Program idea: MathiGraph

Most graphing programs that are available today do what I would call statistical graphing. The user gives the program a series of data that he has calculated or measured, and the program can produce a variety of graphs (say a pie chart, or a scatter plot).

However, when you want to graph a mathematical equation, such a graphing program is cumbersome to use (you have to first generate the data using the formula), and often doesn't produce the desired layout.

MathiGraph would take a completely different approach to graphing by working entirely with mathematical equations rather than with data. This would address the needs of a different class of users, namely mathematics teachers, researchers, and students.

MathiGraph would need to:

• be easy and quick to use - students could learn a lot by experimenting with different equations, which you would be able to type in or edit at the click of a mouse.
• be flexible - teachers especially may want to hide various elements of the graph, such as axis numbering, in order to train the students to think abstractly.
• produce high-quality output - researchers and text book writers need to produce graphs that look good in mathematical publications.

I know of no program that satisfies all three of these needs. There is a popular graphing calculator on the Macintosh which is easy to use, but is not at all flexible. The high-end programs Maple and Mathematica are more flexible, but are hard to use because the settings must be changed using text commands. I know of no program that, with minimal effort, produces a picture of good enough quality to be published in a book.

Solution:

Here are some features that MathiGraph would have, in order to cater for the above needs:

• Ease of use would be obtained by having many parameters calculated automatically. This way you would only have to type in the equation, and everything else would be done for you.
• Once the computer has automatically decided on the axis size and placement (plus many other things), you would have the flexibility to modify just about every aspect of the graph, as well as adding headings, labels, dots, pointers, and other aids to explanation.
• The computer can do a lot more with an equation than with a simple series of data. The program would automatically detect if the equation has an asymptote, and would automatically smooth out a graph which curves a lot. This way the graph will look good, even to a professional's eye. It will be able to create PostScript output which can be drawn at any resolution.

This program would take mathematical graphing software to a completely new level. The program would not just plot a graph dot by dot, but would use a sophisticated algorithm to determine the best way to plot an equation.