9.5 Analysis On the Sum of Two Periodic Functions, John M. H. Olmsted and Carl G. Townsend, 3:1, 1972, 33-38 The Quadratic Polynomial and Its Zeroes, C. A. Long, 3:2, 1972, 23-29, 5.1.5 On the Use of Functions, William E. Hartnett, 3:2, 1972, 25-28, 9.8 A Geometric Approach to the Orders of Infinity, Harold L. Schoen, 3:2, 1972, 74-76, C, 0.2 A Construction of the Real Numbers, E. A. Maier and David Maier, 4:1, 1973, 31-35 Riemann Integration in Ordered Fields, John M. Olmsted, 4:2, 1973, 34-40 A Further Note on the Orders of Infinity, Harold L. Schoen, 5:1, 1974, 80-81, C, 0.2 A Linear Integral Transform with a Simple Kernel, Walter W. Bolton and Sterling C. Crim, 6:1, 1975, 5-7 The Countability of the Rationals Revisited, Keith Gant and Dean B. Priest, 6:3, 1975, 41-42, C An Interesting Use of Generating Functions, Aron Pinker, 6:4, 1975, 39-45, 0.6, 5.4.2 Can the Complex Numbers Be Ordered?, Richard C. Weimer, 7:4, 1976, 10-12 Newton's Inequality and a Test for Imaginary Roots, Carl G. Wagner, 8:3, 1977, 145-147 Another Proof of the Arithmetic-Geometric Mean Inequality, Elmar Zemgalis, 10:2, 1979, 112-113, C The Generalized Arithmetic-Geometric Mean Inequality, David H. Anderson, 10:2, 1979, 113-114, C Testing a Graph's Symmetry, V. N. Murty, 10:2, 1979, 116-117, C A Note on the Cauchy-Schwartz Inequality, Jack C. Slay and J. L. Solomon, 10:4, 1979, 280-281, C A Rational Approximation to SQR(n), Carl P. McCarty, 11:2, 1980, 123-124, C Extending Bernoulli's Inequality, Ervin Y. Rodin, 11:2, 1980, 124-125, C Elementary Derivation of a Formula for Approximating n!, David H. Anderson, 11:3, 1980, 201-202, C A Quick Test for Rational Roots of a Polynomial, Leo Chosid, 11:3, 1980, 205-206, C, 0.7 How Close are the Riemann Sums to the Integral They Approximate?, V. N. Murty, 11:4, 1980, 268-270, C Altitudes ad Infinitum, Martin Berman, 11:5, 1980, 300-304 Uniqueness of Power Series Representations, Garfield C. Schmidt, 12:1, 1981, 54-56, C, 5.4.2 Applying Complex Arithmetic, Herbert L. Holden, 12:3, 1981, 190-194, 0.6, 5.3.1, 9.3 Corrections to an Earlier Capsule, Richard Johnsonbaugh, 12:3, 1981, 204-206, C A Note on Parallel Curves, Allan J. Kroopnick, 13:1, 1982, 59-61, C Continued Fractions and Iterative Processes, Jean H. Bevis and Jan L. Boal, 13:2, 1982, 122-127, 0.7 Still Another Proof of the Arithmetic-Geometric Mean Inequality, Norman Schaumberger, 13:2, 1982, 159-160, C Power Series for Practical Purposes, Ralph Boas, 13:3, 1982, 191-195, 5.4.2 A First Course in Continuous Simulation, Richard Bronson, 13:5, 1982, 300-310, 1.2 Products of Sets of Complex Numbers, Byron L. McAllister, 14:5, 1983, 390-397 Mean Inequalities, Frank Burk, 14:5, 1983, 431-434, C Convexity in Elementary Calculus: Some Geometric Equivalences, Victor A. Belfi, 15:1, 1984, 37-41 Income Tax Averaging and Convexity, Michael Henry and G. E. Trapp, Jr., 15:3, 1984, 253-255, 0.8, 5.1.5, 5.7.1 The Maximum and Minimum of Two Numbers Using the Quadratic Formula, Dan Kalman, 15:4, 1984, 329-330, C, 5.1.4 Income Averaging Can Increase Your Tax Liability, Gino T. Fala, 16:1, 