Essay #1
The focus of my first essay is an alternative way to estimate the land area of the state of Georgia. I will discuss and use the Monte Carlo approach to probability in finding the area. To see an example of how to use the Monte Carlo approach and for a brief explanation you may click on this example.
Once you understand the Monte Carlo appraoch,
you are then ready to tackle the original problem which is: Using
the Monte Carlo approach, esitmate the land area of Georgia. This
method is great for all levels of mathematics. In just this single
problem, students will be tested on slope, writing equations,
solving systems of equations, graphing, ratios and proportions,
and measurements. Also, the student will learn a bit about geography.
I have prepared a solution to the proposed probelm complete with
a write-up, which further explains Monte Carlo's approach
and explains how to use it to solve the problem, and a spreadsheet that further illustrates Monte Carlo's approach
at work.
Essay #2
In my second essay, I search for a convenient formula for finding the area of any figure on a pegboard. To fully inderstand the problem I was facing and how I went about solving it, click on this essay. I also created a GSP document to help me visualize the various scenarios I tested, as well as a spreadsheet to organize my results.
Essay #3
One topic that is consistently convered at some point in a high school mathematics curriculum is investigations of various functions and their formulas. For instance: Given the standard formula for a parabola (y = ax^2 + bx +c), how do manipulations to the coefficients a, b, and c affect the graph of the function? I have investigated this topic using parabolas, cubics, and exponential functions.
Essay #4
What is the center of gravity and why is it significant? In the following essay I will explain the center of gravity and show how to find it for any triangle and quadrilateral.
Essay #5
An interesting topic in high school mathematics that is, often times, not covered in enough detail is number patterns. One may also refer tohese number patterns as sequences. In my fifth essay, I investigate a few patterns. The method I will use in doing this is based on the theory of finite differences. Given a line, I use points to divide that line. How many lines are created when one point is used to divide a line? When two points are used? When "n" points are used? Likewise, given a plan, how many new regions does dividing that plane by one line produce? Dividing by two lines? Dividing by "n" lines? Finally, given a sphere, how many regions are produced when the one plane is used to divide the sphere? When two planes are used? When "n" planes are used? I realize that drawing figures and diagrams would be very beneficial in constructing recursive formulas. However, instead of making long list and working with the recursive formula, I will only use a small number of trials and find closed formulas.
Please e-mail Walt Massey at wpm14@aol.com