Pi: The Unknown Essay

2031 words - 9 pages

Pi, the most talked about yet the least known about, is the ratio of the circumference of a circle over the diameter, and is one of the most important numbers ever to be used in mathematics. The world of Pi is very interesting, detailed, and complex. There is a very large history of how pi was found and of different ways mathematicians and civilizations calculated Pi. A few of the many examples of the calculation of pi are from Archimedes, Ahmes, the Chinese, the ancient Babylonians, and also the ancient Egyptians. In today’s society there are also many real world uses of Pi.

Pi has a very rich and detailed history since it's creation long ago. It has been a well known ratio for ...view middle of the document...

This was a very important step in calculating Pi to the modern known number of Pi. We experimented with this method and got to about 3.14 after using a 96 gon. Although in our experiment we did not draw a full circle with polygons inscribed and circumscribed, instead we took a shortcut and figured out the inner angles measurement and then used simple trigonometry to find the perimeter of both the inscribed and circumscribed regular polygons. Which we then divided by the diameter to find the range of , which then we averaged together to find approximation of pi.

The Chinese also later discovered this wondrous number, but were not as accurate as the legendary mathematician, they just used the number 3 for a long time. After the ideas of mathematicians like Archimedes spread to China and other places on the east they started to make more advanced calculations as well. Zu Chongzhi one of the best chinese mathematicians of the time, was the first person to come up with accurate first six digits of Pi. He calculated it to 3.141592 also known as 355/113, sadly many of his books and works have been lost, therefore no one knows exactly how he actually came up with his calculations.

Egyptians were not a civilization to be left behind though. A famous mathematician by the name of Ahmes, discovered another fantastic method to come up with this magical number. He wrote in the Rhind Papyrus, “Cut off 1/9 of a diameter and construct a square upon the remainder; this has the same area as the circle”. This gives an approximation of pi of about 3.1605. Some people even believe that the egyptians used Pi in the construction of the pyramids, and that is the reason for such great constructions. The Rhind Papyrus as you can see on the right (http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Egyptian_papyri.htm) calculates that an area of a circle is equal to eight ninths of a diameter squared (this is the same as Ahmes method because Ahmes is the author of this Papyrus), a=(8/9 d)2, and they also know a=pr2and that diameter is equal to 2 times the radius. So they used substitution to say pr2=(8/9 2r)2 (p = pi, r= radius). From there they divided by r2, to get p=(8/9 2)2which you can simplify to p=(16/9)2which equals to 3.1605. As you can see many mathematicians and civilizations in general have calculated an approximation of pi and have created unique methods of doing so.

Pi is also very popular and well used in today's society. This is a big deal because it is more important to apply the use of Pi in real world situations, than just memorizing equations and decimal places. One example of where Pi is used today is in the field of engineering. Engineers use the ratio of pi to calculate equations which helps them construct different components and create moving parts for machines and other equipment. Pi also plays a big role in the TV and radio world. People who work for television or radio companies use Pi to calculate lengths of signals from...

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