0.2 		Algebra

Mathematics, A Solitary Game, Olof Hanner, 1:2, 1970, 5-16, 4.1
Gog and Gug, Howard W. Eves, 1:1, 1970, 8, C
The Irrationality of Certain Numbers, Peter A. Lindstrom, 1:1, 1970, 30-31, 9.3
A Computer-Oriented Multiplication Algorithm, John Peterson, 1:2, 1970, 106, C
A Geometric Approach to the Orders of Infinity, Harold L. Schoen, 3:2, 1972, 74-76, C, 9.5
Pascal's k-Simplex, Dale Woods and Mary Jane Kohlenberg, 4:3, 1973, 38-43
Teaching Inequalities Involving Absolute Values, Frances W. Lewis, 4:2, 1973, 87-90, C
Maximize x(a-x), L. H. Lange, 5:1, 1974, 22-24, 0.7, 5.1.4
A Geometric Approach to Linear Programming in the Two-Year College, Pat Semmes, 5:1, 1974, 37-40, 9.10
A Further Note on the Orders of Infinity, Harold L. Schoen, 5:1, 1974, 80-81, C, 9.5
Investigations of Linear and Reciprocal Functions by the Line-to-Line Technique, David R. Duncan and Bonnie H. Litwiller, 6:2, 1975, 2-7, 0.7
Distributivity with Respect to All Four Rational Operations, Myles Greene, 6:2, 1975, 10-12
Mathematical Induction: If Student k Understands It, Will Student K + 1?, Judith L. Gersting, 6:2, 1975, 18-20, 0.9
Easter Revisited, Daniel T. Bleck, 6:3, 1975, 38-40
Functional NotationÑAn Intuitive Approach, Ann D. Holley, 7:3, 1976, 14-15, 1.2
Finding Super Accurate Integers, Pasquale Scopelliti and Herbert Peebles, 7:3, 1976, 52-54, 0.7, 9.6
Mathematics and Computing without Computers, William S. Dorn, 8:2, 1977, 101-105
The Perfect Curve: at Least for Grades, Lawrence Sher, 8:3, 1977, 148-152
Operational and Intuitive Algebra, Betsey Whitman and Donald Cook, 8:3, 1977, 155-161
Stirling's Triangle of the First Kind-Absolute Value Style, Hugh Ouellette and Gordon Bennett, 8:4, 1977, 195-202, 6.3
An Elementary Construction of the Common Log Tables, James H. Jordan, 8:5, 1977, 274-278
Fractions Without Quotients: Arithmetic of Repeating Decimals, Richard Plagge, 9:1, 1978, 11-15
Applicable Mathematics in Two Year Colleges, Ralph Mansfield, 9:3, 1978, 148-153
Completing the SquareÐA Laboratory Approach, Charles G. Moore, 9:4, 1978, 215-218
Stirling's Numbers of the Second KindÑProgramming Pascal's and Stirling's Triangles, Satish K. Janardan and Konanur G. Janardan, 9:4, 1978, 243-248, 6.3
Some Pre-Calculus Algebra, John Staib, 10:2, 1979, 89-95
The Discovery of a Generalization: An Example in Problem Solving, Hugh Ouellette and Gordon Bennett, 10:2, 1979, 100-106, 0.3
Polygonal Roots, Barnabas B. Hughes, 10:5, 1979, 313-318, 0.7
Distance from a Point to a Line, Warren B. Gordon, 10:5, 1979, 348-349, C
A Technique for Determining When a General Quadratic Expression is Factorable, Leo Chosid, 10:5, 1979, 354-355, C, 0.7
Luddhar's Method of Solving a Cubic Equation with a Rational Root, R. S. Luthar, 11:2, 1980, 107-110, 0.7
Computer Solution of Alphametics, Sarah Brooks, 11:2, 1980, 111-114
Why Not Teach Synthetic Multiplication?, Kenneth R. Kundert, 11:2, 1980, 121-122, C
A Precalculus Approximation of n!, Norman Schaumberger, 11:3, 1980, 202-204, C, 5.4.2
An Error-Detecting Check by Substitution, Charles G. Moore, 11:5, 1980, 326-327, C
A "Proof" that M=N, W. Thurmon Whitley, 12:3, 1981, 211, C
