C880 Task 4

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Western Governors University *

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Mathematics

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Feb 20, 2024

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docx

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1 The History of the Quadratic Equation and Why it is Important for Students There are many concepts in High School Algebra that have a diverse history in our world. One concept that is used often in Algebra is the quadratic equation. Like many other concepts in mathematics, the quadratic equation has its background in Babylon. The history of the quadratic equation is a massive history that exceeds 4000 years. “The earliest known records are Babylonian clay tablets from about 1600 BCE where the diagonal of a unit square is given to five decimal places of accuracy” (Rogers & Pope, 2015). In Babylon, there was a clay tablet discovered that is an acceptable source for not only working with number bases, but also with irrational numbers and quadratic problems (Rogers & Pope, 2015). The Babylonians developed more of an algorithm which would in turn lead to the development of the quadratic equation. Another civilization that helped create the quadratic formula was the Islamic civilization during the 9 th century. Muhammad ibn Musa al-Khwarizmi wrote an algebra book titled The Calculation of al-Jabr and al-Muqabala, where al-jabr is the source of our current day word algebra (Allaire & Bradley, 2001). In his book he referenced six different types of quadratic equations, however all of his types were made up of positive numbers. With the different types of equations, he also gives the rule to solve them as well as a geometric proof which is our current day ‘completing the square’ (O’Connor & Robertson, 1996). A more current day example of the quadratic equation comes from the seventeenth century with the writing of the book La Géometrie by René Descartes and the eighteenth century with Thomas Carlyle. Descartes wrote about a solution for the quadratic equation by using geometry. His construction only shows the positive root. Carlyle uses Cartesian coordinates to solve the quadratic equation. With Carlyle’s method, one would graph a circle on a coordinate grid where the diameter has the endpoints (0,1) and (-b,c). The solutions would be found
2 wherever the circle intersected the x-axis or there would be no solution if there was no intersection. In order for a student to get a better understanding of a topic, sometimes it is better to know the historical background of that topic. For example, a teacher cannot teach Reconstruction without first teaching the history of the Civil War. The same is true for algebraic concepts. If a teacher were to explain the historical background of each concept before actually teaching the concept, the student would get a better understanding of how the concept was formed. Sometimes it is easier to appreciate something when you know where it started. The history can show where a concept got its name or why certain symbols are used. Teaching or explaining the background of some concepts could help a student better appreciate them because they may have a connection to the culture where the concept originated. Having this knowledge could pique the interest of even the most reluctant learner, because almost everyone appreciates where they came from. If a student were from France or knows that their ancestors originated from there, they may be interested in knowing the René Decartes was influential in the quadratic equation.
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