1985, 53-55, C, 0.8 Picturing Functions of a Complex Variable, Bart Braden, 16:1, 1985, 63-73 Geometrically Asymptotic Curves, Dan Kalman, 16:3, 1985, 199-206, 5.1.5 Graphing the Complex Roots of a Quadratic Equation, Floyd Vest, 16:4, 1985, 257-261, 0.2, 0.7 On Hypocycloids and their Diameters, I. J. Schoenberg, 16:4, 1985, 262-267, 5.6.1 Relating Differentiability and Uniform Continuity, Irl C. Bivens and L. R. King, 16:4, 1985, 283, C Why is a Restaurant's Business Worse in the Owner's Eyes Than in the Customers'?, Wong Ngoi Ying, 18:4, 1987, 315-316, C Another Proof of the Inequality Between Power Means, Norman Schaumberger, 19:1, 1988, 56-58, C A General Form of the Arithmetic-Geometric Mean Inequality via the Mean Value Theorem, Norman Schaumberger, 19:2, 1988, 172-173, C, 5.1.2 Parameter-generated Loci of Critical Points of Polynomials, F. Alexander Norman, 19:3, 1988, 223-229, 0.7, 5.1.5 A Classroom Approach to Involutions, Joseph Wiener and Will Watkins, 19:3, 1988, 247-250, C Involutions and Problems Involving Perimeters and Area, Joseph Wiener and Henjin Chi and Hushang Poorkarimi, 19:3, 1988, 250-252, C, 9.3 A Discrete l'Hopital's Rule, Xun-Cheng Huang, 19:4, 1988, 321-329, 5.1.1 Random Walks on Z, Robert I. Jewett and Kenneth A. Ross, 19:4, 1988, 330-342, 7.2 Bounds on the Perimeter of an Ellipse via Minkowski Sums, Richard E. Pfiefer, 19:4, 1988, 348-350, C Equivalent Inequalities, Jim Howard and Joe Howard, 19:4, 1988, 350-352, C Looking at the Mandelbrot Set, Mark Bridger, 19:4, 1988, 353-363, 9.8 Codes that Detect and Correct Errors, Chester J. Salwach, 19:5, 1988, 402-416, 9.4 The Fundamental Periods of Sums of Periodic Functions, James Caveny and Warren Page, 20:1, 1989, 32-41, 0.6 Another Proof of Jensen's Inequality, Norman Schaumberger and Bert Kabak, 20:1, 1989, 57-58, C Graphing the Complex Zeros of Polynomials Using Modulus Surfaces, Clff Long and Thomas Hern, 20:2, 1989, 98-105, 0.7, 5.1.5 The Curious Fate of an Applied Problem, Alan H. Schoenfeld, 20:2, 1989, 115-123, 5.1.5, 8.3 Another Proof of Chebysheff's Inequality, Norman Schaumberger, 20:2, 1989, 141-142, C Subharmonic Series, Arthul C. Sogal, 20:3, 1989, 194-200, 5.4.2 Two Elementary Proofs of an Inequality (and 1 1/2 Better Ones), William C. Waterhouse, 20:3, 1989, 201-205 The Root Mean Square—Arithmetic Mean—Geometric Mean—Harmonic Mean Inequality, Roger B. Nelsen, 20:3, 1989, 231, C, 0.4 Evolution of the Function Concept: A Brief Survey, Israel Kleiner, 20:4, 1989, 282-300, 2.2 The AM-GM Inequality via x^(1/x), Norman Schaumberger, 20:4, 1989, 320, C Discrete Dirichlet Problems, Convex Coordinates, and a Random Walk on a Triangle, J. N. Boyd and P. N. Raychowdhury, 20:5, 1989, 385-392 FFF #9. The Countability of the Reals, Ed Barbeau, 20:5, 1989, 403, F, 9.1 FFF # 10. The Uncountability of the Plane, Ed Barbeau, 20:5, 1989, 403-404, F, 9.1 Power Series and Exponential Generating Functions, G. Ervynck and P. Igodt, 20:5, 1989, 411-415, C, 5.4.2 Generalizations of a Complex Number Identity, M. S. Klamkin and V. N. Murty, 20:5, 1989, 415-416, C A Generalization of the limit of [(n!)