Inventor's Paradox, Man-Keung Siu, 12:4, 1981, 267, C
Misguided Mathematical Maxim-Makers, Betsy Darken Smith, 12:5, 1981, 309-316, 1.2
A Classroom Approach to Pythagorean Triples, Norman Schaumberger, 13:1, 1982, 61-62, C
Selection of a Fair Currency Exchange Rate, Allen J. Schwenk, 13:2, 1982, 154-155, C, 0.8
An Alternate Method for Solving Radical Equations, Bill Bompart, 13:3, 1982, 198-199, C
The Thrills of Abstraction, P. R. Halmos, 13:4, 1982, 243, 1.2
Isomorphisms on Magic Squares, Ali R. Amir-Moez, 14:1, 1983, 48-51, 5.4.1, 9.2, 9.3, 9.4
A Logarithm Algorithm for Four-Function Calculators, David Cusick, 14:4, 1983, 322, 5.3.2
The Address Problem, Michael Tennor, 14:5, 1983, 407-414, 9.3
Approximation of Square Roots, Leon Wejntrob, 14:5, 1983, 427-430, 0.7, 9.6
Antisubmarine Warfare: Passive vs. Active Sonar, L. Whitt and K. Wilk, 14:5, 1983, 434-435, C
Is the Venn Diagram Good Enough?, Mou-Liang Kung and George C. Harrison, 15:1, 1984, 48-50, 9.1
A Geometrical Interpretation of the Weighted Mean, Larry Hoehn, 15:2, 1984, 135-139, 0.4, 7.3
On Problems with Solutions Attainable in More Than One Way, Jean Pedersen and George Polya, 15:3, 1984, 218-228, 0.4, 5.4.2
Complex Roots Made Visible, Alec Norton and Benjamin Lotto, 15:3, 1984, 248-249, C, 0.7
Pythagorean Systems of Numbers, Joseph Wiener, 15:4, 1984, 324-326, C, 0.4, 9.3
An Approach to Problem-Solving Using Equivalence Classes Modulo n, James E. Schultz and William F. Burger, 15:5, 1984, 401-405, 9.3
The Factorial Triangle and Polynomial Sequences, Steven Schwartzman, 15:5, 1984, 424-426, C, 5.4.1, 6.3
Right Triangles with Perimeter and Area Equal, William Parsons, 15:5, 1984, 429, C, 0.4
What Do I Know? A Study of Mathematical Self-Awareness, Philip J. Davis, 16:1, 1985, 22-41, 9.3
Nested Polynomials and Efficient Exponential Algorithms for Calculators, Dan Kalman and Warren Page, 16:1, 1985, 57-60, C, 0.7, 9.6
Behold! The Arithmetic-Geometric Mean Inequality, Roland H. Eddy, 16:3, 1985, 208, C, 0.3
Instances of Simpson's Paradox, Thomas R. Knapp, 16:3, 1985, 209-211, C, 7.3
Approximating Solutions for Exponential Equations, Norman Schaumberger, 16:3, 1985, 211-212, C
Graphing the Complex Roots of a Quadratic Equation, Floyd Vest, 16:4, 1985, 257-261, C , 0.7, 9.5
A New Divisibility Algorithm, Joseph Whittaker, 16:4, 1985, 268-276, 9.3
A Discrete Look at 1 + 2 + ... + n, Loren C. Larson, 16:5, 1985, 369-382, 0.9, 3.1, 3.2, 5.4.2, 6.3
Routine Problems, Sherman Stein, 16:5, 1985, 383-385, 5.1.5, 1.2
A Babylonian Geometrical Algebra, James K. Bidwell, 17:1, 1986, 22-31, 0.3
Irrationality Made Easy, Robert Bumcrot, 17:3, 1986, 243-244, C
The Change of Base Formula for Logarithms, Chris Freiling, 17:5, 1986, 413, C, 5.3.2
A Guide to Computer Algebra Systems, John M. Hosack, 17:5, 1986, 434-441, 4.1, 5.1.2, 5.1.5, 5.2.3, 5.2.4, 5.2.5
Behold! The Graphs of f and f inverse are Reflections about the Line y=x, Ayoub B. Ayoub, 18:1, 1987, 52, C, 5.3.2
Powers and Roots by Recursion, Joseph F. Aieta, 18:5, 1987, 411-416, 0.7, 6.3
FFF #1. The Zero Function, Ed Barbeau, 20:1, 1989, 49-50, F (also 20:2, 1989, 133)
