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The number ànis used in math all the time, for finding the circumferences and areas of circles, amongst other things, but how much do students really understand about àn? They know that it stands for the number .14 and that if you¡¦re going to pass any of the higher math levels you have to be familiar with the equations its used in, but how did such a number come to be, and how are its uses applied?
In order to find nànmathematicians use algorithms. A common and simple algorithm to use isnà/ = /1 / 4/ 4/5 6/5 6/7¡Kand so on. This particular method for finding ànwas discovered by John Wallis.
The number Pi has been around since ancient Babylonian time and has been in use, in some form, as early as the creation of the wheel. Reference is even made to the concept of àn in the Bible. Around four thousand years ago the Babylonians and the Egyptians discovered that the ratio of the circumference of a circle to its diameter was about . Since circles were all around them, big and small, they made the important conclusion that ratio was a very valuable tool. It would not be until 1706 that mathematicians would begin associating this ration with the Greek letter Pi. During the fifth century B.C. Hippias of Elis discovered the quadratrix, a curve that could be used to determine à through a geometric construction. In the third century Archimedes of Syracuse found a method where àncould be found to any degree of accuracy required. He
took a circle and inscribed a regular hexagon within the circle and circumscribed one about the circle. He then, by using successive bisections, inscribed and circumscribed regular polygons within and about the circle with sides of 1, 4, 48, and finally 6 sides.
Advancements in using à are being made all the time. Now there are computers that can take ànto billions of places.
People have been fascinated by this irrational number throughout history. In September of 1, Dr. Kanada of the University of Tokyo calculated 06, 158, 40, 000 decimal digits of Pi. Then, in 00, Dr. Kanada and his team broke their own record by calculating 1.411 trillion digits. Even more devoted to ànis Hiroyoki Gotu, who memorized an amazing 4,000 of its digits.
The most accurate fraction to represent the number ànnis 10448 / 15, which is accurate to 0.00000001056%, but the accepted and more commonly used fraction is /7, which is accurate to 0.0405%.
ànis so astounding because in any exact circle the circumference/diameter equals à|nnnPincan be used in all sorts of equations and applications. Some of the more common equations are the area of a circle ànxnr, the circumference of a circle nànx r x, the volume of a sphere 4/ x nànxnr, and the surface area of a sphere 4nxnànnxnr. This and other concepts of à are easily applied to every day life. For instance, when working on fighter jets you frequently need to calculate areas of arc lengths for fitting equipment in. Also in this line of work, ànnis necessary for machining parts for the aircraft. Sine waves, used in signal processing, radio, TV, telephones and more, have a fundamental period of nà|nnOne example of the many uses of ànnis the navigation field. When planes fly great distances they are actually flying on the arc of a circle. The path must be calculated in order to make sure there is enough fuel. On this note, ànnis also used to locate someone on a globe. Pi occurs in hundreds of equations in many sciences including those describing the DNA double helix, a rainbow, ripples spreading from where a raindrop fell into water, superstrings, general relativity, normal distribution, and distribution of primes. Pi is a fundamental constant in the world of math and science.
On a lighter note, the number à has become such an important part of our math world that it has its own day. On March 14 (/14) students around the country come together and celebrate Pi Day. Younger students participate in activities such as making a ¡§Pi¡¨ necklace where each bead represents a number and a slightly bigger bead is used to represent the first number . This is to introduce the idea that ànis never ending. You can do a lot more stuff with Pi when it is in binary format - like drawing weird pictures of it, or even listening to it. As Pi has an infinite number of places, it is quite possible that any message you liked could be heard somewhere in Pi. Others write reports on the history of Pi, and perhaps a lucky few get to eat a pie of their very own.
The questions about Pi are never ending, and like the number itself, we may never know all the answers. There is so much to know about ànand each new fact leads to one more of those unanswerable questions. àntruly has a world of its own and excluding those devoted individuals set on diving into it, I think most would rather just eat regular pie.
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