[ in response to Lou Talman @ Math Forum, re "spherical geometry" becoming important, in tandem with geography and graph theory, typos fixed, hyperlinks, local color added ]
I don't think that spherical *geometry* (or any other non-Euclidean geometry) was ever particularly important as a high school topic. If you meant spherical *trigonometry*, that's a horse of another color.
Geometry, trigonometry whatever. The fine points of your "non-Euclidean" are of some interest though. I take it up in more detail in geometry-pre-college.
And your suggestion that it was displaced by Newtonian calculus is arguable, at the very least.
Joe Clinton showed me the spherical trig books that used to get air time pre the big push to gateway everyone through Calc (moooo!). Fast Food Nation indeed.
Spherical trig may just have died on the vine when it was no longer expected that high school graduates could become surveyors and/or navigators with no further formal education.
Yeah, a presumptuous class thing. As we're learning in South Africa, it makes perfect sense to get young boys on the water, sailing, before they get recruited into landlubber gangs, and a lot of distracting politics (Lara did an excellent story about this awhile back on CBS -- she's chief foreign correspondent and an RSA native).
Navigation arts make a big come back in my scenario. We don't *let* it "die on the vine" the way they did in the dark ages 1900s (but then they didn't have the GIS/GPS tech we now take for granted, poor slobs).
In education, such deaths are usually quite protracted, and that explains the "recent memory" part.
- --Lou Talman
I'm glad you too feel secure in your model. Nice isn't it?