FFF #5.  A Howler about Products of Logarithms, Ed Barbeau, 20:3, 1989, 226, F (also 20:4, 1989, 318 and 21:3, 1990, 218)
FFF #7. An Exponential Equation, Ed Barbeau, 20:4, 1989, 317, F (also 20:5, 1989, 404)
Quick Function Evaluation, Daniel S. Yates, 21:1, 1990, 51, C, 5.1.5
FFF #25. Solving an Inequality, Ed Barbeau, 21:4, 1990, 303, F
Geometrical and Graphical Solutions of Quadratic Equations, E. John Hornsby, Jr., 21:5, 1990, 362-369, 0.4
China's 1989 National College Entrance Examination, Bart Braden, 21:5, 1990, 390-393, 0.4, 0.6, 1.2
FFF #38. How to Solve a Quadratic Equation, Ed Barbeau, 22:2, 1991, 132, F (also 24:4, 1993, 345 and 25:4, 1994, 310)
FFF #39. The End Justifies the Mean, Ed Barbeau, 22:3, 1991, 220, F
FFF #40. Perron's Paradox, Ed Barbeau, 22:3, 1991, 221, F, 9.1 (also 23:3, 1992, 205 and 24:3, 1993, 231)
FFF #42. A Characterization of Finite Geometric Sequences, Ed Barbeau, 22:3, 1991, 221, F
Positivity from Evaluation of a Single Point, Henry Mark Smith, 22:3, 1991, 230-231, C, 5.1.5
FFF #46. A Straightforward Cancellation, Ed Barbeau, 22:5, 1991, 403-404, F, 3.2
FFF #49. Two Transcendental Equations, Ed Barbeau, 23:1, 1992, 36, F, 5.3.2
FFF #52. An Application of the Cauchy-Schwartz Inequality, Ed Barbeau, 23:2, 1992, 142, F, 9.5
Infinitely Many Different Quartic Polynomial Curves, Nitsa Movshovitz-Hader and Alla Shmukler, 23:3, 1992, 186-195, 0.7
The Joy of Mathematics: A Mary P. Dolciani Lecture, Peter Hilton, 23:4, 1992, 274-281, 1.2
A Serendipitous Application of the Pythagorean Triplets, Susan Forman, 23:4, 1992, 312-314, C, 9.3
Commutativity of Polynomials, Shmuel Avital and Edward Barbeau, 23:5, 1992, 386-395, 6.3, 0.7
FFF. Matrices and the TI-81 Graphics Calculator, Constance J. Gardner, 24:1, 1993, 64, F, 4.1
FFF #58. A Rational Combination of Two Transcendentals, Ed Barbeau, 24:3, 1993, 229, F, 5.3.2
FFF #59. A Formula that Works Only for n=1, Ed Barbeau, 24:3, 1993, 229-230, F, 0.9
FFF #60. A Two-Valued Function, Ed Barbeau, 24:3, 1993, 230, F, 5.3.2
FFF #65. Solving a Cubic, Ed Barbeau, 24:4, 1993, 344, F, 0.7 (also 25:4, 1994, 311)
FFF #67. A Superficial Volume Problem, Randall K. Campbell-Wright, 25:1, 1994, 35, F
FFF #70. Reading a Calculator Display, Sandra Z. Keith, 25:1, 1994, 36, F, 5.1.3
Approaches to the Formula for the nth Fibonacci Number, Russell Jay Hendel, 25:2, 1994, 139-142, C, 4.5, 5.4.2, 9.3, 9.5
Extending Bernoulli's Inequality, Ronald L. Persky, 25:3, 1994, 230, C, 9.5
FFF #84. A Method for Solving a Cubic Equation, Ed Barbeau, 26:1, 1995, 35-36, F, 0.7
FFF #86. Watch Your Ears!, Bruce Yoshiwara, 26:1, 1995, 36, F
FFF #87. Do You Know How to Split the Atom?, Milt Eisner, 26:1, 1995, 37, F
The Product of Four (Positive) Numbers in Arithmetic Progression is Always the Difference of Two Squares (Proof Without Words), Roger B. Nelsen, 26:2, 1995, 131, C
A Geometric Approach to Linear Functions, Jack E. Graver, 26:5, 1995, 389-394, C, 0.4, 6.3
FFF #97. A Surd Equation, Ed Barbeau, 27:1, 1996, 45, F (see also 27:3, 1996, 204-205)
FFF #105. The Remainder Theorem, Richard Laatsch, 27:4, 1996, 282, F, 9.4
FFF #113. The Disappearing Solution, Ed Barbeau, 28:2, 1997, 120, F  (see also 30:1, 1999, 40-43, 30:2, 1999, 132, 30:4, 1999, 307)
