BJ,

Some proofs in geometry I think are very important, especially the proofs that are constructive. The Quandaries and Queries service has been helping people with mathematics problems since 1995 and I have been surprised by the number of people who seem to lack a geometric sense. I am thinking of concepts such as finding the area of a polygon by subdividing it into triangles. I don't mean going through the details of finding the areas of the triangles, just the concept. You can't convert square feet to cubic yards because they measure different things, area and volume. Why is it that the area of a triangle is half the base times the height? This is not a magic formula, it has a proof that involves paper and scissors.

These things become second nature to us by having experience with the concepts and by seeing the structure of the subject. Experiencing the way the proofs on geometry build on each other helps to instill geometric sense.

I hope this helps,
Penny