Common Measures, Highest Common Factors and the Game of Euclid

A. Gardiner
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A. Gardiner: University of Birmingham, Department of Mathematics

Chapter Chapter II.3 in Infinite Processes, 1982, pp 40-50 from Springer

Abstract: Abstract In Chapter II. 1 we gave an indirect proof of the non-existence of a common measure for certain pairs of line segments (such as the side and diagonal of a square). In this chapter we shall develop a direct, constructive procedure for finding a common measure of two segments when a common measure exists. In the next chapter we shall complement the discussion of Chapter II. 1 by using this constructive procedure to give a second proof that the side and diagonal of a square do not have a common measure.

Date: 1982
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DOI: 10.1007/978-1-4612-5654-0_5

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