Saturday, July 07, 2018

Platonic Five

The curriculum we're working on restores polyhedrons to their rightful place, which does not mean we're confined to only Euclidean approaches.

Debate teams understand that mathematics evolves as a dialectic.  It's not all there already, to be chiseled out from stone.  We need those communications.

An issue facing some curriculum writers is where and what to censor.  Do we need the Real Numbers as currently defined?  A computational thinking course spends less time on those, given numbers have discrete digital representations, with symbols like the Greek letter pi suggesting algorithms we might set running indefinitely.

We do want the Platonic Five, that much is obvious, starting early.  V + F == E + 2.  The concept of Duality.  The Platonics are closed under this operation of taking the dual.  However we may also combine duals by criss-crossing edges, begetting new polyhedrons by this process.

Cube + Dual(Cube) == Cube + Octahedron = Rhombic Dodecahedron (RD).

Dual(RD) = Cuboctahedron (1, 12, 42, 92...)

Icosahedron + Dual(Icosahedron) = Icosa + Pentagonal Dodeca = Rhombic Triacontahedron (RT).

These transformations, along with the Jitterbug, are familiar to all our young pretty early.  We'll be sharing these animations in kindergarten in the form of wallpaper and screen savers.

What says Shiraz?