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The first to use an electronic computer (the ENIAC) to calculate π [25] 70 hours 2,037: 1953: Kurt Mahler: Showed that π is not a Liouville number: 1954 S. C. Nicholson & J. Jeenel Using the NORC [26] 13 minutes 3,093: 1957 George E. Felton: Ferranti Pegasus computer (London), calculated 10,021 digits, but not all were correct [27] [28] 33 ...
S n is the approximation after taking n terms. Each subsequent subplot magnifies the shaded area horizontally by 10 times. (click for detail) He used the first 21 terms to compute an approximation of π correct to 11 decimal places as 3.141 592 653 59. He also improved the formula based on arctan(1) by including a correction:
But for =, it converges impractically slowly (that is, approaches the answer very gradually), taking about ten times as many terms to calculate each additional digit. [ 79 ] In 1699, English mathematician Abraham Sharp used the Gregory–Leibniz series for z = 1 3 {\textstyle z={\frac {1}{\sqrt {3}}}} to compute π to 71 digits, breaking the ...
In addition to calculating π, Shanks also calculated e and the Euler–Mascheroni constant γ to many decimal places. He published a table of primes (and the periods of their reciprocals) up to 110,000 and found the natural logarithms of 2, 3, 5 and 10 to 137 places. During his calculations, which took many tedious days of work, Shanks was ...
Google engineer Emma Haruka Iwao has calculated pi to 31 trillion digits, breaking the world record.
The south-pointing chariot device was first invented by the Chinese mechanical engineer Ma Jun (c. 200–265 AD). It was a wheeled vehicle that incorporated an early use of differential gears to operate a fixed figurine that would constantly point south, hence enabling one to accurately measure their directional bearings.
where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.
To calculate the profitability index, you first need to determine the present value of the expected future cash flows from the investment. This involves discounting the future cash flows back to ...