Mathematics Historical Report - Pythagoras

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Historical/Cultural Report
Famous Mathematician: Pythagoras

Pythagoras’ Theorem is actively used and is a crucial part of trigonometry in present-day mathematics. Pythagoras, living approximately from 570 – 495BC, in Greece, is believed to have founded the Pythagoras’ Theorem among a cult, which Aristotle believed to be the beginning of an advance in Mathematics. In fact, there is evidence that the theorem had been discovered and used perhaps a thousand years earlier than Pythagoras by the ancient Chinese (Haylock, 2010). Although there is dissent among the issue of who constructed the Theorem, it plays a fundamental role in today’s mathematics, particularly in measurements and equipment. It also led into the study of Geometry and trigonometry, having a central bearing as a base on its development.

The rule of Pythagoras is applied to determine an unknown side in right angled triangles, or to express that the triangle shown is a right-angled triangle. A right-angled triangle contains a right angle (90°) and the theorem includes an equation to determine whether a triangle is or isn’t right-angled.

Haylock (2010) also identifies a concept, as the Pythagorean triple as three natural numbers that could be the lengths of the three sides of a right-angled triangle. For example, 5, 12 and 13 form a Pythagorean triple because 52 + 122 = 132. Other well known examples of Pythagorean tripes are 3, 4, 5 (because 9 + 16 = 25) and 5, 12, 13 (because 25 + 144 = 169).

As mentioned earlier, there are a range of real life scenarios wherein Pythagoras’ Theorem is used. Naturally, one individual would not be faced with all these scenarios, instead a range of individuals in their respective fields, could use Pythagoras’ Theorem on a daily basis. Students are the first collective group that is faced with the Theorem on a daily basis as they study geometry and trigonometry. They are exposed to a range of equations that require them to work through step-by-step. The following examples are a few selected from how Pythagoras is used in daily life. a) Finding the length of a ladder needed to reach your roof. Most households face this issue and there is reassurance knowing that there is a direct calculation accessible that can help in retrieving the answer. Students may be able to test this as an experiment and use a practical approach to retrieve answers. This scenario can be applicable in many situations; in the classroom, in the home environment, at a hardware store etc. b) In a baseball game, finding the distance between base 2 and home run. When watching a baseball game, the distance that the ball needs to be thrown from base 2 to the home plate, may interest many members of the audience, particularly many boys in the classroom environment. The theorem allows for this distance to be calculated in a simple method. This distance (hypotenuse) is easily found out, as the value of both sides remains the same at any baseball field, while also containing 90° angles. In order to explain the theorem, a sports field is a prudent excursion that can help students understand and apply the equation to their daily lives. c) While two friends are navigating between point A, B and C, determining whether the triangle given is a right angled triangle, and subsequently, the distance between them both. If Bob is waiting for his friend at point A, and Harry, his friend is at point B, how far are they from each other? Furthermore, which direction should they roughly walk towards to meet each other? Pythagoras allows for the friends to realize how far they need to travel before meeting each other, and using further concepts of trigonometry, can determine at which angle they need to travel. d) In architecture and design, determining the length of a leg when the other leg and longer side (hypotenuse) is known. If a ramp is being designed, and...
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