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History of Continued Fractions and Padé Approximants
The history of continued fractions is certainly one of the longest among those of mathematical concepts, since it begins with Euclid's algorithm for the great est common divisor at least three centuries B.C. As it is often the case and like Monsieur Jourdain in Moliere's "Ie bourgeois gentilhomme" (who was speak ing in prose though he did not know he was doing so), continued fractions were used for many centuries before their real discovery. The history of continued fractions and Pade approximants is also quite im portant, since they played a leading role in the development of some branches of mathematics. For example, they were the basis for the proof of the tran scendence of 11' in 1882, an open problem for more than two thousand years, and also for our modern spectral theory of operators. Actually they still are of great interest in many fields of pure and applied mathematics and in numerical analysis, where they provide computer approximations to special functions and are connected to some convergence acceleration methods. Con tinued fractions are also used in number theory, computer science, automata, electronics, etc ...
Opium’s Long Shadow
The League of Nations Advisory Committee on the Traffic in Opium and Other Dangerous Drugs, created in 1920, culminated almost eight decades of political turmoil over opium trafficking, which was by far the largest state-backed drug trade in the age of empire. Opponents of opium had long struggled to rein in the profitable drug. Opium’s Long Shadow shows how diverse local protests crossed imperial, national, and colonial boundaries to gain traction globally and harness public opinion as a moral deterrent in international politics after World War I. Steffen Rimner traces the far-flung itineraries and trenchant arguments of reformers—significantly, feminists and journalists—who viewed op...
