley, Reiner Martin. On the Number of Divisors of n in a Special Interval: 10847
    80 -- 81Kenneth Stolarsky, O. P. Lossers, et al.. A Characterization of a Quadratic Polynomial: 10848
    81 -- 82Richard Bagby, Michel Battaile. The Determinant of a Matrix of Sines: 10849
    82 -- 83Wolfdieter Lang, Saïd Amghibech. On a Matrix Obtained from the Catalan Generating Function: 10850
    83 -- 84Dragoslav S. Mitrinovic, Slavko Simic. Special Functions from Long Ago: 5626
    102 -- 0Bruce P. Palka. Editor's Endnotes
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