The Perfect Circle - Pi

Why study such problems, since irrational numbers do not

exist?" -Leonold Kronecker 1882
Since the year 2000 BCE humanity has been in the pursuit of perfecting the number for the ratio of a circle. Today it is called Pi. When humanity discovered this number they changed the world and accelerated technology and mathematics to the point we are at today. It is amazing that an irrational, essentially unreal, number has caused a real impact on society. Since the first approximation of Pi it has been improved upon all across the world and through many cultures. One man cannot be credited to the discovery of Pi, as it was a human achievement.

Both the Egyptians and the Babylonians are the first historically documented discoverers of Pi. They each had slightly different estimations, 3.1605 and 3.125 respectively. (Blatner p.57) Pi is 3.14159... It is irrational, so it goes on forever as far as modern technology knows. This means that neither one of these cultures was far off at all. A feat even more impressive considering that the concept of the number zero had not yet come into existence.

About a thousand years later the Chinese came up with the ratio of a circle equaling three. (Blatner p.57) The Bible also states the ratio of a circle as three, "ten cubits from the one brim to the other: it was round all about, and a line of thirty cubits did compass it round about" (The Holy Bible, 1 Kings 7:23) dated around 550 BCE. These were inaccurate for their times, but are significant because it shows how the mathematical ideas had spread to all corners of the world.

In the third century BCE Archimedes of Syracuse found a number very close to that of the modern day Pi. He did this by using the principle of exhaustion, using polygons with a circle inscribed between them. He increased the number of sides of each polygon till he stopped, coming up with the idea that Pi is somewhere in between 223/71 and 22/7. The most accurate value for the ratio of a circle that Archimedes achieved was 3.1416. He was off by roughly only one ten thousandth of Pi. (Posamentier p.59) This is more accurate than the number that is taught to be used in math classes today, 3.14 comparatively.

In 1706 William Jones decided to give the number a face with the symbol π. He chose this symbol because the Greek letter π is pronounced like the letter 'p' for perimeter. (Dr. Math) Over the years mathematicians have since began to out do each other in the calculations of Pi. The most published calculated digits of Pi are 1,241,100,000,000. Just over 1.2 trillion digits and it took nearly four years of work from ten people. (Kanada) This feat of human intelligence was only possible by the use of a super computer, which would not have been possible to build with out our knowledge of Pi.

Pi does more in our lives than help us know more about it. There are many ways that it has created things for humanity. No one knows quite how the Egyptians were able to construct The Pyramids, but a theory exists that they were able to calculate it, even with their basic knowledge of Pi. If the circumferences of The Pyramids are divided by twice their height, much like the circumference of a circle is divided by twice its radius, also known as its diameter, and then it equals 3.14. This coincidently enough is Pi. (Zajac) When the Romans constructed the Pantheon in Rome, they constructed the Oculus. This was a great architectural achievement, one that could not have been done without the properties of Pi. (Graßhoff p.98) Romans also used Pi for their accomplishments in engineering. (Blatner p.21) "Religiously and scientifically Pi reached the Sassanid Persian Culture in 550BCE and it supported the astrological and astronomical underpinnings of their religion, Zoroastrianism." (Blatner p.30) Zoroastrianism still holds over 300,000 believers today. (Kjeilen) Pi has obvious connections to the sciences of astrology and astronomy. It is used to calculate and plot the revolutions and paths of objects in space. NASA uses the property of Pi to calculate rotational motion and rocket launches. (Rao) When it comes to cars, speedometers, and odometers alike have need of Pi. In order to calculate the speed that a car is traveling and the distance it has traveled, Pi is used to determine the answer. If the size of the wheel was to increase by even just one inch, both the speedometer and odometer would be off, and need to be recalculated by using Pi. The list is virtually endless, but anything and everything that is circular in any way shape or form, and requires even the slightest degree of accuracy requires Pi.

Despite the vast length of contemporary Pi, only 39 digits are required to calculate the circumference of the known universe. This is within the accuracy of the diameter of a hydrogen atom. (Schroeder p.221) What then is the point of the human effort to calculate a seemingly infinite number of digits of Pi?

It is because it has always been human nature to create perfection. A perfect circle is only perfect in imagination, because it is impossible to calculate the exact ratio of a circle. Since everything that is remotely circular in shape or movement requires the value of Pi, none of these things that humanity has created using Pi are perfectly accurate. Mathematicians and scientists simply decide that they are close enough, virtually perfect. "Pi represents a deep universal mystery, how is it that something this basic, this fundamental to math and to science, could turn out to be so incredibly difficult to pin down?" (Blatner, BBC) As it stands, humanities quest for perfection is only successful in theory with 2πr, also known as πd. The perfect circle is possible through formulated thought, but it is impossible in practice due to Pi's irrationality, and technically not existing because of it.

Works Cited

Blatner, David. "3.14 and the rest." BBC (2008): n. pag. Web. 6 Dec 2009.

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Blatner, David. The Joy of Pi. New York, NY: Walker and Company, 1997. Print.

Dr. Math, . "About Pi." Math Forum at Drexel University (2009): n. pag. Web. 5 Dec

2009. .

Graßhoff, Gerd. The Pantheon in Rome: Contributions. Norderstedt, Germany: Books on

Demand, 2009. 98. Print.

Kanada, Yasumasa. "Current Published World Record of Pi Calculation." Information

Technology Center, University of Tokyo (2005): n. pag. Web. 5 Dec 2009. .

Kjeilen, Tore. "Zoroastrianism." Looklex Encyclopaedia (2009): n. pag. Web. 5 Dec

2009. .

Posamentier, Alfred S., and Ingmar Lehmann. Pi: A Biography of the World's Most

Mysterious Number. Amherst, NY: Prometheus Books, 2004. Print.

Rao, Shanti. "Rotational Motion and Rocket Launches." 1993. Caltech, Web. 5 Dec

2009. .

Schroeder, Manfred. Fractals, Chaos, Power Laws. New York, NY: W. H. Freeman,

1991. Print.

The Holy Bible, New International Version. Jean E. Syswerda. Grand Rapids, MI:

Zondervan, 1985. Print.

Zajac, John. "Who Built The great Pyramid?." Great Pyramid (1996): n. pag. Web. 5 Dec

2009. .