Mathematics and Economics Research Paper: The History of the Quadratic Equation

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The History of the Quadratic Equation
(2519 words)
1.0 General Introduction
As taught in most high schools, the quadratic formula x1,2=(-b/2a) ± (1/2a)(b2-4ac)1/2 provides a solution to a generic equation in the form of ax2 + bx + c = 0. The development of mathematical concepts and equations take the nature of deducibility, logicality, and rectilinearity as much as possible, and the historical development of these concepts has been continuous, logical, and rectilinear. This implies that one mathematician has been picking up ideas from where another one left it. However, this paper uses a quadratic formula to show the historical development of mathematics has not followed the rectilinearity of other mathematical concepts, but there have been parallel developments, confluences, and interconnections in its development and the paper will show the interrelated social, political, cultural, and religious issues connected with the development of the quadratic equation. To explain the history of the quadratic equation, this paper reviews a brief history of the quadratic equation focusing on the Egyptian contributions, the Babylonian and Chinese input, the concepts of Pythagoras and the Euclid, the Brahmagupta’s concepts, and the Al-Khwarizmi’s ideas, and finally the ideologies of Rene Descartes. To supplement this discussion, this paper provides a discussion on the practical application of the quadratic equation in determining the sales that earn a profit to a business.
2.0 A brief history of quadratic equations
The engineers in Egypt, China, and Babylon were smart and intelligent humans who understood that the area of a square scales with its side lengths. The engineers knew that it was possible to store nine times more bales of hay by tripling the square of a loft. Besides, they understood how to compute areas of more complex designs such as T-shapes, rectangles, and many other shapes. The only problem they encountered was how to calculate the sides of the shapes, such as the length of the sides beginning from a known area. Unfortunately, this is what most of their clients required. Since this was the original problem of understanding how to scale a certain shape with the total area and knowing what is needed in terms of sides and length and the walls to make a working floor plan, it troubled the engineers to work out a method to resolve the issue (Mathnasium). This problem could be solved using a quadratic equation as understood historically and by today’s mathematicians.
Fig 1 The modern quadratic equation (Delbert)
1 Egyptian contribution
One of the most original concepts that resulted in a quadratic equation was the realization that it was related to the very pragmatic issues that as a result required a dirty and quick solution. However, Egyptian engineers did not understand numbers and equations the way they are understood by modern mathematicians. They followed rhetorical, descriptive, and hard to understand concepts. However, most Egyptian Wisemen, including priests, scribes, and engineers knew the shortcomings of these approaches and came up with methods to circumvent this issue. Instead of learning a formula ...