Why quadratic equations can save your life

The fit between the ellipse, described by a quadratic equation, and nature seemed quite remarkable at the time. It was as though nature said: "Here is a curve that people know about, let's make some use of it." Understanding why this was the right curve had to wait till Galileo and then Newton. The answer is perhaps the single most important reason that quadratic equations matter so much: it is the link between quadratic equations and acceleration. It was Galileo who first spotted this link at the beginning of the 17th century.

Most people have heard of Galileo, a colourful Professor of Mathematics at the University of Pisa. The final part of his career centred on an epic battle with the Spanish Inquisition on the validity of the Copernican view of the solar system. However, before this he devoted much of his life to a study of how things move. Long before Galileo, the Greek scientist Aristotle had stated that the natural state of matter was for it to be at rest. Aristotle also said that heavier objects fell faster than lighter ones. Galileo challenged both of these pieces of accepted wisdom. At the heart of Galileo's work was an understanding of dynamics, which has huge relevance to such vital activities as knowing when (and how) to stop our car and also how to kick a drop goal

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- 101 uses of a quadratic equation

See also Applications of differential equations