Essay Example on the Pythagorean Theorem: A Pillar of Mathematics.

Introduction

A theorem can be referred to as a statement or position on something evident by a chain of reasoning or truth on a certain idea and is mostly represented by the use of symbols or formulae (Maor, 2019). Theorems represent certain principles in theories and can be proven to be true. Moreover, the idea can be used in various fields, including mathematics and physics (Maor, 2019). Notably, the Pythagorean Theorem makes the pillar of trigonometry, algebra, and also calculus. Also, it helps us in understanding the relationship between measurements of sides of a right angle (Ribenboim, 2008). For instance, the adjacent sides of a given triangle, the right angle, and its hypotenuse. Fermat's Last Theorem revolves around mathematical integers in an equation. Theorems can be applied in our real-life situations, including architecture, constructions, navigations, surveying of landscapes, measuring square angles, and so forth (Ribenboim, 2008). This paper seeks to look at the history of Pythagorean Theorem and Fermat’s Last Theorem and how they can be used in real-life situations.

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Step 1. Investigate and display 1

Pythagorean theorem is recorded in history as one of the oldest theorems in the history of civilization (Zhang & Yu, 2009). This theorem was formulated and named by the popular Greek mathematician known as Pythagoras, who is believed to be born 569 B.C. He believed that numbers ruled the universe, and he wrote many geometric proofs. Pythagoras is documented as the founder of the Pythagorean School of mathematics in Italy, and that is why he is still referred to as the greatest mathematician and philosopher (Ribenboim, 2008). It is recorded that Pythagoras was elated when he discovered this theorem; he even offered an n oxen sacrifice to show appreciation for the hard work. According to Sierpinski (2003), the Pythagorean Theorem is all about the triangles forming a right angle whereby the area of the square built upon the hypotenuse of a right triangle is equal to that of the squares in the remaining sides. Two hundred years later, a Greek mathematician called Eudoxus developed a way to counter what Pythagoras proposed. Eliudis recorded as the first person to name and prove Book 1 and proposition 47, which is now popularly referred to as Eliud 1 47. The Pythagorean Theorem is traced to Babylon and Egypt beginning of 1900 B.C, whereby the first results were first shown on a 4000-year-old Babylonian Tablet currently referred to as the Plimpton 322 (Maor, 2019). It is also believed that as far as 1000 B.C.E, the Chinese people used this theorem.

Step 2. Investigate and display 2

Fermat’s Conjecture states that no three positive integers a, b, and c can fulfill the equation an + bn = cn for any integer with a value bigger than 2. According to Ribenboim (2008), it is recorded that at around 1637, Fermat investigated the famous Pythagorean Theorem and noted down in the margin of a book because he did not have enough space to proof his proponents that an + bn = cn as a general equation had no solutions in the positive integers especially if n represented an integer that is greater than 2. This is the reason why his claims later came to be referred to as the Fermat's Last Theorem, which stood a test of time unresolved for at least three centuries. Later on, great strides were made when a great mathematician by the name Andrew wiles finally proved Fermat’s theorem in 1994, which can be equated to 350 years since it was first proposed (Maor, 2019). According to Cornell et al. (2013), Fermat’s last theorem remains very significant because it was so difficult to prove that it could be applied to any infinite number in a given equation where n is deemed to be a number greater than 2.

Step 3. Analyze

Comparisons and Contrasts between Pythagorean Theorem and Fermat’s Last Theorem.

Step 4. Observe and Collect

Mathematics makes part of our daily lives and can be applied in every activity (Cornell et al., 2013). Pythagorean theorem is known as a geometrical theorem, while Fermat’s last theorem is an integer’s theorem (Ribenboim, 2008). There are several ways these theorems can be used in real-life applications. For example, the PythagoreanTheoremand Fermat’s Last Theorem can be used in,

Architecture and construction work- An architect is required to calculate the length of all diagonals connecting them (Ribenboim, 2008). Be it when constructing a house, you may need to know the length of your roofing to that of the walls so that you can provide the right materials to support each angle.

For Navigation of distance whereby you can use different routes against time to determine the shortest and longest routes to reach a destination/point.

Fermat’s last theorem can be used in classroom sessions like physics classes. It can also be used when drawing the Elliptical curves used in the creation of digital signatures and computer encryption (Ribenboim, 2008).

Step 5. Reflect

I have sat in several lecture classes learning about mathematics. Many people find mathematics to be a very challenging subject. However, I believe the observation of real-life issues can help a great deal in understanding mathematics. For instance, when you visit the construction site and see how site engineers plan and calculate before laying the ground, this becomes a very authentic experience to anyone interested in understanding geometry and the Pythagorean Theorem. Observation helps us get hands-on experience in understanding a certain concept. Also, I believe observation prepares our minds on what real-life situations are and where the knowledge you get from school can be applied.

Conclusion

In a nutshell, theorems represent a position or statement on something and can be proven. Theorems deal with mathematics. Scholars like Pythagoras and Fermat have given their proponents on the theorems, and also mathematicians like Eliud and Andrew have gone ahead to proves some of the theorems. Pythagorean Theorem and Fermat's last theorems deal with the geometry of numbers and integers. These have helped us in understanding the relationship between measurements of sides of a right angle- for instance, the adjacent sides of a given triangle, the right angle, and its hypotenuse. Notably, Fermat's Last Theorem revolves around mathematical integers in an equation. Theorems can be applied in our real-life situations, including architecture, constructions, navigations, surveying of landscapes, measuring square angles, and so forth, knowledge from these theorems can be applied in real-life situations, including architectural works, constructions, navigations and so forth.

References

Cornell, G., Silverman, J. H., & Stevens, G. (Eds.). (2013). Modular forms and Fermat’s last theorem. Springer Science & Business Media. http://www.math.rug.nl/~top/Coverings.pdfMaor, E. (2019). The Pythagorean theorem: a 4,000-year history. Princeton University Press.

Ribenboim, P. (2008). Fermat’s last theorem for amateurs. Springer Science & Business Media.

Sierpinski, W. (2003). Pythagorean triangles (Vol. 9). Courier Corporation

ZHANG, X. Y., & YU, P. (2009). Hierarchical Ordering of Schematic Knowledge Relating to Pythagorean Theorem Problems——the Explanation Based on Relational-representational Complexity Model [J]. Journal of Mathematics Education, 4. http://en.cnki.com.cn/Article_en/CJFDTotal-SXYB200904014.htm