Discover the Fascinating Origin of the Ratio Pi - Essay Sample

Introduction

Pi is one of the most used mathematical symbols in history. Its common knowledge that the value of Pi is 3.14, but, arguably, few people know the origin of the ratio. Essentially, the ratio emanated from nature. It is the proportion between the circle's perimeter and its diameter. It is not easy to point at the person who initially became aware of the constant proportion between the circle's perimeter and its diameter. However, it seemed that human civilization as early as 2550 BC was aware of it. The initially recorded algorithm for computing the value of pi was geometrically done by the use of polygons by the Archimedes, a Greek mathematician.

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With polygonal algorithm dominating for over 1000 years, thus pi is occasionally denoted as the Archimedes constant. According to Rajput (2016), Archimedes calculated both higher and lower bound of pi by sketching a regular hexagon both outside and inside a circle. In addition, he consecutively doubled the figure of the sides till he reached a ninety-six sided even polygon. By computing the circumference of those polygons 3.1408< p< 3.1429.

Therefore, the Archimedes' higher bound of 3.1408 may have caused the understanding of a general belief that p is equivalent to 22/7. At about 150AD, Ptolemy, a Greek-Roman scientist, gave a rate of pi to be 3.1416 in his almagest. Possibly, he may have obtained it from either Apollonius of Perga or Archimedes (Rajput, 2016). Mathematicians adopting polygonal procedures made it to 39 figures of pi by 1630, a record which was broken back in 1699 when inestimable sequences were adopted to reach 71 characters.

In ancient China, the value for pi (around 1 AD) included 3.1547, approximately 3.1623 around 100 AD, and approximately 3.1556 around the third century (Hao & Fang, 2017). At around 256AD, Liu Hui, an arithmetician from the Wei kingdom, came up with a polygon-based iterative procedure. He used it together with a 3072 sided polygon to get a significance of Pi of 3.1416. Later, Liu invented an efficient technique of calculating pi then got a figure of 3.14, characterized by a 96-sided polygon by assuming an advantage of the fact that the variances in the area of consecutive polygons make a symmetrical series with a figure of 4. At around 480 AD Zu Chongzi, a Chinese arithmetician deliberated that 3.1415926< p<3.1415927 and thus suggested the approximation of pi to be 355/113 = 3.14159292035 and 22/7 as 3.142857142857 which he concluded to be a close-ratio and an approximate ratio respectively (Hao & Fang, 2017). With the precise value for its seven initial decimal digits, the value lingered as a perfect estimate of pi accessible for the next over 800 years.

With Jamshid al-Kashi, the Persian astronomer came up with nine sexagesimal digits, accounting for approximately 16 decimal digits (Azarian, 2019). In 1424 the Persian came up with a polygon of 3*2^28 sides, which held the world record for approximately 180 years. In 1579 Francois viete, a French mathematician attained a nine-digit with a 3*2^17 sided polygon.

In 1593 Adrian van Roomen, a Flemish mathematician, came into a conclusion of 16 decimal places using 2^30 sided polygon. Van's interest in pi was almost certain because of his friendship with Ludolph van Ceulen (Purewal, 2020). Ideally, Roomen worked majorly on trigonometry and also the calculation of cords in a circle. The major milestone that he was able to achieve was, he solved the problem of Apollonius by the use of the new method in solving intersecting hyperbolas.

In 1596 Ludolph van Ceulen, a Dutch mathematician, reached 20 digits, a record which increased to hit a 35 digits point. As a result, the pi was referred to as Ludolphian number up to until the 20th century in Germany. The mathematician took pride in his achievement that he requested that the pi figure be inscribed on his gravestone.

In 1621 Willebrand Snellius, a Dutch scientist, reached thirty-four digits. As a distinguished mathematician, he came up with a new method for calculating pi, which was the first of its kind since ancient times. Willebrand Snellius got a dramatic improvement by suggesting that the perimeter of the inscribed polygon of a given n side converges to pi double as faster as a perimeter of an inscribed polygon. According to Perkovac (2016). It is through the discovery that it was the first proved by Christian Huygens back in 1654. Using the above discovery, Snell got seven digits of pausing ninety-six sided polygon and thus got 34 digits of pi with n of 2^30.

In 499 AD, Aryabhata, an Indian astronomer who is also known for introducing the concept of Zero, valued pi at 3.1416. In other words, what he meant was that the perimeter of a circle with an approximate width of 20000=62832. However, we are aware that pi value is the ratio of the perimeter to the diameter hence 62832/20000 = 3.1416. With this value of pi, it was more accurate to five figures (Agarwal, Agarwal & Sen, 2016). Therefore we can infer from the above statements that Aryabhata understood that he was talking about a mathematical constant. The reason is that he uses the term rule to mean that the value remains constant even when the other numbers are bound to change. From his work, he referred to the term approached to denote that the value was not exact but rather an approximation. Moreover, much is not discussed how he came about the Pi; instead, he found it evident that there was no need to explain much.

Conclusion

In conclusion, the calculation of pi was transformed in 16 and 17th centuries, with the development of infinite series. Ideally, infinite series permitted mathematician scholars to calculate pi with high accuracy than Archimedes and others who employed geometrical techniques. Pi estimation attracted the interest of many mathematicians with all the same interest in reaching an accurate and reliable pi. Archimedes has overtime being a re-known father of Pi because of his contributions and giving a pi of up to 5-digit accuracy.

References

Agarwal, R., Agarwal, H., & Sen, S. (2016). Birth, growth and computation of pi to ten trillion digits (2013). In Pi: The Next Generation (pp. 363-423). Springer, Cham.

Azarian, M. K. (2019). An Overview of Mathematical Contributions of Ghiyath al-Din Jamshid Al-Kashi [Kashani]. Mathematics Interdisciplinary Research, 4(1), 11-19.

Hao, X. H., & Fang, Y. X. (2017). The Development of PI Algorithm in China. Journal of Liaocheng University (Natural Science Edition), (2), 5.

Perkovac, M. (2016). Measurement of mathematical constant p and Physical Quantity Pi. Journal of Applied Mathematics and Physics, 4(10), 1899-1905.

Purewal, S. (2020). A brief history of pi. PCWorld. Retrieved from https://www.pcworld.com/article/191389/a-brief-history-of-pi.html

Rajput, D. (2016). PI-The Value and its Origin.