On Jul 25, 2007, at 10:53 PM, Peter Lissaman wrote: >> 2. DIFFERENTIABILITY AND CONTINUITY (Nicholas Thompson) > Nick: Let me be your math consultant! Taught that stuff at Caltech > many years!! The mathematicians are horn swogglin' you with mis- > understood function theory! A'course the f'n roof is continuous. If > it weren't the rain would come through! It is trivial to write a > continuous function, f(x) defined for 0<x <=c and g(x) defined for > c<x<1 with f(c) = g(c), with the peak at x=c and a different slope > for x=c, than for x>c. But the function is continuous. Just like a > roof ridge. A geometric function has, at each point, some degree > of continuity, denoted by C N, where N is the order of the first > discontinuous derivative. The triangular roof frame rafter is C1, > meaning continuous in ordinate, discontinuous in slope. Smoother > shapes have continuity of higher derivatives. Analytic functions > have infinite continuity (thanks to M. Cauchy!). Airfoils have to > be very smooth, but they can't be infinity smooth, since we need to > tailor the pressure distribution to control separation, and the > trailing edge must usually be sharp. Some of my airfoils of the > olden days, when we did this by hand, were C16 ....
This is abs-fab! .. I hadn't realized that continuity had been categorized in quite this way. The Mother Of Truth sez: http://en.wikipedia.org/wiki/Parametric_continuity .. which alas is still a stub. I bet you'd be popular if you filled it out! -- Owen ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
