On Fri, May 11, 2012 at 9:26 PM, Bill Gosper <billgosper@gmail.com> wrote:
Long before XKCD named it, I was a big fan of teacher-trolling-by-proxy. All you need is an bright evil kid who can feign a look of innocent bewilderment. E.g., for algebra, "x^4+4 doesn't factor, does it?" Geometry: "How long are the two equal chords that trisect the area of the unit disk?" Or, "To construct the tangent to a circle at a given point, why are you showing us this complicated compass procedure with perpendicular bisectors, etc., when all you need is to add four more points at random, join all five in a star, draw two more lines, and you're done, no compass needed?" (See http://www.tweedledum.com/rwg/tan.htm .) Calculus: Which convergence test should I use for sum (csc n)/n^2 ?
[...] Here's a nice one from Neil: Gee, if the area of a sphere is d/dr of 4/3 π r^3 = 4 π r^2, then the area of a cube must be d/ds of s^3 = 3 s^2 ! This should take care of all sorts of polyhedra! --rwg Why don't you say sphere area = π d^2? Are you secretly one of those τ people?