^(1/n)]/n = e^(-1), Norman Schaumberger, 20:5, 1989, 416-418, C, 5.1.1 FFF #15. Another Proof that 1 = 0, Ed Barbeau, 21:1, 1990, 36, F (also 21:2, 1990, 128) Ways of Looking at n!, Diane Johnson and Roy Dowling, 21:3, 1990, 219-220, C Harmonic, Geometric, Arithmetic, Root Mean Inequality, Sidney Kung, 21:3, 1990, 227, C, 0.4 Tabular Integration by Parts, David Horowitz, 21:4, 1990, 307-313, C, 5.2.5, 5.4.2 The Cauchy Integral Formula, David P. Kraines and Vivian Y. Kraines and David A. Smith, 21:4, 1990, 327-329, C A Chaotic Search for i, Gilbert Strang, 22:1, 1991, 3-12, 6.3, 5.1.3 FFF #29. A Simple Description of Sets of Reals, Ed Barbeau, 22:1, 1991, 39, F FFF #30. Is There a Nonmeasurable Set?, Ed Barbeau, 22:1, 1991, 39, F FFF #31. Is There a Nonmeasurable Set (Part 2)?, Ed Barbeau, 22:1, 1991, 40, F FFF #32. A Function Continuous only on the Rationals, Ed Barbeau, 22:1, 1991, 40, F (Also 23:3, 1992, 204) The Root-Finding Route to Chaos, Richard Parris, 22:1, 1991, 48-55, 6.3, 5.4.1 Fractals Illustrate the Mathematical Way of Thinking, Yves Nievergelt, 22:1, 1991, 60-64, C Sofware Review: Chaos and Fractal Software, Jonathan Choate, 22:1, 1991, 65-69, 6.3, 6.7 Another Proof of a Familiar Inequality, Norman Schaumberger, 22:3, 1991, 229-230, C FFF #51. The Converse to Euler's Theorem on Homogeneous Functions, Ed Barbeau, 23:1, 1992, 37-38, F FFF #52. An Application of the Cauchy-Schwartz Inequality, Ed Barbeau, 23:2, 1992, 142, F, 0.2 FFF #53. Opening the Floodgates, Ed Barbeau, 23:2, 1992, 142-143, F Weighted Means of Order r and Related Inequalities: An Elementary Approach, Francois Dubeau, 23:3, 1992, 211-213, C FFF. Surjective Functions, Ed Barbeau, 23:4, 1992, 305, F Inverse Problems and Torricelli's Law, C. W. Groetsch, 24:3, 1993, 210-217, 9.10 Local Conditions for Convexity and Upward Concavity, Donald Francis Young, 24:3, 1993, 224-228 Six Ways to Sum a Series, Dan Kalman, 24:5, 1993, 402-421, 5.4.3 Strictly Increasing Differentiable Functions, Massimo Furi and Mario Martelli, 25:2, 1994, 125-127 Approaches to the Formula for the nth Fibonacci Number, Russell Jay Hendel, 25:2, 1994, 139-142, C, 0.2, 4.5, 5.4.2, 9.3 The Chebyshev Inequality for Positive Monotone Sequences, Roger B. Nelsen, 25:3, 1994, 192, C Extending Bernoulli's Inequality, Ronald L. Persky, 25:3, 1994, 230, C, 0.2 An Optimization Oddity, R. H. Eddy and R. Fritsch, 25:3, 1994, 227-229, C, 5.1.4 Cutting Corners: A Four-gon Conclusion, S. C. Althoen and K. E. Schilling and M. F. Wyneken, 25:4, 1994, 266-279, 0.4, 0.5 Leibniz and the Spell of the Continuous, Hardy Grant, 25:4, 1994, 291-294, 2.2 A New Look at an Old Function, e to the i theta, J. G. Simmonds, 26:1, 1995, 6-10 Continuity on a Set, R. Bruce Crofoot, 26:1, 1995, 29-30 Can We See the Mandelbrot Set?, John Ewing, 26:2, 1995, 90-99, 6.3 FFF #88. A Consequence of the Nearness of Rationals to Reals, Mark Lynch, 26:3, 1995, 221, F (see also 28:4, 1997, 286-287) The Hyperbolic Number Plane, Garret Sobczyk, 26:4, 1995, 268-280, 0.7 More Mathematical Gems, Ross A. Honsberger, 26:4, 1995, 