I started off making a simple spirograph emulator for my 14 year old
daughter (nickname: Shazza) and its grown into a monster called
ShazzagraphUltra. It creates beautiful and extremely cool effects by doing
things that you could never do with a physical spirograph using virtual
pens.
Its also very mathematical, at a number of levels. Most obviously, the
number of loops that are required to complete each pattern is a function
of
the greatest common divisor (gcd) of the relative diameters of the circles
-
interesting to get students studying basic number theory to see if they
can
work out exactly what it is ...
The sequence in which the "lobes" are drawn shows some basic group theory
....
There are square shazzagraphs as well as circular ones. This raises some
practical problems, seeing as how pi is irrational, so the patterns would
never finish. Nor is it (quite) as simple as scaling the square's
dimension
by pi, due to what happens in the corners - I had to use a simple linear
transform. Can anybody identify the justification for using the transform
that I did?
And then there is the whole epicycloid thing and parametric equations - a
bit of a diversion in a Calc I class.
It uses the Microsoft .Net framework (which is auto-installed in the
unlikely event its not already on your PC), and is an 800k download. I
haven't bought a digital certificate for it (about $1000 I think) so you
will get a warning on install, but I wrote every line of code in it, and
it
downloads direct from my ISP account held in the same name as I have been
posting to all of these mathematics news groups for over 10 years. Also, I
can prove my daughter's nickname is Shazza.
Here it is:
http://www.members.optusnet.com.au/webbfamily/shazzaUltra/publish
or
http://tinyurl.com/2oyjxp
Can also be enjoyed with Pink Floyd and the lights down low ...
Peter Webb
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