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## Search Loci: Convergence:

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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

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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.