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August 31

What is this function?

Link to alphawolfram: http://www.wolframalpha.com/input/?i=%28x+%2B3%29+%2F+%28x-2+%29 . --Jubilujj 2015 (talk) 19:04, 31 August 2015 (UTC)[reply]

@Jubilujj 2015: A rational function.--Jasper Deng (talk) 19:38, 31 August 2015 (UTC)[reply]

A Möbius transformation. Bo Jacoby (talk) 19:45, 31 August 2015 (UTC).[reply]

Calculations of pi

The article approximations of pi includes many series for not pi itself, but (up to multiplication by algebraic numbers) its reciprocal. Wouldn't it be somewhat costly to have to recover pi from its reciprocal?--Jasper Deng (talk) 19:30, 31 August 2015 (UTC)[reply]

Not so much. If you examine the Computational complexity of mathematical operations, you'll see that division has the same complexity as multiplication (IIRC a division is 3 times as expensive), whereas approximating pi is that times the log of the number of digits. So the reciprocal is comparatively cheap, and is justified for obtaining a more efficient series. -- Meni Rosenfeld (talk) 19:45, 31 August 2015 (UTC)[reply]

Moreover, sometimes having the reciprocal saves you a division, as when you want the diameter, given the circumference. — Sebastian 04:39, 4 September 2015 (UTC)[reply]