281-283, 9.3 The Mean of the Squares Exceeds the Square of the Means (Proof Without Words), Roger B. Nelsen, 26:5, 1995, 368, C Recursive Formulas for zeta(2k) and the Dirichlet function L(2k-1), Xuming Chen, 26:5, 1995, 372-376 A Complex Approach to the Laws of Sines and Cosines, William V. Grounds, 27:2, 1996, 108, C, 0.6 Why Polynomials Have Roots, Javier Gomez-Calderon and David M. Wells, 27:2, 1996, 90-94, 5.1.2, 5.7.1 A Terminally Discontinuous Function, James L. Hartman, 27:3, 1996, 211-212, C A Serendipitous Encounter with the Cantor Ternary Function, L. F. Martins and I. W. Rodrigues, 27:3, 1996, 193-198 FFF #107. All Complex Numbers Are Real, Walter Reno, 27:4, 1996, 283, F Dynamic Function Visualization, Mark Bridger, 27:5, 1996, 361-369, 5.1.5, 5.8 Countability via Bases Other Than 10, Pat Touhey, 27:5, 1996, 382-384, C When Is a Function's Inverse Equal to Its Reciprocal?, Robert Anschuetz II and H. Sherwood, 27:5, 1996, 388-393 An Application of Elementary Geometry in Functional Analysis, Ji Gao, 28:1, 1997, 39-42, 0.4 A Proof that Polynomials Have Roots, Uwe F. Mayer, 28:1, 1997, 58, C FFF #116. Life at Infinity and Beyond, Albert Eagle, 28:3, 1997, 198-199, F Exploiting a Factorization of x^n-y^n, Richard E. Bayne, James E. Joseph, Myung H. Kwack, and Thomas H. Lawson, 28:3, 1997, 206-209, C The World's Biggest Taco, David D. Bleecker and Lawrence J. Wallen, 29:1, 1998, 2-12, 5.2.7, 5.3.4 The Fundamental Theorem of Algebra, Michael D. Hirschhorn, 29:4, 1998, 276-277 Galileo’s Ratios (Proof Without Words), Alfinio Flores, 29:4, 1998, 300, C FFF #131. A New Identity for the Ceiling Function, Ed Barbeau, 29:4, 1998, 302, F Interval Arithmetic and Analysis, James Case, 30:2, 1999, 106-111, 0.1 From Euler to Fermat, Hidefumi Katsuura, 30:2, 1999, 118-119, 9.3 Continuous Versions of the (Dirichlet) Drawer Principle, Pawel Strzelecki, 30:3, 1999, 195-196 Computers and Advanced Mathematics in the Calculus Classroom, Kurt Cogswell, 30:3, 1999, 213-216, C, 5.2.9 FFF #154. How the factorial works, Norton Starr, 30:5, 1999, 385, F (see also Seymour Haber, 35:1, 2004, 42) FFF #155. Floored by an Olympiad problem, the editor, 30:5, 1999, 386, F Partially Differentiable, Yes; Continuous, No, David Calvis, 31:1, 2000, 42-47 AM ≥ GM (Mathematics Without Words), Norman Schaumberger, 31:1, 2000, 68, C A Child’s Garden of Fractional Derivatives, Thomas Osler and Marcia Kleinz, 31:2, 2000, 82-88 π is the Minimum Value for Pi, C. L. Adler and James Tanton, 31:2, 2000, 102-106 Linear Functions and Rounding, Jack E. Graver and Lawrence J. Lardy, 31:2, 2000, 132-136 FFF #157. Fourier Analysis is Trivial, Peter M. Jarvis, 31:3, 2000, 207, F A Variety of Triangle Inequalities, Herbert Bailey and Yanir Rubinstein, 31:5, 2000, 350-355, 9.7 Sequences of Chords and of Parabolic Segments Enclosing Proportional Areas, Timothy Feeman and Osvaldo Marrero, 31:5, 2000, 379-382, 5.2.6, 5.2.8 Tension in Generalized Geometric Sequences, Bill Goldbloom-Block, 32:1, 2001, 44-47 FFF #170. Strange dependence, Ollie Nanyes, 32:1, 2001, 49, F The Cantor Set Contains ¼? Really?, sarah-marie belcastro and Michael Green, 32:1, 2001, 55-56, C A Proof That Proves, A Proof That Explains, and A Proof That Works, Seannie Dar, Shay Gueron, and Oran Lang, 32:2, 2001, 115-117, F, 0.9 Algebraic Cantor Numbers?, Edwin Rosenberg, 32:3, 2001, 200, C Rational Approximations to Power Expansions, Maria Cecilia K. Aguilera-Navarro, Valdir C. Aguilera-Navarro, Ricardo C. Ferreira and Neuza Teramon, 32:4, 2001, 276-278, 5.4.3 FFF #178. Not Many Real Sets, Ed Barbeau, 32:5, 2001, 363, F FFF #179. A Wrong Version of Stirling’s Formula, Keith Brandt, 32:5, 2001, 363-365, F, 5.1.1 Cantor, 1/4, and its Family and Friends, Ioana Mihaila, 33:1, 2002, 21-23 FFF #184. Spreading the continuity, Russ Euler, 33:1, 2002, 39, F FFF #185. Integrating around a closed contour, Dale Buske, 33:1, 2002, 39-40, F Mixed Partial Derivatives and Fubini’s Theorem, Asuman Aksoy and Mario Martelli, 33:2, 2002, 126-130 Moving a Couch Around a Corner, Christopher Moretti, 33:3, 2002, 196-200, 5.1.4 FFF #195. Infectious continuity, Russ Euler and Jawad Sadek, 33:3, 2002, 227, F Comparing Sets of the Empty Set, Allen J. Schwenk, 33:3, 2002, 232-233, C, 9.1 Applications of Differentials, Li Feng, 33:4, 2002, 295, C, 5.1.3 When is 1/(a-b) = 1/a + 1/b, Anyway?, Eugene Boman and Frank Uhlig, 33:4, 2002, 296-300, 4.1 Cartoon: Justice Scores, John Schommer and Steve Campbell, 33:4, 2002, 331, C Irrationals in the Cantor Set, Edwin Rosenberg, 33:5, 2002, 394, C Investigating Possible Boundaries Between Convergence and Divergence, Frederick Hartmann and David Sprows, 33:5, 2002, 405-406, C, 5.4.2 Off on a Tangent, Russell A. Gordon and Brian C. Dietel, 34:1, 2003, 62-63, C, 5.1.3 Odd-like (Even-like) Functions on (a, b), Zhibo Chen, Peter Hammond and Lisa Hazinski, 34:1, 2003, 64-67, C, 5.2.9 Keyboard Inequalities, Monte Zerger, 34:1, 2003, 67, C, 0.2 FFF #204. An inequality, Ed Barbeau, 34:2, 2003, 134, F FFF #205. Another inequality, Michel Bataille, 34:2, 2003, 134-135, F On the Monotonicity of (1+1/n)^n and (1+1/n)^(n+1), Peter R. Mercer, 34:3, 2003, 236-238, C Generalizations of the Arithmetic-Geometric Mean Inequality and a Three Dimensional Puzzle, Hidefumi Katsuura, 34:4, 2003, 280-282 The Tangent Lines of a Conic Section, Daniel Wilkins, 34:4, 2003, 296-303, 0.5 For What Functions Is f-1(x) = 1/f(x)?, Sharon MacKendrick, 34:4, 2003, 304-311, 0.2 FFF #215. Consequences of an integral equality, Ed Barbeau, 34:4, 2003, 313, F, 5.2.9 FFF #217. A Riemann sum, Holly M. Hoover, 34:4, 2003, 314, F, 5.4.2 The Rationals are Countable – Euclid’s Proof, Jerzy Czyz and William Self, 34:5, 2003, 367-369 The HM-GM-AM-QM Inequalities, Philip Wagala Gwanyama, 35:1, 2004, 47-50, C, 5.7.1 Cauchy’s Mean Value Theorem Involving n Functions, Jingcheng Tong, 35:1, 2004, 50-51, C (see also Richard Beck, 35:5, 2004, 384) On the Values of Pi for Norms on R2, J. Duncan, Daniel H. Luecking, and C. M. McGregor, 35:2, 2004, 84-92 A Generalized Magic Trick from Fibonacci: Designer Decimals, Mrjorie Bicknell-Johnson, 35:2, 2004, 125-126, C, 0.1 Periodic Points for the Tent Function, David