[math-fun] (doubtless) old segment trick
Given pts A,B in n-space, instead of representing the segment AB by tA + (1-t)B and later checking 0<t<1, just use uA + B, scaling whatever gets added by u+1, and later check u>0. E.g., to see if AB intersects the plane thru P with normal N, solve for u N.(uA+B)=(u+1)N.P, where N.P can be precomputed. The actual intersection is (uA+B)/(u+1). --rwg GREAT PLANES PLANET GEARS PS, apropos Jeopardy!, the TV at Deedees Vegetarian Buffet last nite showed Crorepati, an exact homologue of Philbin's Millionaire show (perhaps minus the lifelines). But winnings were displayed as Rs x,xx,xxxxx instead of $ x,xxx,xxx. (And the quizmaster can break into song.) The math question seemed easy enough: Which of the following is greater than 86? <Four strange words ending in "asi".> Oops.
participants (1)
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R. William Gosper