The relationships between the number of different spacers in an arrangement of square tiles and the dimensions of the tiles in the same arrangement.
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| Submitted: Thu Jul 11 2002
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Introduction We have been given the task of investigating the relationships between the number of different spacers in an arrangement of square tiles and the dimensions of the tiles in the same arrangement. I will begin my investigation by researching square arrangements of tiles, and then move onto rectangular arrangements. I will then investigate triangle arrangements. Stage 1 - Square arrangements The spacers that will be used in this investigation are - + Spacer T Spacer L Spacer I began by drawing 5 different arrangements of tiles, beginning with a 1x1 arrangement, and finishing with a 5x5 arrangement. I drew these on a separate piece of graph paper. (See sheet S1). The results gathered from these sketches are shown here: Pattern number Number of Squares + Spacers T Spacers L Spacers 1 1 0 0 4 2 4 1 4 4 3 9 4 8 4 4 16 9 12 4 5 25 16 16 4 The rule for the number of squares is xy. The pattern for the L spacers appears to be a rule, as L spacers only occur on the corners of the...


