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Maths Coursework by Yasir Al-Wakeel The Phi-Function A Function in mathematics is the term used to indicate the relationship or correspondence between two or more quantities. It was first used in 1637 by a French mathematician by the name of Rene Descartes to designate a power xn of a variable x. Later, Gottfried Wilhelm Leibniz in 1694 applied the term to various aspects of a curve, such as its slope. The most widely used meaning until quite recently was defined in 1829 by the German mathematician Peter Dirichlet. Dirichlet conceived a function as a variable y, called the dependent variable, having its values fixed or determined in some definite manner by the values assigned to the independent variable x, or to several independent variables x1, x2, ..., xk. The Phi-Function is a means of breaking down numbers. It is defined as the number of positive integers less than n,...

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