Sprows, 35:2, 2004, 133-135, C Almost Alternating Harmonic Series, Curtis Feist and Ramin Naimi, 35:3, 2004, 183-191, 5.4.2 The Rationals of the Cantor Set, Ioana Mihaila, 35:4, 2004, 251-255 Tangent Lines and the Inverse Function Differentiation Rule, Maurizio Trombetta, 35:4, 2004, 258-261, 5.1.3 The Taxicab distance is a metric (Proof Without Words), Angelo Segalla, 35:4, 2004, 261, C FFF #229. An Asian-Pacific inequality, Ed Barbeau, 35:5, 2004, 382-383, F Approaching ln x, James V. Peters, 36:2, 2005, 146-147, C, 5.3.2 An Elementary Proof of the Monotonicity of (1+1/n)^n and (1+1/n)^(n+1), Duane W. DeTemple, 36:2, 2005, 147-149, C, 5.3.2 Proofs Without Words: Galileo’s Ratios Revisited, Alfinio Flores, 36:3, 2005, 198, C, 5.4.1 If F(x) equals the integral from x to 2x of f(t) dt is Constant, Must f(t) = c/t?, Tian-Ziao He, Zachariah Sinkala, and Xiaoya Zha, 36:3, 2005, 199-204, 5.2.1 FFF #239. Big and little hyperplanes, Elliott Cohen, 36:4, 2005, 315, F Self-Integrating Polynomials, Jeffrey A. Graham, 36:4, 2005, 318-320, C, 5.2.1 A Paradoxical Paint Pail, Mark Lynch, 36:5, 2005, 402-404, C, 5.2.6, 5.2.7 A Two-Parameter Trigonometry Series, Xiang-Qian Chang, 36:5, 2005, 408-412, C, 9.3 Pythagoreas by the Cross Ratio, Rebecca M. Conley and John H. Jaroma, 37:1, 2006, 50-52, C A Card Trick and the Mathematics Behind It, Gabriela R. Sanchis, 37:2, 2006, 103-109, 9.2 From Chebyshev to Bernstein: A Tour of Polynomials Small and Large, Matthew Boelkins, Jennifer Miller, and Benjamin Vugteveen, 37:3, 2006, 194-204, 5.1.5 FFF #255. Maximum distance between circumference points, Evangelos N. Panagiotou, 37:4, 2006, 291-292, F Stirling’s formula via Riemann sums, R. B. Burckel, 37:4, 2006, 300-307, C FFF #256. Ptolemy’s inequality in space, Ed Barbeau, 37:5, 2006, 380-381, F FFF #265. The kinematics of jogging, Ralph Boas and Hanxiang Chen, 38:2, 2007, 133-134, F Newton’s Method and the Wada Property: A Graphical Approach, Michael Frame and Nial Neger, 38:3, 2007, 192-204, 6.3, 9.7 A Geometric View of Complex Trigonometric Functions, Richard Hammack, 38:3, 2007, 210-217, 0.6, 4.3 An Elementary Proof of an Oscillation Theorem for Differential Equations, Robert Gethner, 38:4, 2007, 301-303, C, 6.2 An Area Approach to the Second Derivative, Vania Mascioni, 38:5, 2007, 378-380, C, 5.1.3 The Convergence Behavior of fα(x) = (1 + 1/x)^(x + α), Cong X. Kang and Eunjeong Yi, 38:5, 2007, 385-387, C, 5.1.1, 5.3.2 FFF #273. A functional equation, Ed Barbeau, 39:1, 2008, 49-50, F The Pearson and Cauchy-Schwarz Inequalities, David Rose, 39:1, 2008, 64, C, 5.5, 7.3 FFF #279. A plausible inequality, Ed Barbeau, 39:3, 2008, 228, F From Mixed Angles to Infinitesimals, Jacques Bair and Valerie Henry, 39:3, 2008, 230-233, C, 9.7 Centaurs: Here, There, Everywhere!, Dimitri Dziabenko and Oleg Ivrii, 39:4, 2008, 267-272, 6.3, 9.3 FFF #283. A counterexample to Liouville’s Theorem, Mark Lynch, 39:4, 2008, 300, F Report from the Ambassador to Cida-2, Clifton Cunningham, 39:5, 2008, 337-345, 9.3 FFF #288. Maximizing a rational function, Ed Barbeau, 39:5, 2008, 385-386, F, 5.1.4