Mathematical recreations and essays . 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, Eulers problem consists therefore in finding whether agiven geometrical figure can be described by a point movingso as to traverse every line in it once and only once. A moregeneral question is to determine how many strokes are neces-sary to describe such a figure so that no line is traversed twice:this is covered by th
Mathematical recreations and essays . 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, Eulers problem consists therefore in finding whether agiven geometrical figure can be described by a point movingso as to traverse every line in it once and only once. A moregeneral question is to determine how many strokes are neces-sary to describe such a figure so that no line is traversed twice:this is covered by the rules hereafter given. The figure maybe either in three or in two dimensions, and it may be repre-sented by lines, straight, curved, or tortuous, joining a numberof given points, or a model may be constructed by taking anumber of rods or pieces of string furnished at each end witha hook so as to allow of any number of them being connectedtogether at one point. The theory of such figures is included as a particular case 172 UNICURSAL PROBLEMS [CH. IX Id the propositions proved by Listing in his Topologie*. Ishall, however, adopt here the methods of Euler, and I shallbegin by giving^ some definitions, as it will enable me to putthe argument in a more concise form. A nod
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