Showing posts with label Pi Day 2015. Show all posts
Showing posts with label Pi Day 2015. Show all posts

Constant Pi Day Don’t Expect

All About Everything
Every year on March 14 in honor of the mathematical Constant Pi Day Don’t Expect. Years, 15, was in accordance with the first five digits of the decimal representation of 3.1415 is the date: Saturday after a century event. The celebrations around and eat cake and "Pie-Kus" (three syllables in the first line, the second and four haiku) turn composition. But perhaps a better way to commemorate the day was really trying to understand why it is so important.

He can not as a ratio of two to be unreasonable terms means. There is simply no way to write the decimal continue indefinitely without ever installed in a repeating pattern. No less Pythagoras declared with a universe of intelligent design incompatible denied the existence of such numbers.

However Pius is the ratio of the circumference of a circle to its diameter, is itself everywhere. For example, in the source and the mouth of the average length of a gently sloping meander is pi times the straight line distance over. You get the idea. That our universe a mathematical convenience and does not remember us Subscribe.

Early mathematicians realized pi’s usefulness in calculating areas, which is why they spent so much effort trying to dig its digits out. Archimedes used 96-sided polygons to painstakingly approximate the circle and showed that pi lay between 223/71 and 22/7. By the time Madhava (in India, around 1400) calculated pi to over 10 decimal places using his groundbreaking infinite series (which regrettably bears Leibniz’s name), it was already more than accurate enough to address all practical applications. Pursuing pi further had essentially become a mathematical challenge.

With the advent of computers, pi offered a proving ground for successively faster models. But eventually, breathless headlines about newly cracked digits became less compelling, and the big players moved on. Recent records (currently in the trillions of digits) have mostly been set on custom-built personal computers. The history of pi illustrates how far computing has progressed, and how much we now take it for granted.

So what use have all those digits been put to? Statistical tests have suggested that not only are they random, but that any string of them occurs just as often as any other of the same length. This implies that, if you coded this article, or any other, as a numerical string, you could find it somewhere in the decimal expansion of pi. Of course, that’s relatively meaningless, since you don’t know where to find the material you want. An apt metaphor for an age when we are being asphyxiated by mushrooming clouds of information.

But pi’s infinite randomness can also be seen more as richness. What amazes, then, is the possibility that such profusion can come from a rule so simple: circumference divided by diameter. This is characteristic of mathematics, whereby elementary formulas can give rise to surprisingly varied phenomena. For instance, the humble quadratic can be used to model everything from the growth of bacterial populations to the manifestation of chaos. Pi makes us wonder if our universe’s complexity emerges from similarly simple mathematical building blocks. Constant Pi Day Don’t Expect
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