Here are some of the kinds of tasks you can accomplish when you become a calculator programmer:
• You can program complex formulas for repeated use. For example, you have several offers of mortgage plans. Once you have developed a simple program containing the amortization formula, you can enter the principal, the monthly interest rate (the annual rate/12) and the number of months over which you will be paying to calculate your monthly payment. With this program you can now compare the various offers.
• You can collect data. For example, you can see what chance you have of winning money playing the MegaMillions lottery with its \$90,000,000 grand prize hundreds of times. Here are the results of purchasing 100,000 \$1 lottery tickets.
• (Note: Given this kind of return, you can save a great deal of money simply playing the lottery on your calculator.)
• You can carry out complex computations to solve problems. For example, finding the center of a circle in coordinate geometry is a straightforward task based on the standard geometric construction. The calculations are complex, however, and often lead to errors. Here is a screenshot of the results of one such calculation.
• You can run interesting experiments. Here is a screenshot of the results of the so=called Chaos Game. These results are based on a simple procedure. Given three points in the plane, beginning at one of them randomly choose one of those points and mark a location half-way there. Then from that new point repeat the process, again choosing one of the initial three points and going half-way to it. When this is repeated hundreds of times by a simple program, the so-called Sierpinski triangle results;
• Here is another example: a fractal curve resulting from a simple given process that is not random, but that leads to a non-repeating design.
• You can program and play complex games. Here, for example, is a stage in the Game of Life.
• And here is a stage in a sudoku game.
• Some of these examples require advanced programming skills, but others may be accomplished after studying only a chapter or two of this text.