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Supplements to Articles in The College Mathematics Journal

2014

For "Locating Unimodular Roots" by Michael A. Brilleslyper and Lisbeth E. Schaubroeck, (May): This Mathematica notebook gives dynamic recreations of some results from the article and outlines explorations of additional related topics.

For "Integer Solutions to Box Optimization Programs" by Vincent Coll, Jeremy Davis, Martin Hall, Colton Magnant, James Stankewicz, and Hua Wang (May): The following Sage code generates rational solutions to the box problem described in the article. For more information, see stankewicz.net/optimization.html.

@interact
def _(n = 12):
    assert type(n) == Integer
    @interact(controls=[('m', slider(0,n,1,1))])
    def _(**kwargs):
        m = kwargs['m']
        var("x y")
        contour_plot.options["axes"]=True
        ell = implicit_plot(x^2 - x*y + y^2 ==1,(x,-2,2),(y,-2,2))
        pt1 = point((-1,0),pointsize=80,rgbcolor=(1,0,0))
        pt2 = point(((-(m/n)^2 + 1)/((m/n)^2 - (m/n) + 1),(-(m/n)^2 + 2*(m/n))/((m/n)^2 - (m/n) + 1)),pointsize=80,rgbcolor=(1,0,0))
        pt3 = point((0,(m/n)),pointsize=80,rgbcolor=(0,0,0))
        line = plot((m/n)*(x+1),(x,-2,2),color='green')
        show(ell + pt1 + line + pt2 + pt3)
        print "t = "+str(m/n)
        print "x = "+str(n^2 - m^2)
        print "y = "+str(2*m*n - m^2)
        print "z = "+str(m^2 - m*n + n^2)
        print "Roots = "+str((m*n - m^2)/2)+", "+str((2*n^2 + m*n - m^2)/6)

2013

For "Collaborative Understanding of Cyanobacterial Growth in Lake Ecosystems" by Meredith Greer, Holly A. Ewing, Kathryn L. Cottingham, and Kathleen C. Weathers (November) Data for Gloeo Modeling (xlsx).

For Kenneth Schilling's "Derivative Sign Patterns in Two Dimensions" (March) Web Addendum (pdf).

2012

For Timothy Jones' "Euler's Identity, Leibniz Tables and the Irrationality of Pi" (November): End Notes (pdf)

2011

For Stephen M. Walk's "The Intermediate Value Theorem is NOT Obvious—and I AM Going to Prove It to You" (September): Proofs Leading to the Intermediate Value Theorem (pdf)

For Michael A. Jones' "Chutes and Ladders for the Impatient" (January), MAPLE file.

2010

For Richard Kreminski's, "Taylor’s theorem: the elusive c is not so elusive" (May): Proofs of Theorems 2 and 3, plus other materials(pdf)

For Rick Mabry’s "The Hardest Straight-in Pool Shot" (January), proofs of all nine FACTS, written on napkins. Separate napkins (pdfs):

Facts 1-3
Fact 4
Fact 5
Fact 6
Fact 7
Fact 8
Fact 9

All the napkins in one wad: Facts 1-9

2009

For Barry Cox and Stan Wagon’s "Mechanical Circle-Squaring" (September, pp 238-247), Mathematica generated simulations:

Geneva Drive Maltese Cross
Drilling a Square Hole
Drilling a Square Hole (Three Dimensions)
Drilling a Hexagonal Hole

Dummy View - NOT TO BE DELETED