Mathematical recreations and essays . rent construction, for it can bedescribed completely by always following the hedge on oneside (either the right hand or the left hand), and no node isof an order higher than three. Unless at some point the route to the centre forks andsubsequently the two forks reunite, forming a loop in whichthe centre of the maze is situated, the centre can be reachedby the rule just given, namely, by following the wall on oneside—either on the right hand or on the left hand. Nolabjnrinth is worthy of the name of a puzzle which can bethreaded in this way. Assuming that t
Mathematical recreations and essays . rent construction, for it can bedescribed completely by always following the hedge on oneside (either the right hand or the left hand), and no node isof an order higher than three. Unless at some point the route to the centre forks andsubsequently the two forks reunite, forming a loop in whichthe centre of the maze is situated, the centre can be reachedby the rule just given, namely, by following the wall on oneside—either on the right hand or on the left hand. Nolabjnrinth is worthy of the name of a puzzle which can bethreaded in this way. Assuming that the path forks asdescribed above, the more numerous the nodes and the highertheir order the more difficult will be the maze, and thedifficulty might be increased considerably by using bridges andtunnels so as to construct a labyrinth in three an ordinary garden and on a small piece of ground, oftenof an inconvenient shape, it is not easy to make a maze whichfulfils these conditions. Here is a plan of one which I put up. in my own garden on a plot of ground which would not allowof more than 36 by 23 paths, but it will be noticed that noneof the nodes are of a high order. 188 UNICURSAL PROBLEMS [CH. IX Geometrical Trees. Eulers original investigations wereconfined to a closed network. In the problem of the maze itwas assumed that there might be any number of blind alleysin it, the ends of which formed free nodes. We may nowprogress one step further, and suppose that the network orclosed part of the figure diminishes to a point. This lastarrangement is known as a tree. The number of unicursaldescriptions necessary to completely describe a tree is calledthe base of the ramification. We can illustrate the possible form of these trees by rods,having a hook at each end. Starting with one such rod, wecan attach at either end one or more similar rods. Again,on any free hook we can attach one or more similar rods,and so on. Every free hook, and also every point where twoor
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