Any Math Based Program Ideas?

I was looking for a small project to do, and I want to do it with something related to Math. (I've only been up to pre-calculus, so nothing too advanced). Do you guys have any ideas for any somewhat large projects I can make which might be used to a math problem of some kind? The only thing I've really made so far is a program to solve a linear system of equations. Any other ideas?
Math is fun:

Or perhaps simpler (for which there are several implementations, particularly in graphics):
* I have a line that goes through (3D) points A and B
* I have an object that is represented by list of points
* I want that the object rotates 42 degrees around the line (i.e. update its points and if a point is on the line, then it won't move at all)

The link above discusses methods that come up with the A, B, and angle based on some other data.
Rotation definition here:

Slightly easier than quaternions!
Yeah, I mentioned I only have knowledge up to precalculus...

Anyway, lastchance, I'll think about the rotation one.
The list of unsolved computer science problems isn't really isn't something you can just program, in my opinion. But that wiki page links to a lot of interesting concepts that could be applied with programming.

I agree with keskiverto, I would combine the math with graphics. If you know something about solving linear systems of equations, that's pretty much what solving a matrix Ax = b is. You could make an image editor where you can perform mathematical operations on photos.

However, I think a lot of fun comes with calculus and beyond. You could make a 3D GUI program where the user can generate as 3D solid of revolution, for example.

Signal/Image processing is a huge subject with lots of mathematics in it. This can involve convolutions, Fourier transforms, statistics, or differential equations, depending on what you want to do.

You could also look into programming Parametric surfaces, which you could look at and rotate in 3D in your program.
Hi. Hope I am not too late to introduce some ideas.

Perhaps you can develop a program that takes the derivative of a polynomial using the power rule? The power rule is a very easy rule to follow for differentiating a polynomial (it doesn't even require precalculus to understand it). For example, if we look at single term polynomial axn, we can use the power rule to find its derivative, which is naxn-1, where a is your coefficient and x is your variable. This means if we are given 2x3+4x2+2x+5, we can take each term and apply the power rule to it, which gives us: 6x2+8x+2. Notice that if you have a constant in the polynomial when taking its derivative, the constant will just go away, and if you have a term where the x is the the power of 1, the x will just go away.

Another example: Take the polynomial 4x2+2x3+5x. Using the power rule, we can take its derivative to be 8x+6x2+5

If you want something more difficult, you design a program using something like SFML or SDL that generates a graph given a function.
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