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Arc – an unbroken part of the circle. Two endpoints are always the
Arc – an unbroken part of the circle. Two endpoints are always the

... If a line is ___________ to a circle, then the line is __________________ to the radius ...
ARMSTRONG NUMBERS: 153 = l3 + 53 + 33 Gordon L. Miller and
ARMSTRONG NUMBERS: 153 = l3 + 53 + 33 Gordon L. Miller and

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... proof that there is a constant c such that cx/ log x ≤ π(x) (many number theory books have this proof; see for example [MT-B]). Another method of proof is to deduce a contradiction from assuming there are only finitely many primes. One of the nicest such arguments is due to Furstenberg (see [AZ]), w ...
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Approximations of π



Approximations for the mathematical constant pi (π) in the history of mathematics reached an accuracy within 0.04% of the true value before the beginning of the Common Era (Archimedes). In Chinese mathematics, this was improved to approximations correct to what corresponds to about seven decimal digits by the 5th century.Further progress was made only from the 15th century (Jamshīd al-Kāshī), and early modern mathematicians reached an accuracy of 35 digits by the 18th century (Ludolph van Ceulen), and 126 digits by the 19th century (Jurij Vega), surpassing the accuracy required for any conceivable application outside of pure mathematics.The record of manual approximation of π is held by William Shanks, who calculated 527 digits correctly in the years preceding 1873. Since the mid 20th century, approximation of π has been the task of electronic digital computers; the current record (as of May 2015) is at 13.3 trillion digits, calculated in October 2014.
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