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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Archimedes Of Syracuse And Sir Isaac Newton: On The Quadrature Of A Parabola, Wyatte C. Hooper
Archimedes Of Syracuse And Sir Isaac Newton: On The Quadrature Of A Parabola, Wyatte C. Hooper
Journal of Humanistic Mathematics
Good mathematics stands the test of time. As culture changes, we often ask different questions, bringing new perspectives, but modern mathematics stands on ancient discoveries. Isaac Newton’s discovery of calculus (along with Leibniz) may seem old but is predated by Archimedes’ findings. Current mathematics students should be familiar with parabolas and simple curves; in our introductory calculus courses, we teach them to compute the areas under such curves. Our modern approach derives its roots from Newton’s work; however, we have filled in many of the gaps in the pursuit of mathematical rigor. What many students may not know is that …
“It’S All For The Best”: Optimization In The History Of Science, Judith V. Grabiner
“It’S All For The Best”: Optimization In The History Of Science, Judith V. Grabiner
Journal of Humanistic Mathematics
Many problems, from optics to economics, can be solved mathematically by finding the highest, the quickest, the shortest—the best of something. This has been true from antiquity to the present. Why did we start looking for such explanations, and how and why did we conclude that we could productively do so? In this article we explore these questions and tell a story about the history of optimization. Scientific examples we use to illustrate our story include problems from ancient optics, and more modern questions in optics and classical mechanics, drawing on ideas from Newton’s and Leibniz’s calculus and from the …