If we hadn't learnt plannar (is that correct?) geometry . . .

Euclidian geometry is what is normally taught in high school. It roughly follows the real world, but has some significant differences (how do you draw a line infinately long and infinately thin? No cheeting with the little arrows at the end!)

Oddly, geometry was one of the few subjects I really liked. Perfectly logical, and you could figure stuff out on your own just by scratching diagrams out on paper during boring classes.

In the general case, programmers don't need a great deal of math experiance, but the ability to prove things, as taught in geometry, is vital. Set theory is also useful (type systems and relational database theory are based on set theory), but higher mathmatics than that may or may not be useful, depending on the type of problems you solve.