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Cycles Upon Cycles: An Anecdotal History of "Higher Curves" in Science and Engineering

Student-Run Applied & Math Seminar

Speaker: Rida Farouki, UC Davis
Location: 2112 MSB
Start time: Wed, Mar 5 2008, 12:10PM

We present an eclectic history of the role of certain transcendental curves known generically as "roulettes" (produced by the rolling motions of lines and circles) in various scientific and engineering applications. The examples encompass the use of epicycloids and circle involutes in defining gear tooth profiles; cycloids as the geometrical and mechanical basis of Huygens' isochronous pendulum clock, and as the solution of the brachistochrone problem; and the use of epitrochoids in describing planetary orbits and the combustion chamber of the Wankel rotary engine. These case studies provide sobering evidence that, compared to modern endeavors, whatever ``geometric design research'' of the pre-computer era lacked in labor-saving computational gadgetry was compensated for by mathematical/physical insight and ingenuity.