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Microcomputer-assisted Discoveries: Euclidean Algorithm and Continued Fractions

Clark H. Kimberling

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Abstract

Students can use microcomputers to cut through algorithms and computations to gain mathematical insights. This approach is especially true for the Euclidean algorithm, so often used to find the greatest common divisor (GCD) of two positive integers. The Euclidean algorithm also yields continued fractions, at least far enough for students to find patterns and discover truths about numbers.

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What this paper is about

Students can use microcomputers to cut through algorithms and computations to gain mathematical insights. This approach is especially true for the Euclidean algorithm, so often used to find the greatest common divisor (GCD) of two positive integers. The Euclidean algorithm also yields continued fractions, at least far enough for students to find patterns and discover truths about numbers.

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Available abstract

Students can use microcomputers to cut through algorithms and computations to gain mathematical insights. This approach is especially true for the Euclidean algorithm, so often used to find the greatest common divisor (GCD) of two positive integers. The Euclidean algorithm also yields continued fractions, at least far enough for students to find patterns and discover truths about numbers.

Key concepts: Euclidean algorithm, Greatest common divisor, Euclidean geometry, Microcomputer, Euclidean domain, Computation, Divisor (algebraic geometry), Euclidean distance

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