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How-to video on YouTube
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MORE Parametric Curve creations
summer 2017 - Continued explorations with my process for creating complicated parametric planar curves from just a single pair of non-piecewise equations. In addition to notching up the level of diffuculty, I also made a video explaining the process.
summer 2020 - Batman Reimagined article published in NCTM journal Mathematics Teacher: Learning & Teaching PK–12.
Single how-to video split up and reposted as this YouTube playlist of shorter videos.
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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 jump-discontinuity functions to incorporate multiple distinct pieces into a single equation pair.
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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.
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Grapher
Pics
(TI-83/84 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.
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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."
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Unit
Circle Angles
(Flash)
04Oct2010 - Program to help students identify
"special" angles on the x-y 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.
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Unit
Circle Practice
(Flash)
24May2010 - Program to help students practice
evaluating basic trigonometric expressions of angles on a unit circle
under time constraints.
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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.
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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
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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 specifically-defined tangent lines.
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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.
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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.
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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.
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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%.
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Conics
as bounded by tangent lines
(Geogebra)
14Jan2009 - Based an an old-time "string
art" activity, I stumbled upon some familiar shapes bounded by specifically-defined
tangent lines.
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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.
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Tangrams
(Geogebra)
30Nov2008 - An exercise in which I explored some
previously-unfamiliar features in Geogegra to make a computerized version
of the classic tangram puzzle.
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Programming
teaser
(Flash)
08Oct2008 - A
simple Flash animation made to familiarize students with some very basic
computer code.
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Cryptogame
(Flash)
10Aug2008 - Intended as a hangman-type 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.
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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.
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Letter
Arithmetic - Division
(Flash)
25Aug2004 - Follow-up to the multiplication version
of my first "Word Arithmetic" computer adaptation, involving
long division instead of multiplication.
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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 0-9, and the player
must correctly match them.
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