By John Crossley, David Leigh-Lancaster
Explores the movement of the way rules of quantity have grown all through historical past. Illustrates many of the actual difficulties and subtleties of quantity, together with calculation, measuring, counting, and utilizing machines.
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Extra resources for Growing Ideas of Number (The Emergence of Number)
14) which is a rational number. Therefore our original r is indeed rational. 9o = 1, and similarly for any other number ending in repeated 9s. 4. This gives rise to continued fractions. John Wallis, in his book Opera Mathematica (1972), laid some of the basic groundwork for continued fractions. It was in this work that the term ‘continued fraction’ was first used. An excellent treatment can be found in Chrystal (1888–89, vol. 2). 24) Define the anthyphairesis of a and b as EA(a; b) = [q0, q1, q2 …].
On an old calculator of mine from about 1980, taking the square root twenty-three times, starting from 2, yielded the answer exactly 1. See also Deakin (2004). 1 From lines to numbers Measuring transforms lengths and other quantities into numbers. Therefore, on the one hand, it allows us to reproduce lengths and so on; on the other hand, just like counting, measuring is a homomorphism from (aspects of) the world to numbers. In this chapter, I shall consider how the idea of measuring, using numbers, developed.
By the end of the sixteenth century such styles of number were beginning to be accepted as mathematically respectable entities. Stevin (1548–1620), writing in 1585 (after the death of Bombelli, whom I treat below), has a section (Struik, 1958, vol. 532): That there are no absurd, irrational, irregular, inexplicable or surd numbers. It is a very vulgar thing among authors of arithmetics to treat numbers such as 8 and the like, which they call absurd, irrational, irregular, inexplicable, surds, etc.