The History of Pi Essay Example

modern mathematicians a glimpse into the technique used to solve problems. The Rhind Papyrus received its name fromAlexander Henry Rhind (1833-1863) who was both a Scottish lawyer as well as an Egyptologist (PiDay International, 2008). Alexander Rhind was able to procure the papyrus in a market located in Luxor, Egypt.

This document is sometimes referred to as the Ahmes Papyrus as well and takes its name from the Egyptian scribe who created it (PiDay International, 2008). The Rhind Papyrus contains over 80mathematical problems that shows the methods used to find the answer.

Years after Rhind Papyrus was originally purchased, it was finally decoded. One of the problems contains the rule to finding the area of a circle. According to the decoded information, the Egyptians showed that the calculation for pi was 3. 16 or for a more exact answer 256/81 (Dyer, 2008).

The Bible is a compilation of various books. Unlike the previous two examples of ancient mathematics, this example has been read continuously all over the world and can be found in more than a few households. In I Kings 7:23-26, a large cauldron from the Temple of Solomon is described: “He made the Sea of cast metal, circular in shape, measuring ten cubits from rim to rim and five cubits high. It took a line of thirty cubits to measure around it. Below the rim, gourds encircled it - ten to a cubit.

The gourds were cast in two rows in one piece with the Sea.

The Sea stood on twelve bulls, three facing north, three facing west, three facing south and three facing east. The Sea rested on top of them, and their hindquarters

were toward the center. It was a handbreadth in thickness, and its rim was like the rim of a cup, like a lily blossom. It held two thousand baths. ” (NIV) (Dutch, 2002, ¶ 4).

Phoenician artisans created this cauldron. This description includes information such as depth, volume, wall thickness, but an estimate of pi was also included. As the definition states, pi is a ratio. The ratio stated in this statement is 30/10.

Theordore Rybka solved for pi using this biblical information and obtained the answer as three (Dutch, 2002). In China a mathematician by the name of Liu Hui, half of a century later used a method that would be similar to that of Archimedes. However, Liu’s method produced an even larger number. Liu’s method included a polygon that had 3,072 sides.

Still in China, a father and son improved the method further. With their strengths in mathematics and astronomy, Tsu Ch’un-Chih and Tsu Ken-Chih achieved a result of Pi= 355/113 totaling 3. 1415929.

In Hindu a teacher, writer on mathematics and an astronomer by the name of Arya Bhatta believed his rule for pi; simply adding four to 100 and multiplying by 8 then adding 62,000 resulted in a value that was similar to that of former mathematicians. However, he felt his method was approachable, but it was only an approximation and would later a fellow mathematician would prove him differently.

In Germany, during the 17th century, a mathematician by the name of Gottfried Leibniz worked on a new method to calculate Pi. Gottfried’s method of computing was called the “infinites series” method.

During this time, the method for calculating Pi was more analytical then

geometric. Getting a little closer to name, I can pronounce and are familiar with, Mr. Isaac Newton. Newton’s method uses a combination of the historical method of geometric and the more current method, which today is call calculus.

Whereas the Chih men used a full circle, Mr. Newton used a semi-circle with a radius of ? , which put him in a 16 decimal range of pi. He wrote about his calculations 1671, however, it was not published until later. Pi to 100 places was first discovered by John Machin.

He created this formula in 1706 and created to calculate pi easier by hand. Machin’s method created a new and more efficient way to compute pi to multiple decimal places.

Machin created this method by conjoining two different formulas. Machin combined his own formula to calculate pi and the Taylor series to compute pi accurately to 100 decimal places. (MucIlveen, 2007) This formula was later used to calculate pi to 707 decimal places. This creative formula for pi has lasted through the times and is still commonly used today.

The method of calculating pi by hand is used by numerous individuals in the present times and has been said to be frequently used by computer programmers.

Probability was another method discovered to estimate the value of pi. “Buffon’s Needle” experiment is a method when used finds an estimated value of pi, probability. This experiment to finding an estimated value of pi is simple but time consuming. This method requires patience because a pin about one inch long that is dropped numerous times, to get close to the valueof pi. The 1 inch pin is dropped on a flat

surface with parallel lines marked on it about 1 inch apart. MucIlveen, 2007) The reactions are recorded to find how many times the needle dropped crossing the lines on the table versus how many times the needle did not cross any lines.

This method’s answers are recorded and can be calculated to find a close approximation of pi. Each time this experiment has been attempted numerous people have come close to the value of pi. The person whom discovered this experiment was George Buffon and it was in the year 1901. In the 20th century Srinivasa Ramanujan, a very talented mathematician found new formulas for pi.

However, his findings were not published and would go unnoticed, because they were seen as theories and did not have any proof. Later, it would be rediscovered by Mr.

Ramanujan’s mentor G. H. Hardy a very well know English mathematician that Ramanujan’s finding had to be true and saw value in his finding. The work of these two men made it possible to unlock over 17million decimals of pi. Continuing the quest for further development, in 1947 D.

F. Ferguson was able to unlock 808 digits of pi with the desktop calculator, which made room for the electronic digital computer that was created later.