FFF #120. A Quick (?) Proof of Irrationality, Richard Askey, 28:4, 1997, 286, F
Visualizing the Complex Roots of Quadratics (Proof Without Words), Shaun Pieper, 28:5, 1997, 359, C, 0.7
FFF #124. The Number of Tickets Sold, Robert W. Vallin, 29:1, 1998, 34-35, F
FFF.  Distributing Addition over Multiplication, S. R. S. Sastry, 29:3, 1998, 221, F
FFF #136. Surprising Symmetry, David Wells, 29:5, 1998, 407, F
FFF #137.  Drenching a sphere, David Cantrell, 30:1, 1999, 39, F
Multiplying and Dividing Polynomials Using Geloxia, Jeff Suzuki, 30:1, 1999, 50-53, C
The Trinomial Triangle, James Chappell and Thomas Osler, 30:2, 1999, 141-142, C, 3.2
An Identity for n(n+1)(n+2)(n+3)+1, Alfinio Flores, 30:3, 1999, 247, C
FFF #148.  An exponential mess, Eric Chander, 30:4, 1999, 306, F
FFF.  Mathematical oxymorons, Richard Francis, 30:4, 1999, 308, F
Things I Have Learned at the AP Reading, Dan Kennedy, 30:5, 1999, 346-355, 5.1.1, 5.1.2, 5.2.1, 5.2.6, 5.4.2, 6.1
a^2+b^2 ³ 2ab (Mathematics Without Words), Alfinio Flores, 31:2, 2000, 106, C
FFF #156. An Imaginary Absolute Value?, Peter M. Jarvis and Paul S. Shuette, 31:3, 2000, 207, F
Binomials to Binomials, Thomas Osler, 31:3, 2000, 211-212, C, 6.3
Colin MaclaurinÕs Quaint Word Problems, Bruce Hedman, 31:4, 2000, 286-289
Tangents without Calculus, Jorge Aarao, 31:5, 2000, 406-407, C, 0.7, 5.1.3
a^3 + b^3 >= a^2*b + ab^2 (Mathematics Without Words), Norman Schaumberger, 32:1, 2001, 38, C
FFF #169. Strengthening a theorem on linear fractional transformations, Peter M. Jarvis, 32:1, 2001, 49, F
Linear Relations Between Powers of Terms in Arithmetic Progression, Calvin Long and Boyd Henry, 32:2, 2001, 135-137, C, 3.2
Factoring Quadratics, Stephen Kaczkowski, 32:3, 2001, 203-204, C
There Are No New Word Problems, Charles Marion, 32:3, 2001, 238-239, C
Another Look at Factoring Polynomials, Scott J. Beslin and Douglas J. Baney, 32:4, 2001, 273-275, 9.4
FFF #181. Finding Asymptotes, Carl Libis, 32:5, 2001, 366, F, 5.1.5
FFF #183. Dimensions of a yard, a student, 33:1, 2002, 39, F
FFF #186. The illegal moves method for quadratics, John C. and Holly M. Hoover, 33:1, 2002, 40, F
FFF #187. Cancelling exponents, Ross Honsberger, 33:1, 2002, 41, F
Solutions to x+y=xy (Mathematics Without Words), Roger Nelsen, 33:2, 2002, 130, C, 0.6
FFF #188. An appeal to symmetry, a student, 33:2, 2002, 137, F
Sums of Roots and Poles of Rational Functions, Paul Deiermann, 33:2, 2002, 148-149, C
What is This? F(g(hung)) = hung in effigy, Marvin Johnson, 33:3, 2002, 225, C
The Roots of a Quadratic, Leonard Gillman, 33:3, 2002, 237-238, C, 0.7
FFF #198. An answer hard to get at, Li Zhou, 33:4, 2002, 310, F
The Exponential Formula, the Editor, 33:4, 2002, 349, C
Lewis CarrollÕs Amazing Number-Guessing Game, Richard F. McCoart, 33:5, 2002, 378-383, 9.2
Quadratic and Exponential Formulas, David Marcus, 34:1, 2003, 49, C
FFF #201. Solution of a rational equation, Carl Libis, 34:1, 2003, 50-51, F
FFF #203. Toothpicks, Elaine Simmt, 34:1, 2003, 52, F
FFF. Factoring quadratics, Ed Barbeau, 34:1, 2003, 53, F
Keyboard Inequalities, Monte Zerger, 34:1, 2003, 67, C, 9.5
