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The interplay between generality and individuality, deduction and construction, logic and imagination - this is the profound essence of live mathematics. Any one or another of these aspects of mathematics can be at the center of a given achievement. In a far reaching development all of them will be involved. Generally speaking, such a development will start from the "concrete" ground, then discard ballast by abstraction and rise to the lofty layers of thin air where navigation and observation are easy; after this flight comes the crucial test of landing and reaching specific goals in the newly surveyed low plains of individual "reality." In brief, the flight into abstract generality must start from and return again to the concrete and specific.
Richard Courant
Loci: Convergence
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Extracting Square Roots Made Easy: A Little Known Medieval Method
Conclusion and About the Author
Conclusion
Today you get square roots with many correct decimal places instantly with your calculator or computer. However, as we saw with the fourth and fifth approximations of \(\sqrt{5},\) far greater accuracy can be achieved by means of a few easy calculations invented more than 800 years ago.
About the Author
Friedrich Katscher was born in Vienna in 1923. He is a lifelong Viennese who studied theoretical physics and mathematics and was science editor of a newspaper. Since the 1960s, he has been active as a historian of mathematics, giving lectures at the Vienna Technological University (Technische Universität Wien) and specializing in Italian Renaissance mathematics. His ability to speak German, English, French, Italian, and Spanish aids him in his mathematics history research. He invites you to correspond with him about this article and about Italian Renaissance mathematics via email (dr.katscher.vienna@chello.at).
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Katscher, Friedrich, "Extracting Square Roots Made Easy: A Little Known Medieval Method," Loci (June 2010), DOI: 10.4169/loci003494