. Mathematical recreations and essays. Mathematical recreations; Geometry; Bees; Cryptography; Ciphers; String figures; Magic squares. 180 UNICURSAL PROBLEMS [CH. IX in the route given above the double-two can be put between 0-2 and 2-3 or between 1-2 and 2-4). Hence the total number of unicursal arrangements of the 15 dominoes is 2"a. If we arrange the dominoes in a straight line, then as we may begin with any of the 15 dominoes, the total number of arrangements is a. We have next to find the number of unicursal routes of the pentagon delineated above in figure A. At the node 0 th
. Mathematical recreations and essays. Mathematical recreations; Geometry; Bees; Cryptography; Ciphers; String figures; Magic squares. 180 UNICURSAL PROBLEMS [CH. IX in the route given above the double-two can be put between 0-2 and 2-3 or between 1-2 and 2-4). Hence the total number of unicursal arrangements of the 15 dominoes is 2"a. If we arrange the dominoes in a straight line, then as we may begin with any of the 15 dominoes, the total number of arrangements is a. We have next to find the number of unicursal routes of the pentagon delineated above in figure A. At the node 0 there are four paths which may be coupled in three pairs. If 01 and 0 2 are coupled, as also 0 3 and 0 4, we get figure B. If 01 and 0 3 are coupled, as also 0 2 and 0 4, we get figure G. If 0 1 and 0 4 are coupled, as also 0 2 and 0 3, we get figure Figure B. Figure G. Figure D. Let us denote the number of ways of describing figure B by b, of describing figure G by c, and so on. The effect of suppressing the node 0 in the pentagon A is to give us three quadrilaterals, B, G, D. And, in the above notation, we have a = b + c + d. Take any one of these quadrilaterals, for instance D. We can suppress the node 1 in it by coupling the four paths which meet there in pairs. If we couple 1 2 with the upper of the paths 14, as also 13 with the lower of the paths 1 4, we get. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Ball, W. W. Rouse (Walter William Rouse), 1850-1925. London, Macmillan
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Keywords: ., bookcentury1900, bookdecade1920, booksubjectgeometry, bookyear192