How (Not) to Solve Quadratic Equations, Yves Nievergelt, 34:2, 2003, 90-104, 9.6
Clarifying Compositions with Cobwebs, Nial Neger and Michael Frame, 34:3, 2003, 196-204, 6.3
FFF #210. Summing squares by averages, Shailesh Shirali, 34:3, 2003, 224, F
FFF #211. A surd equation, Carl Libis, 34:3, 2003, 225, F
FFF #212. ab^k = (ab)^k, Carl Libis and Parviz Khalili, 34:3, 2003, 225, F
For What Functions Is f-1(x) = 1/f(x)?, Sharon MacKendrick, 34:4, 2003, 304-311, 9.5
The Band Around a (non)Convex Set, Jack Stewart and Annalisa Crannell, 34:5, 2003, 377-379, 0.7, 9.4
A Rational Root Theorem for Imaginary Roots, Sharon Barrs, James Braselton, and Lorraine Braselton, 34:5, 2003, 380-382, 0.7, 9.4
When Equalities Are Not Equal: Missing Mathematical Precision in Teaching, Texts, and Technology, Michael J. Bosse and N. R. Nandakumar, 34:5, 2003, 383-389
Finding the Tangent to a Conic Section Without Calculus, Sidney H. Kung, 34:5, 2003, 394-395, C, 5.1.3
An Inverse, Ted Ridgway, 35:2, 2004, 104, C
HeronÕs Area Formula: What About a Tetrahedron?, Reuben Hersh, 35:2, 2004, 112-114, 0.4, 9.7
The root mean square of a and b (Mathematics Without Words), Ruma Falk, 35:3, 2004, 170, C
FFF #224. The square root of -1 is real, Teik-Cheng Lim, 35:3, 2004, 214, F
FFF #225. Extraneous roots, Ed Barbeau, 35:3, 2004, 214-215, F
FFF #227. Who needs exponents?, Carl Libis, 35:4, 2004, 297-298, F
Algebra in Respiratory Care, David F. Snyder, 35:4, 2004, 300-302, C, 9.10
Introducing the Sums of Powers, Jeff A. Suzuki, 35:4, 2004, 303-304, C
FFF #228. An exponential equation, Ed Barbeau, 35:5, 2004, 382, F, 5.3.2
Discovering Roots: Ancient, Medieval, and Serendipitous, Bryan Dorner, 36:1, 2005, 35-43, 2.1, 4.5, 9.3
A Perplexing Polynomial Puzzle, I. B. Keene, 36:2, 2005, 100, C
FFF #235. A lot of values, Ed Barbeau, 36:2, 2005, 141-142, F
Roots of Integers, Revisited, Andrea Rothbart, 36:4, 2005, 317, C   (see also 36:1, 56)
Truck Drivers, a Straw, and Two Glasses of Water, Kevin Iga and Kendra Kilpatrick, 37:2, 2006, 82-92, 6.3
FFF. BEDMAS, Jack Weiner, 37:2, 2006, 123-124, F
FFF #258. Right on target!, Larry Braden, 37:5, 2006, 381-383, F
FFF #260. Increasing a square to a square, Chris Fisher, 38:1, 2007, 43, F, 9.3
FFF #263. Reciprocating for success, M. A. Khan, 38:2, 2007, 131-132, F
Quirky Quadratics, Christopher S. Withers and Saralees Nadarajah, 38:3, 2007, 178, C, 0.7
Teaching Tip: A Function is a Bow, Salvatore Anastasio, 38:3, 2007, 184, C
FFF #266. The escaped criminal, Ed Barbeau, 38:3, 2007, 218, F
FFF #268. An algebra problem, anonymous, 38:3, 2007, 220, F
FFF. An ÒArtificeÓ of Hall and Knight, John Webb, 38:4, 2007, 297-299, F
FFF #269. ÒVery funny, PeterÓ, Ed Barbeau, 38:5, 2007, 375, F
FFF #275. More striking results, Peter Schumer and Michael A. Jones, 39:1, 2008, 50, F, 5.1.1
Quote: Math as Metaphor, Ayaan Hirsi Ali, 39:4, 2008, 300, C
Missteps in Mathematics Books, Jerome Dancis, 39:5, 2008, 280-382, F, 0.1
FFF #287. Logging the solutions of an equation, Ed Barbeau, 39:5, 2008, 383-384, F, 5.3.2
Sam LoydÕs Courier Problem with Diophantus, Pythagoras, and Martin Gardner, Owen OÕShea, 39:5, 2008, 387-391, C, 0.7, 9.2