Pi History - The Digits of Pi - the future
The Illustrated History of Pi
The Digits of Pi - the future  

Even with trillions of digits of pi already calculated, there is still lots of horizon.

Because the digits of pi are literally endless.

Even the early work of mathematician Arya Bhatta in the 5th century CE had suggested that the value of pi was irrational and could only be "approached" but not definitively calculated.  

In 1761 the German mathematician proved that pi was in fact irrational, meaning that it could not be written as the ratio of two integers.  

Finally, in 1882, Ferdinand von Lindemann, another German mathematician, had published his proof that pi was a 'transcendental' number: a complex number which is non-algebraic, meaning it is not a solution of a non-zero polynomial equation with rational coeffecients.

This left pi as a number whose digits were literally infinite - providing a challenge which was the 'perfect storm' for computers and their programmers.

  Codicil:  Putting it in Context  
  Simon Newcomb, a late 19th century Canadian mathematician, science-fiction author, and all-round "polymath" had commented on the practical utility of pi as follows:  “Ten decimals are sufficient to give the circumference of the earth to the fraction of an inch [assuming the earth were a perfect circle which it is not], and thirty decimals would give the circumference of the whole visible universe to a quantity imperceptible with the most powerful telescope.” (quoted in Mathematics and the Imagination by Edward Kasner and James Newman.)

  Given Newcomb's observation, it raises the obvious question as to why the quest to calculate ever-greater and more prodigious numbers of decimal places has continued, and will likely continue, not only unabated, but with ever-increasing enthusiasm.  
  The answer can best be found in words spoken by British mountain climber George Mallory in 1924, as he set out to climb and conquer the summit of Mount Everest (a mission in which both both Mallory and his climbing partner disappeared).  
  Mallory's famous answer:  "Because it's there".  
  Although Sir Edmund Hillary (New Zealand) and Tenzing Norgay (Nepal) did finally reach the summit of Everest, in 1953, each year hundreds of climbers set out to reclimb it and claim new titles:  first solo ascent, first winter ascent, first oxygenless ascent, fastest ascent, youngest person , frist legally blind person, oldest person, most ascents - and then, most ascents coupled with a challenge to other records (most people on a single day).  
  Like Everest, Pi will never truly be conquered.  
  For pi, the sky - and beyond - is the limit.  
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