HistoryoftheQuadraticEquationSketch.pptVIP

History of the Quadratic EquationSketch 10 By: Stephanie Lawrence Jamie Storm Introduction Around 2000 BC Egyptian, Chinese, and Babylonian engineers acquired a problem. When given a specific area, they were unable to calculate the length of the sides of certain shapes. Without these lengths, they were unable to design a floor plan for their customers. Preview Egyptian way of finding area Babylonian and Chinese method Pythagoras’ and Euclid’s contribution Brahmagupta’s Contribution Al-Khwarzimi’s Contribution Egyptian’s Contribution Their Problem Babylonian and Chinese Contribution Started a method known as completing the square and used it to solve basic problems involving area. Babylonians had the base 60 system while the Chinese used an abacus. These systems enabled them to double check their results. Pythagoras’ and Euclid’s Contribution In search of a more general method Brahmagupta’s Contribution Indian/Hindu mathematician Gives an almost modern solution of the quadratic equation, allowing negatives Brahmagupta’s formula: s=a+b+c+d 2 s=semiperimeter Al-Khwarizmi’s Contribution An Arab Mathematician Al-Khwarizmi’s Contribution Gave a classification of the different types of quadratics which include: The Discussion Ex: One square and ten roots of the same are equal to thirty-nine dirhems. (i.e. What must be the square that when increased by ten of its own roots, amounts to thirty-nine?) Can you Show this Geometrically? We draw a square with side x and add a 10 by x rectangle. Back to The Discussion X is the unknown; the problem translates to x2+10x=39 Try One One square and 6 roots of the same are equal to 135 dirhems. (i.e. What must be the square which, when increased by 6 of its own roots amounts to 135?) Extra Information Methods and justifications became more sophisticated over time From the 9th Century to the 16th Century, almost all algebra books started their discussions of quadratic equations with Al-Khwarizmi’s example In