Tight Weave
This manipulative allows you to see the purple rug (1 yard square) and the first few stages of adding gold squares.
Click on the button at the upper right to see successive stages, and then to Reset. This manipulative allows you to see the purple rug (1 yard square) and the first few stages of adding gold squares.
It should become clear that more and more of the purple is replaced by gold, although graphics limitations make it impossible to visually represent more than a few stages of the process. We can, however, calculate the number of square yards of gold at any stage, as on page 22. Enter a whole number for any desired stage and press Calculate Area. The area is displayed as a decimal. Even though the limit of the amount of gold is obviously 1 (square yard), for sufficiently large values of n, it is displayed as the repeating decimal 0.99999... .