A continued fraction is a mathematical expression written as a fraction whose denominator contains a sum involving another fraction, which may itself be simple or itself a continued fraction. If the process of nesting fractions this way terminates in a simple fraction the result is called a finite continued fraction, and if it continues indefinitely the result is an infinite continued fraction; the special case in which every numerator equals one and every denominator is a positive integer is called a simple, or regular, continued fraction. Any positive rational number can be written as a finite simple continued fraction, and any positive irrational number can be written as an infinite simple continued fraction. Different fields of mathematics favor different terminology: in number theory the unqualified term continued fraction usually means a simple continued fraction, with the broader case called a generalized continued fraction, while in complex analysis and numerical analysis the unqualified term usually refers to the broader, general case.
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Source Wikipedia: Continued fraction
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1. Wikipedia: Continued fraction
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Nearly two thousand years passed before Bombelli (1579) devised a technique for approximating the roots of quadratic equations with continued fractions in the mid-sixteenth century.
In Branch: Number Theory, Lead paragraph
In number theory, the unqualified term continued fraction usually refers to simple continued fractions, whereas the general case is referred to as generalized continued fractions.
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