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| Some of us know them with affection, others only see fear and loathing in the tricky little blighters, but one thing is for sure, quadratic equations come up time and again at school and in life, often just when you never expected them. When a projectile is cast into the air, for example a stone being thrown or a cannon ball being shot, the path it takes forms a parabola. Quadratic equations can be used to describe such paths. In fact, if gravity is involved, quadratic equations are likely to be there too. They can be involved in a wide number of everyday and not-so usual things, from describing the path of a kicked football to the moon landing. The shape of a parabola created by a quadratic equation can be used in a parabolic satellite receiver or a radio telescope where the shape helps to concentrate signals at a certain point. Parabolas can be used to support architecture like bridges, buildings and other structures, and can even describe the path of a water fountain. Quadratic equations can be used to create amazing beauty too in the form of fractals. The Julia set and Mandelbrot set of fractals, which can be explored in so much depth and wonder, depend on quadratic equations for their creation. ## History of Quadratic EquationsThe history of quadratic equations can be traced back to evidence left by ancient Babylonians in clay tablets. Around the 8th century BC in ancient India the Indian mathematic Baudhayana wrote a book about geometrical rules for construction and arrangement of altars. He used quadratic equations of the form shape ax^{2} = c and ax^{2} + bx = c,
indicating methods to solve them. Around 400 BC Babylonian mathematicians used a method known as "completing the square" to solve several quadratic equations with positive roots, but they did not obtain a general formula. Euclid described a more abstract geometric method around 300 BC. A mathematical text called the Bakshali Manuscript, written in India between 200 B.C. and 400 AD developed the solution of quadratic equations further using algebra. In 9th Century Arabia,
Al-Khwarizmi independently developed a set of formulas
which worked where the answers were positive numbers.
A full solution to quadratic equations was first introduced
in Europe by Abraham bar Hiyya Ha-Nasi (known also with the Latin name
Savasorda) with his book on algebra and geometry known as the Liber
embadorum in 1145 AD.
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