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 Discussion: Research Area Topic: Kissing is secret of Calculus and the wheel

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 Subject: Kissing is secret of Calculus and the wheel Author: Sonny Date: May 28 2004
Isaac Barrow taught his student, Isaac Newton, the secret of differentiation:
secant of a
curve becomes tangent to a point of the curve. And Barrow taught Newton the
secret of
integration: as bar graphs under and over a curve shrink to segments up to
curve, their sum is
area under the curve. When a line just touches a point, mathematicians call this
"a point of
osculation", from Latin for "kissing". So kissing is secret of the calculus.
(Karl Menger taught me this in his book, "Calculus".) Also, a wheel can be
considered topologically as "a stack of circles". Each circle touches just just
one point of the flat it rolls on: a
kissing-segment. ONLINE, http://members.fortunecity.com/jonhays/kissing.htm
shows this for differentiation by animation. I need help in animating this for
integration, with full credit.