Is there a simple perfect squaring of a 1366 by 768 rectangle?

geometry geometric-construction tiling rectangles art

Solution 1:

I looked through some of the data on Squaring.Net (actually, copies at the Internet Archive, since the site is currently down), and there is no $1366\times768$ simple perfect squared rectangle of order $17$ or less; there may be one of higher order, but that's harder to check. But there is a $1354\times764$ simple perfect squared rectangle of order $17$, so if you can accept a six-pixel border on the left and right and a two-pixel border at the top and bottom, this will do the job. It looks like this:

1354x764 squared rectangle (Click on the image for the full-size version.)

The Bouwkamp code for this rectangle dissection is $17\ 1354\ 764\ (389, 403, 311, 251)\ (60, 191)\ (83, 157, 131)\ (375, 14)\ (9, 74)\ (361, 65)\ (322)\ (296)$.

EDIT: As Servaes points out, I overlooked an even better $1366\times766$ alternative, also of order $17$:

1366x766 squared rectangle

Its Bouwkamp code is $17\ 1366\ 766\ (419, 288, 258, 401) (115, 143) (203, 85) (200) (179, 365) (347, 72) (275) (193, 7) (186)$.

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