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An objective and practical method for describing and understanding ratios. (English) Zbl 0835.01001

The basic problem is, as the author says, to compare two lengths in a way that is independent of any measurement system, or choice of unit, or even to carry out the comparison in a purely geometrical way that does not introduce any intermediate system of units; to find those ratios of small numbers based on the Euclidean algorithm which approximate the number particularly closely; and to identify at what point the approximation procedure becomes more accurate than the tolerances in the original measurements. He discusses respectively arithmetic with ratios, incommensurable ratios and decimal fractions.

MSC:

01A20 History of Greek and Roman mathematics
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