

Parametric Curve creations
summer 2015  Starting with an email request from a stranger, I set out to find a way to graph an entire design with just a single pair of parametric equations. The initial "jaw" logo utilized piecewise definitions, and even the second "jaw" logo used a different equation pair for each letter. Thereafter I used a variety of techniques and even included jumpdiscontinuity functions to incorporate multiple distinct pieces into a single equation pair.



Geogebra
Lesson Materials
(Geogebra)
2012  Click image to go to other site where
I compile some of the Geogebra
files that I use in my lessons for student use.



Grapher
Pics
(TI83/84 Graphing Calculators)
1Oct2011  After a "batman equation"
got some attention amongst nerdy circles this summer, I set out to create
my own images from mathematical functions/relations.



Parallel
Parking
(pencil/paper and Geogebra)
20Nov2010 update (25Dec2009
original)  After a mainstream news report on a British mathematician
who derived a formula for parallel parking, I attempt to improve upon
it following input and discussion with colleagues.
Updated
to include metric versions of the interactive animations, plus a variation
for "Perpendicular Parking."



Unit
Circle Angles
(Flash)
04Oct2010  Program to help students identify
"special" angles on the xy coordinate plane in both radian
and degree measure. This is intended as a precursor to the Unit Circle
Practice program I made back in May.



Unit
Circle Practice
(Flash)
24May2010  Program to help students practice
evaluating basic trigonometric expressions of angles on a unit circle
under time constraints.



Word
Arithmetic
(pencil/paper, Excel, Flash)
21May2010  27 custom versions of my favorite
childhood math game which I regularly solved in Dell puzzle magazines.
Also see "Letter Arithmetic" programs listed below.



Right
Triangles for which P = A
(pencil/paper)
06Jan2010  For the past two decades my mind
has continually returned to an AIME
contest problem which asked: How many right triangles exist for which
the perimeter in linear units is equal to the area in square units. I
had found an algebraic solution long ago, but recently at a faculty meeting
I started trying to find other ways to solve this problem from my youth,
preferably utilizing different branches of math (algebraic, trigonometric,
graphical,…). Here are the results. In short time I had five different
solutions, reminding me of the beautiful interconnectedness of math by
which many different paths from a single problems still lead to a shared
solution.
 Click
image for PDF with full explanation and solutions



Cycloids
as bounded by tangent lines
(Geogebra)
28May2009  While cycloids are typically defined
by polar equations, this exploration demonstrates them to be areas bounded
by specificallydefined tangent lines.



Mathematical
face
(Geogebra)
03Mar2009  For reasons that I've since forgotten,
I became compelled one day to see how well I could draw a face as a family
of functions in which a single parameter is varied for a set of equations.



Sine
cradle
(Geogebra)
26Feb2009  Based on an extra credit problem
I made up several years ago in which students were challenged to come
up with a function whose graph is "cradled" by the basic sine
wave. In this exploration, one such function graph is altered by varying
a single parameter.



Cycloids
& Trochoids as traced by a point on a rolling wheel
(Geogebra)
26Feb2009  After a student asked me a "what
if" question about a circle rolling around another circle, I launched
into my own exploration into the types of shapes that can be formed by
such a construction.



Buffon's
Needle
(Flash)
15Feb2009  Created after
seeing a Calculus exercise concerning the mathematics behind Buffon's
Needle experiment. In this experiment, the probability that a needle dropped
randomly on a planar surface containing parallel lines (spaced one needle
length apart) will touch a line is found to be 2/pi, or about 63.66%.



Conics
as bounded by tangent lines
(Geogebra)
14Jan2009  Based an an oldtime "string
art" activity, I stumbled upon some familiar shapes bounded by specificallydefined
tangent lines.



Rational
Functions
(Geogebra)
12Jan2009  While using Geogebra in my Calculus
class to demonstrate how horizontal, vertical, and slant asymptotes are
determined by the parameters in a rational function, I inadvertently came
across some interesting shapes.



Tangrams
(Geogebra)
30Nov2008  An exercise in which I explored some
previouslyunfamiliar features in Geogegra to make a computerized version
of the classic tangram puzzle.



Programming
teaser
(Flash)
08Oct2008  A
simple Flash animation made to familiarize students with some very basic
computer code.



Cryptogame
(Flash)
10Aug2008  Intended as a hangmantype game in
which students would try to figure out words or phrases from the day's
lesson, the interface turned out to be too clunky for me to use in class.
A useful programming exercise for me nonetheless.



Math
Dice Game
(Flash)
18Aug2007  Computerized version of a dice game
I used to play as a kid. The numbers on the white dice are to be used
in a mathematical expression that equals the sum of the two black dice.



Letter
Arithmetic  Division
(Flash)
25Aug2004  Followup to the multiplication version
of my first "Word Arithmetic" computer adaptation, involving
long division instead of multiplication.



Letter
Arithmetic  Multiplication
(Flash)
12Sep2003  My ambitious first venture into Flash
programming. Based on "Word Arithmetic," which were my favorites
in the Dell puzzle magazines I used to buy as a kid. Each letter in the
multiplication problem is randomly matched to a digit 09, and the player
must correctly match them.
