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The first half of the seventeenth century saw the origins of the Calculus in the work of many mathematicians dotted across Europe. They, in turn, reflected a growth of interest in five problems whi...ch go back to the Greeks, and were raised first in the modern period by Kepler: areas under curves and their volumes when rotated, tangents to curves and lengths of arc, and centres of gravity. The programme is introduced by Graham Flegg, reader in Mathematics at the Open University, and is built around the contribution of Professor Boyer of Brooklyn College, New York. The work of Galileo on the cycloid, extended by Roberval by means of a beautiful argument with infinitesimals and Huygens with evolutes is one part of the story, leading to the successful treatment of the problem of rectifying arcs. The work of Fermat and Barrow on differentiation and integration and their inverse relationship is another. The stage is then set for Newton and Leibniz, who are discussed in the unit only, and not the programme.
Module code and title: AM289, History of mathematics AM289; 07 08-08-1976 1976 00:24:00 + Show more... Jean Nunn; Neil Cleminson Carl Boyer; Graham Flegg BBC Open University Calculus; Pendulums; Quadrature; Tangents Graham Flegg introduces the programme. Stills of Newton, Leibniz and relief globe. Animation of map of Europe with mathematicians over, etc. Flegg lists five problems which occupied 17th century mathematicians and formed the basis of the calculus. Graham Flegg (voice over animation) and then Carl Boyer discuss the 'Method of Indivisibles' for finding areas under curves, used by Archimedes and rediscovered in the 17th century. The contributions of Oresme, Galileo, Cavalieri and Torricelli are briefly described. Animations are used at intervals to illustrate points. Carl Boyer and then Graham Flegg (voice over animation) describe Roberval's method for calculating the area under a cycloid. Carl Boyer introduces Fermat's tangent method Graham Flegg (voice over animation) then describes Fermat's method of tangents which had general application. Boyer discusses Pascal's contribution to various problems connected with the cycloid. Boyer goes on to examine the work of Huygens who, in the course of designing a pendulum clock, rectified the cycloidal curve. Graham Flegg (voice over animation) joins in. Boyer describes the further discoveries in rectifying various curves which were made by Van Heuraet, Wren and Neil. Graham Flegg (voice over animation) sums up the programme with a very brief discussion of Barrow's proof of the inverse relation between tangents and quadrature. 6HT/71767 00525_3181 942 no