Mathematical recreations and essays . s every bridge in it once and only once and return to the starting point. The town is built near the mouth of the river Pregel,which there takes the form indicated below and includes theisland of Kneiphof. In the eighteenth century there were(and according to Baedeker there are still) seven bridges inthe positions shown in the diagram, and it is easily seen thatwith such an arrangement the problem is insoluble. Eulerhowever did not confine himself to the case of Konigsberg, butdiscussed the general problem of any number of islands con-nected in any way by
Mathematical recreations and essays . s every bridge in it once and only once and return to the starting point. The town is built near the mouth of the river Pregel,which there takes the form indicated below and includes theisland of Kneiphof. In the eighteenth century there were(and according to Baedeker there are still) seven bridges inthe positions shown in the diagram, and it is easily seen thatwith such an arrangement the problem is insoluble. Eulerhowever did not confine himself to the case of Konigsberg, butdiscussed the general problem of any number of islands con-nected in any way by bridges. It is evident that the question * * Solutio problematis ad Geometriam situs pertinentis, CommentariiAcademiae Scientiarum Petropolitanae for 1736, Petrograd, 1741, vol. viii,pp. 128—140. This has been translated into French by M. Ch. Henry; seeLucas, vol. I, part 2, pp. 21—33. CH. IX] UNICURSAL PROnrEMS 171 will not be affected if we suppose the islands to diminish topoints and the bridges to lengthen out. In this way we. ultimately obtain a geometrical figure or network. In theKonigsberg problem this figure is of the shape indicated below,the areas being represented by the points A, B, C, D, and thebridges being represented by the lines /, m, n,p, q, r, s.
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