(Roughly) Daily

Posts Tagged ‘long S

Slicing the pi…

 

source

Calculating the value of pi, the mathematical constant that is the ratio of a circle’s circumference to its diameter, is a Sisyphean task– it goes on forever. And from a practical point of view, it’s silly:  resolution to just 39 digits is enough to calculate the circumference of a circle the size of the observable universe with an error no larger than the radius of a hydrogen atom.

Still, the quest continues.  As i09 reports

A pair of pi enthusiasts have calculated the largest chunk of the mathematical constant yet, reaching just over 10 trillion digits. Alexander Yee and Shigeru Kondo, respectively a computer scientist in the US and a systems engineer in Japan, fought hard-drive failures and narrowly missed widespread technical disruptions due to the Japan earthquake to break their previous Guinness world record of 5 trillion digits…

Read the whole story (well, the story-to-date) at “Epic pi quest sets 10 trillion digit record.”

 

As we remember that “pi aren’t square, pie are round,” we might recall that it was on this date in 1675 that Gottfried Wilhelm von Leibniz first used the “long S” as the symbol of the integral in calculus.  Leibnitz’s first such uses were in in private manuscripts; the first public appearance was in his paper “De Geometria,” published in (the appropriately-titled) Acta Eruditorum in June 1686.

The integral of a function of x over the interval [a,b]  (source)

 

Written by (Roughly) Daily

October 29, 2011 at 1:01 am

Waldo, found…

©2009 ~sfumato21

(via Daily What)

As we call off the dogs, we might recall that it was reputedly on this date in 1675 that Gottfried Wilhelm von Leibniz first used the “long s” as the integral symbol in calculus:

It was understood to be Leibnitz’s co-option of the Latin “summa.”

When Newton and Leibniz first published their versions of calculus (in the late 1680s), there was tremendous controversy over which mathematician (and therefore which country, England or Germany) deserved credit.  Newton derived his results first, but Leibniz published first.  The prickly Newton claimed Leibniz had stolen ideas from Newton’s unpublished notes, which Newton had shared with a few members of the Royal Society; a bitter argument ensued, dividing English-speaking mathematicians from continental mathematicians for many years– much to the detriment of English mathematics.   A careful examination of the papers of Leibniz and Newton has convinced scholars that the two arrived at their results independently, with Leibniz starting with integration; and Newton, with differentiation.  It was the symbolically-gifted Leibniz, however, who gave this new branch of mathematics its name.  Newton called his version of calculus the “the science of fluxions”…  One shudders to imagine that on one’s textbook (or in the mouths of schoolchildren…)

Reblog this post [with Zemanta]

Written by (Roughly) Daily

October 26, 2009 at 12:01 am

%d bloggers like this: