On 10/26/07, Bill Gosper <rwmgosper@yahoo.com> wrote:
"Why should Johnny learn the quadratic equation? He'll never use it." Did the spectators at those Renaissance polynomial-solving contests grasp the motivation of the problem? What is the most "mundane" (whatever that means) need for solving a cubic? ... Anyway, there must be lots of "nice" cubics out there that textbooks and puzzlists routinely shun. Suggestions? --rwg
Build an emergency bivouac tent from a 2-metre square mylar sheet and 2 adjustable ski poles: locate them under the sheet so that the side edges sweep down from the central ridge to ground level; and the end edges drape over the pole tops, mid-points secured at the feet, and stretching tautly to the corners. (Or if you prefer, construct an 8-hedral teabag using a pair of similar shells of more modest dimensions.) The pole height e maximising the enclosed volume is the root in the unit interval of the cubic 3 - 4*e - 6*e^2 + 6*e^3 = 0 which alas has 3 real roots, so the Cardan (Tartaglia?) formula is not terribly informative. [In unit teabag terms, the depth equals 0.54676 and the volume 0.1454632612.] WFL