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When that legendary apple fell on Isaac Newton’s head, the question was how fast it was travelling, if its speed was increasing with every foot it fell. The answer required Newton’s and his rival Liebnitz’s greatest invention: the calculus, as Liebnitz called it, or the mathematics of variable motion, or the accelerating apple. It is the geometry of curves and their properties like tangents, arclengths, curvatures and centers of gravity, which the Greek geometry of straight lines couldn’t calculate.

Calculus is the student’s big leap after algebra, introducing Liebnitz’s long lazy S, the integral sign. It’s the jungle gym of the mathematically swift and supple, the quicksand of numerophobes without number. More important, it’s the arithmetic in all the arcs of astronomy, and artillery, too. Even in the age of the pocket calculator it’s a metaphor in all that moves. Robert and Ellen Kaplan’s short course on The Calculus on the first hour of The Connection.
(Hosted by Christopher Lydon)


Robert and Ellen Kaplan, co-founders of “Math Circle.”