FractionalGeometry-Chap2

Prob 246 in the unit square s sketch all those

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Unformatted text preview: 8/27 we find x1 = 4/13. Similar calculations give x2 = 10/13 and x3 = 12/13. Applying Prop. 2.4.1, we see these points x1 , x2 , and x3 constitute a 3-cycle in the sense that T2 (x1 ) = x2 , T2 (x2 ) = x3 , and T1 (x3 ) = x1 . PrxsSol 2.4.2 These forbidden compositions mean the length 2 addresses 11, 21, 31, and 41 are empty. Following the reasoning of Example 2.4.2, we see that every address containing 11, 21, 31, or 41 must be empty. These addresses are of two kinds, illustrated by length 3 addresses. For example, addresses of the form 11i belong to subsquares of 11, necessarily empty because 11 is empty. In general, address digits appended to the right of a forbidden address ij · · · k refer to subregions of the forbidden address ij · · · k , and so needn’t be listed separately. On the other hand, appending address digits to the left of a forbidden address ij · · · k often gives addresses of regions that are not subregions of ij · · · k , and these should be listed separately. See Fig. 2.30. The forbidden addresses...
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This document was uploaded on 02/14/2014 for the course MATH 290B at Yale.

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