New Mathematical Pastimes

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Not only so, but nine triangles may be selected so as to reproduce it on three times the scale and sixteen triangles may be chosen so as to reproduce it on four times the scale, as in fig. 5 1 where arrangement a reproduces triangle b on four times the scale.
Also in the case of the set of 24 right-angled triangles con- nected with four colours, not repeatable, we can select four triangles with the same result as in fig. 51 c and d. The same property is possessed by the squares associated with
...non-repeatable colours as shewn in fig. 51 e and/^ Fig. 51.
PASTIMES BASED UPON THE REGULAR HEXAGON As our degrees are in order distant, So the degrees of our strengths are discrepant.
Heywood's Spider and Flie, 1556.
36. The compartments of the hexagon in the first row of fig. 52 are numbered in circular order. We must define some law with regard to the numbers, or to the colours which they may denote, which leads to a convenient number of hexagons.
If we have six different colours upon each hexagon we are led to a set of 120 because, placing a particular colour, say 6, upper- 4 8 NEW MATHEMATICAL PASTIMES most, we can permute the remaining colours in 5x4x3x2x1 different ways.


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