NOTES TO CHAPTER 3
Figure 2.11. An inscribed right angle subtends a semicircle. side IG. We now know that the angle k FIH is 90º, and from this it immediately follows that the triangles FIG and IGH are similar. In particular, GH IG IG = = IG FG 1 and so IG = 2GH . The construction and this proof of it were known to the Greeks. 7. Julian Lowell Coolidge, The Geometry of the Complex Domain, Oxford 1924, p. 14.
CHAPTER THREE The Puzzles Start to Clear 1. It is traditional to call Wessel a Norwegian, but in fact when he was born Norway was actually part of Denmark, and he spent most of his life in Denmark, dying in Copenhagen. 2. Wessel’s paper was unearthed in 1895 by an antiquarian, and its significance recognized by the Danish mathematician Sophus Christian Juel (1855–1935). For more on this discovery, see Viggo Brun, “Caspar Wessel et l’introduction géométrique des numbres complexes,” Revue d’Histoire des Sciences et de Leurs Applications 12 (1959):19–24. 3. E. T. Bell, Men of Mathematics. Simon and Schuster 1986, p. 234. A joke on this point is the following spoof of recorded telephone company messages that electrical engineers find amusing: “You have reached an imaginary number. If you require a real number, please rotate your telephone by 90º, and try again.”
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