The Boney Blog of Nowhere.

Math 1060 -- Trigonometry

Instructor: Zeph Smith 

 During this course, I came to learn a lot about visual elements in mathematics. I had always struggled to understand these concepts. I always made my way through those portions of classes, but I couldn't really explain any of it to anybody until now. 

This project was used to tie the information we were learning to processes found in the real world. Strangely, I found it very difficult to complete properly, even though I was doing perfectly fine with my classwork up to that point. As soon as it became something more tangible, I struggled with it a little bit. I think this will come in handy when I am teaching because I can illustrate both how things are used in the real world, but also how conceptual mathematics can be much easier than applied mathematics. But that might just be me since it's the one I'm more passionate about.  Either way, Mass-Spring Systems are commonplace in today's society.  A simple backyard trampoline or even a little exercise one "spring" to mind. (No need to hiss). Generally, the size of the trampoline and the recommended weight limit will determine how stiff the springs can be, and therefore how far they can stretch safely without allowing you to smack into the ground, or be thrown off by the recoil.  Another example is original household scale used either in the bathroom for weighing yourself, or in the kitchen for weighing your food. Either way, in these scales (not the electric scales, mind you) the weighing pan (also called a scale, funnily enough) is set atop a spring or spring system which compresses underneath your weight. It can tell you your weight fairly accurately due to the fact that it has a set rigidity and it is known how much weight it takes the spring to compress to various degrees. This process is also used in industrial settings, as well, but is flipped upside down so that the spring  (attached to a hook here) will stretch along a known distance to determine how heavy something is.  Now, even though these things are used so often, it's not to be taken for granted. It's still important to know the basic elements. The amplitude will determine how far up or down the spring stretches (the height stretch on the wave graph). The frequency will tell us how often the spring will oscillate from one end of its amplitude to the other and back in the given time period.  And then the period itself will be the delimiting factor that determines the time boundary in which it is to be measured. All of this is definitely useful. It would be foolish to state otherwise. Naturally, I am inclined toward the other end of the mathematics spectrum, but this course and this assignment have shown me that I can understand both aspects of the field and I can work to improve my visual/spatial abilities in order to become a more well-rounded student/scholar.