lunababy_moonchild wrote:.... the word tiles conjures up bathroom or kitchen .... these tiles are uniform in shape i.e. all are square or rectangle .... that does ensure "completely covering" and "no overlap" ....

Did you know that it is possible to tile (i.e. completely and no overlap) a plane with two different sizes of square tiles? I'm not talking about obvious or ham-handed methods, such as one size for the north half of the room and the other size for the south half, or striping. I'm talking about actual chessboard-style tiling:

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` ┌─────────┬──┐`

│ │ │

│ ├──┴──────┐

│ │ │

┌──┤ │ │

│ │ │ │

├──┴──────┬──┤ │

│ │ │ │

│ ├──┴──────┬──┤

│ │ │ │

│ │ ├──┘

│ │ │

└──────┬──┤ │

│ │ │

└──┴─────────┘

Far from a perfect rendering (it would have worked perfectly on an MS-DOS screen) but you get the idea (I hope). The above pattern can be repeated as far as desired, left, right, up, or down.

The ratio between the sides of the two square sizes -- 1/2, 1/3, 3/5, etc -- is not important. It does not even have to be rational. The same idea works no matter what the ratio.

I actually saw this done once, on the floor of the lobby at a Hilton at 94th and Cicero in suburban Chicago.

Bill Smythe