Initial thoughts

Most of the chunks that touch on mathematical subjects are going to be challenging to write. Our task is to write a book that demonstrates how the various facilities in the Processing language can be used to create pictures. Out task is not to teach mathematics. That said, it is difficult to use the various facilities effectively if one does not have some basic knowledge as to the underlying theory. Getting this balance right is potentially one of the biggest challenges we will face.

Obviously I need to start with what a polynomial is, and what they look like, in terms of their generic form. I'd like to use the old joke that a polynomial is a hungry parrot, but I suspect that's a bit too Pythonesque for most people!

Being restricted to quadratic and cubic equations simplifies the task slightly. I can see these equations being a little scary to some:

• y = ax² + bx + c (quadratic)
• y = ax³ + bx² + cx + d (cubic)

I will probably start off with constants and straight lines, and build up from there:

• y = a (constant)
• y = ax + b (linear)

Apart from showing the effects of altering the various coefficients (a, b, c and d), and a very brief explanation of power notation, I can see little to be gained by going into the maths any further.

I would like, where ever possible, to highlight real world examples of these curves. For example, the parabola, as described by a quadratic equation, is formed as the result of a conic section, and is also used for reflectors with a focal-point, such as satellite dishes and light reflectors.

Whilst waiting for my book to arrive, I will do some background reading.