Mathematical
Recreations
Mathematica Spoken Here
It would be fair to say that I enjoy math. Over the past few years, I have solved some interesting
problems, some of which I had been trying to solve for years. Now that I have a better understanding of
some of these problems, they appear here so that others can enjoy them (or
obsess over them, whatever the case may be).
The
Altitude of an Object in Three Dimensions: When I was younger, I used to launch
model rockets. I always wondered, “How
high did it really go.” Well, for years
I searched for a way to solve this problem, but it was not until I learned
about trigonometric functions that I finally was able to understand it. Here I present the question and give a brief
summary of the two formulas that I derived for its solution.
Interestingly,
I was able to derive two different formulas for the solution of this
problem. I immediately wanted to
compare their values to see if they would return different answers. As it turned out, they did return the same
results as long as the angle measurements were valid. My next problem was graphing these two solutions. They each involved five variables, but I was
able to replace one with a constant for the sake of graphing. However, this still required
four-dimensional graphing, a task that Excel did not handle well. Recently, however, I discovered Mathematica,
and I have used it to plot four dimensional (three spacial + one time) graphs
of each of these solutions.
Various
interesting graphs pertaining to various fields of investigation: Here I have a number of graphs, some animated,
that describe a variety of mathematical situations. Some are interesting because of the mathematics behind them; some
just look neat.
If you are
interested in the code for any of these images (in Mathematica) or a further
explanation of what they are or how they work, please contact me. If you do not have Mathematica, you may be
able to download a free program that can read Mathematica notebooks. You can reach me by e-mail at kayakbuilder2001@yahoo.com or on AIM as NBXL Kayaker.
Last Updated: Jan 22, 2003
