Re: TI-M: How's about something different?

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Re: TI-M: How's about something different?

Okay, I got one for ya.  This is what my research project last semester was
on:

There exist equations that, once fully graphed, will completely fill a two
dimensional plane.  Examples of these are Hilbert-type curves and Peano
Cures, and they are known as space filling curves in general.

basically, you take a line segment of some length, twist that line segment
around in two-dimensional space so much that it completely fills the two
dimensional space.

My question was:  What is the length of that line segment, and why?

The specific equations that I looked at I found in Tom Apostol's
Mathematical Analysis, Second Edition.  It is a common book, should be able
to find it in a good library.  It would take me several minutes to type out
the equations..  so I have attached a picture of the equations..

I know you can convert these equations for use on the TI92/89, by using the
mod, while, and sigma functions.  not so sure on other calculators..  Also,
you cannot do the summations from 1 to infinity, you can only do from 1 to..
probably 4 on the calculator.

Garth



----- Original Message -----
From: <Acidic113@aol.com>
To: <ti-math@lists.ticalc.org>
Sent: Monday, May 15, 2000 10:34 PM
Subject: Re: TI-M: How's about something different?


>
> you know.. I just subscribed about 2 hours ago and I too have noticed a
> couple of key details regarding this list.  Anyone can learn and apply
math..
> it is the universal language.  It is meant to be easy for intelligent
people.
>  How many of you can create math?  I like to read about these new
> experimental theorems; not everyone's "credentials".  I see the same thing
> happening that happens everytime I get a bunch of friends together to play
> AD&D; everyone starts to compete instead of practice teamwork.  I, for
one,
> want to ask for everyone's input.  I have searched tirelessly for an
> interesting mathematical study for the Intel science fair and I am pretty
> adamant about entering.  Does anyone have any suggestions?  I won't steal
> ideas; only tell me ideas that are not being used by yourself or others.
> Thanks
> -Ivan
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