This summer, I had the opportunity to work with Dr. Velez writing a paper on the relationship between the unit circle and the familiar sinusoidal graph that we all know. This paper was written for the Mathematics Teacher.
This paper demonstrated the relationship between the unit circle and the familiar sinusoidal graph through physical means. There are four experiments detailed in this paper and all deal with a “sinusoid-generating machine.” This machine is simply disk or an arm with a post at one end for the attachment of various items. This machine is human powered. That is, it does not have a motor in it to ensure a constant rotation. This is done so that the student has more of an attachment to the experiment itself.
The first and second experiments are simply experiments which have the student move with this rotating machine in order to get the idea of periodicity. The first one, the student is to grab onto the post for attachments and allow her hand to be moved along with the post. The second experiment is for the student to walk with the body touching the post as the machine rotates. This is done to show that sinusoids only one of the x and y coordinates. These unfortunately do not produce any results that we can show, or work with. Only results that they can feel.
The third and fourth experiments record data. The third experiment attaches a water-dripping device to the machine in order to record a sinusoid on a piece of paper. The fourth experiment records sinusoidal data onto the TI calculators via the CBL unit.
During this internship, I learned a great deal about writing mathematical papers, and about the TI calculator itself. Writing mathematical texts are very different than the writing that is done in most English classes due to the exactness that mathematic papers require. It seems that while you may have a simple and elegant idea, there are some small ideas that need explaining. Explaining all of this sometimes drowns out the simple elegant idea that you started out with.
I also learned a learned a great deal about the TI calculators because I had to do a large amount of programming for this paper. I have found that while the programming language that the TI uses is much simpler to write, the trouble-shooting aspect of writing on the calculators can become much more frustrating. Despite this, I feel much more confidant using these calculators now.