Almost every branch of engineering or science uses geometry in a varitey of ways. Not to mention construction and various industrial situtions. Geometry, and geometric reasoning is at the heart of a lot of computer algorithms, which appear to have nothing to do with spatial reasoning - algorithms for scheduling airlines (linear and integer programming) .... .
When we understand space, and problem solving in space, we use that metaphor and pattern to reason about other situations.
It is true that machines can do a lot of calculations with measured quantities - and we should not try to compete with them in those skills. What we need to do is understand the problem well enough to know what is worth measuring, and what calculations will give an answer.
Let me close with a couple of 'real life' (at least real in my life) problems I am working on these days: (a) how can a cell phone company calculate where a cell phone is, if someone dials 911 and then cannot give their location? (It is a new legal requirement that they must be able to do this.) (b) how do you predict what parts of a protein move or are rigid? Motions and rigidity of proteins are central to a number of diseases, such as Mad Cow Disease (or cronic wasting disease which is sweeping the western US and Canada); Cystic Fibrosis; drug treatements for AIDS, .... (c) What patterns of frameworks are rigid or flexible in 3-space?
Nick Scott wrote: > > yea but billiards is common sense, i mean u dont take out a > protractor(however you spell it) and measure the angle. the only thing > you would use goemetry in is computer animation, and that gives you > the measures anyway. so i think geometry is pointless.