History of the Quadratic Equation

Beginning in the “Before Christ” era, the Babylonians were the first to have been recorded demonstrating the equation, circa 400 BC. The form most mathematics students use today is:

To solve a quadratic equation the Babylonians essentially used the standard formula, with the a term being included in the x2 variable. They considered two types of quadratic equations, namely:

Here b and c were positive but not necessarily integers. The form that their solutions took was, respectively:

Al-Khwarizmi also gave a classification system for quadratics. He devotes a chapter to each chapter in his treatise and gives methods in solving each differently:

Notice that in each case this is the positive root from the two roots of the quadratic and the one that will make sense in solving "real" problems. For example problems which led the Babylonians to equations of this type often concerned the area of a rectangle. For example if the area is given and the amount by which the length exceeds the width is given, then the width satisfies a quadratic equation and then they would apply the first version of the formula above (website one).

There are several Old Babylonian mathematical texts in which various quantities concerning the digging of a canal are asked for. They are YBC 4666, 7164, and VAT 7528, all of which are written in Sumerian ..., and YBC 9874 and BM 85196, No. 15, which are written in Akkadian ... . From the mathematical point of view these problems are comparatively simple (Muroi).

The equation is one of the most prominent ideas in mathematics, and is the center of foundation of mathematics itself: algebra. High school and college students may be taking courses of higher mathematics but have all, at one point in their studies, learned and used the quadratic formula. The idea that mathematics has changed over time is opinionative but very provable. From the beginning of time the human race has needed ways to count and manipulate quantities. Great minds throughout the years have studied their predecessors and developed theories molding mathematics and the quadratic formula into what it is today.

The Babylonians used their mathematics not in the way we do today, by teaching, but by building their civilization into what it became. Muroi speaks of how Babylonian mathematics helped create a society and how it helped the Mesopotamian region become as fertile as it was. It is for this reason that they only used positive forms in their answers. Had their use for mathematics been for reasons other than land, monetary, and other non-scientific reasons, they would have had to conclude their method with a negative result.

Other interesting aspects of the Summa was the fact that it studied games of chance. Pacioli studied the problem of points although the solution he gave is incorrect. In general, Pacioli never actually devised his own method of solving the quadratic equation, but instead published a works dealing with the history of certain aspects of mathematics, including all the great mathematicians ideas.

Overall, the quadratic formula has actually shaped civilization into the way it is today. The Babylonians used it to irrigate their land, divide out funds to pay workers, and even mobilize armies. The formula to them was not a way of learning or teaching, but a way of life. Euclid was a man of geometry. He theorized about area

Some topics in this essay:
Western Hemisphere, Middle Ages, Types Quadratics, Fra Luca, Hindu Arabic, Pisa Fibonacci, Continuing Greek, Muroi Babylonians, BC Euclid, BC Hisab, quadratic formula, quadratic equation, squares equal, roots equal, squares equal roots, pacioli's summa, = b/22, completing square, bx =, quadratic equations, middle ages, equal roots x², = b/22 +, mathematics quadratic formula, geometrical pacioli's summa,