You can kill two virtual birds with one stone if you introduce the concepts of version control, a branching tree, forking and so on (Github) -- geek language -- along with Geometry as an example of such: a Github-like tree.
Suppose we add a fork to the tree such that our model of 3rd power growth 1, 8, 27, 64... is a regular tetrahedron of edges N, rather than a cube. Might we develop in this direction to come up with some interesting geometry?
It's already been done (more pioneers welcome) and put in the language of version control, it's not even a threat to say so. Indeed, a "tree" is a mathematical structure, and it's just as well that we should see all of mathematics in terms of one (but then it's also a network).
On Tue, May 7, 2013 at 9:46 AM, Joe Niederberger <email@example.com> wrote: >>The restrictive definition allows its advocates to be certain that an isosceles trapezoid is not a parallelogram. > > *Absolutely* certain. > > It would be nice if these things could be taught in way that lets the students see when things are, for lack of a better term, "conventional", and when they are not. > This reminds me of the discussion a while back about the conventionality of the area measure of the unit square, > which, it became clear, is not universally recognized as such. > > Cheers, > Joe N