The quadratic formula3/15/2023 So, if someone wanted a loft with a certain shape and a certain capacity to store bales of papyrus, the engineer would go to his table and find the most fitting design. This method works much like we learn the multiplication tables by heart in school instead of doing the operation proper. It is known that the Egyptian wisemen (engineers, scribes and priests) were aware of this shortcoming - but they came up with a way to circumvent this problem: instead of learning an operation, or a formula that could calculate the sides from the area, they calculated the area for all possible sides and shapes of squares and rectangles and made a look-up table. We have to note, in this context, that Egyptian mathematics did not know equations and numbers like we do nowadays it is instead descriptive, rhetorical and sometimes very hard to follow. The first aspect that finally led to the quadratic equation was the recognition that it is connected to a very pragmatic problem, which in its turn demanded a 'quick and dirty' solution. And so, this is the original problem: a certain shape 1 must be scaled with a total area, and in the end what's needed is lengths of the sides, or walls to make a working floor plan. However, they didn't know how to calculate the sides of the shapes - the length of the sides, starting from a given area - which was often what their clients really needed. They also found out how to calculate the area of more complex designs like rectangles and T-shapes and so on. They knew that it's possible to store nine times more bales of hay if the side of the square loft is tripled. The Original Problem 2000(or so)BCĮgyptian, Chinese and Babylonian engineers were really smart people - they knew how the area of a square scales with the length of its side. Some mathematical background may be of use to fully understand the described development, however the maths used in this Entry will be kept at a necessary minimum. This Entry will strictly concentrate on the historical development of the quadratic formula. The so-called quadratic formula has been derived in the course of a few millennia to its current form, which is taught to most of us in school. Instead, parallel developments, interconnections and confluences can be found, which - to complicate this stuff even further - are also interrelated with social, cultural, political and religious matters. Using the quadratic formula as an example, it will be shown that the historical development of mathematics is not at all rectilinear. This brings about the common notion that its historical development is similarly as continuous, logical and rectilinear: one mathematician picking up an idea where another mathematician left it. The development, or derivation, of a mathematical idea is usually as logical, deducible and rectilinear as possible. Gives the solution to a generic quadratic equation of the form: This is the quadratic formula, as it is taught to most of us in school: Where did this formula come from? Why did older civilizations need to solve equations of this form in the first place? The following article, taken from h2g2, explores the origins of this famous formula. This formula allows you to find the root of quadratic equations of the form: ax 2 + bx + c = 0. For those students in high school, and even some younger, we are familiar with the quadratic formula, "the opposite of b, plus or minus the square root of b squared minus 4ac, all divided by 2a".
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