1. Majority rules in math right?
2. Did we prove it or did we just all agree?
3. Math is not about computation, but about proving things.
4. When something works well in math, you should milk it.
5. Geometry is something dynamic, not a bunch of stationary objects. Transformations help us see this. If you’re good at geometry, chances are you moved stuff around in your head.
Euclid would agree with #5. Hilbert would be dead-set against it. I've been considering it half my life and am still not sure where I fall, but I can say that geometry statements can always be stated in such a way that #5 is false.
ReplyDeleteI'd love to know more about this, as I was fairly well convinced of #5.
ReplyDeletea key moment in "geometry as transformations":
ReplyDeletethe erlangen program.
i myself am more of a "stationary objects" man.
(fitting your theory since i was an algebra major.)
I think the question about #5 comes from treating it as a philosophical point. From a philosophical point of view, there's a debate there. From a pedagogical point of view there's really no debate. A student learning geometry always benefits from moving stuff around.
ReplyDelete