Puzzle: Perfect rectangles, rectangle perfectly tiled with squares Squaring the rectangle

. . .

Perfect rectangles, completely tiled with squares

When you found a perfect rectangle solution, you have 3 infinite arrays::
1) A fibonacci-spiral, starting with the short side
2) A fibonacci-spiral, starting with the long side
3) Multiply all squares with the same number
(A perfect square gives 2 arrays, because 1) and 2) are equal
A solution is original or 'primarily' when it's not an element of one of the arrays above and it's not constructed of other perfect rectangles.

All following solutions are found using backtracking algorithm in Borland Delphi 6 Personal. They are ordered by length.

Solutions 1 upto 10

Solutions 11 upto 20

Solutions 21 upto 30

Links:

The prime puzzles & problems connection - geometrical dissection
University of Waterloo - Squaring the Square
mathforum puzzles

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