Integrating SQL into everyday algebra, renamed computer algebra in some contexts, involved
implementing a schema of Polyhedra established by Faces of consecutive Edges in turn defined by tail-originating vector pairs.
sqlite> .schema Polyhedra
CREATE TABLE Polyhedra (
greekname CHAR PRIMARY KEY,
shortname CHAR NOT NULL,
vertices NUMERIC NOT NULL,
edges NUMERIC NOT NULL,
faces NUMERIC NOT NULL,
volume NUMERIC NOT NULL);
sqlite> select * from polyhedra;
Tetrahedron,tetra,4,6,4,1
Hexahedron,cube,8,12,6,3
Octahedron,octa,6,12,8,4
"Rhombic Dodecahedron",cell,14,24,12,6
Cuboctahedron,cubocta,12,24,14,20
At the top level, we have those V, F, E columns, good for
self-joining to seek duals (where shape1.V = shape2.F and shape1.F = shape2.V and shape1.E = shape2.E). We also have volumes columns where, breaking with tradition, we also store
tetravolume equivalents -- always whole numbers in the case of
CCP-based Watermans for example, and in our "
boot sequence".
The above covers XYZ, other spatial coordinate systems, and establishes vector geometry in the context of record-keeping (SQL engines), setting the stage for GIS/GPS topics in
future curriculum segments. Ray tracing, x3d / VRML, graphics engines such as VPython (wrapping OpenGL) all fit in to this picture, establishing an integrating geometric bridge between art and science.
Having a web framework serving pages in
the computer algebra classroom, with some students responsible for learning inner workings, is not a big detour away from career-relevant goals, as this form of record-keeping is pervasive in academia, government, private industry.
Traditional algebra topics, such as functions and relations and ordered pair mappings, permutations and combinations, trigonometry & statistics,
get perpetuated forward, with an emphasis on modeling, controlling algorithms and summary visualizations (
MVC).
Planting RSA public key cryptography at the high school level, a core feature of contemporary eCommerce, motivates forays into
number and group theory at lower levels, with much of the curriculum writing still awaiting development.
4D Solutions, a sponsor of
the Oregon Curriculum Network, boasts a serious track record in getting
this flavor of Gnu Math off the ground.
That being said, this is very much a collaborative effort and I have a long list of people to thank, many of whom are continuing to provide our company with valuable feedback and guidance, even yummy gigs and contracts sometimes.
Looking forward to 2009 then!
