## Tuesday, April 21, 2015

### Spherical Trig

I've been brainstorming with my peers on math-teach about how to make spherical trig more accessible, starting with a set of tools and not staring at a lot of cryptic scripting language right off the bat.  On a sphere, the Pythagorean Theorem has a different form.

Imagine a curriculum that used a code such as:  sTem; STem; steM... to highlight which of the four domains (Science, Technology, Engineering, Mathematics) gets the most emphasis in a given Lesson Plan. Multiple letters might be highlighted.  Superimposed (stacked), the Lessons reinforce one another and build up a multi-layered surface (spherical) or system (global matrix).

The acronym STEM is perhaps peculiar to English and need not be taken too seriously.  The pun on STEAM, with A = Anthropology, seems to be one of STEM's chief values as a marketing device.  We get another bridge to the Humanities through Anthro / Animal, thereby unifying the Liberal Arts in true Trivium / Quadrivium fashion.

In Synergetics, the spherical triangle is emphatically a face of a tetrahedron with edges to the planetary center.  Saying "planet" for "system" has a somewhat Little Prince flavor.  But then we already use the word World for a namespace, as in Python World, or Python Planet (both references to the computer language, but of course Monty Python resonates as well).

My travels took me through Salt Lake City recently and I found myself reading about Pink Floyd, the pink flamingo that escaped from the zoo and lived in the wild with the other birds for a number of years.  Brine shrimp are plentiful in those lakes (a patchwork of shallow mini-lakes), though I'm not sure if that's what flamingos actually eat.  Tourists would spot Pink Floyd from time to time, but he or she drifted off and was last seen in Idaho.

Among the tools a student might use:  Google Maps and/or Google Earth for finding locations and getting their lat / long coordinates.  These might be fed to a Web resource (URL) that spits back XYZ coordinates, taking Planet Earth to be centered as some origin.  Straight line distances through the Earth's crust would correspond to chords, whereas on the surface we have geodesics or great circles.  Going from lat / long to XYZ to spherical coordinates helps us translate between data sets.