Graphical Solutions [45B - 60B]

Contributed by Francis Glassborow

Fifty years ago graphical methods of solving equations were often frowned on. Purists considered them too inaccurate. Even those that knew better found that using the tools to extract good solutions by graphical methods required a great deal of computation. However times change and computations are what computers are good at.

This project requires you to write a program that will display one or more functions in a window. In addition the user must be able to zoom in on any point on the display (selected by a mouse button press) by a factor of two. This zoom process must be repeatable through at least thirty steps. I.e. you must be able to zoom in at least one thousand million fold. It must be possible to obtain the position of the mouse cursor scaled to the current offsets and zoom factor.

If you successfully complete this project you will have a tool for the graphical solution of equations in one or two variables to at least fifteen significant figures by simply locating a point of intersection and progressively zooming in on it.

Program elements

This project requires a careful and correct provision for evaluating functions to very high levels of precision. While the initial stages can be developed using simple polynomials a completed project should manage all normal mathematical functions. Exactly what range of functions will depend on the mathematical expertise of the student. The project demonstrates a range of computational problems as well as allowing graphical solutions of quite complicated equations in one or two variables.