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 SquareArithmetic MeanGeometric MeanHarmonic 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
A Monte Carlo AM e 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
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