Ad Quadratum is a convenient and profound technique in which continuous scaling of size can be given to square shapes, either from a centre or periphery. The differences in scale are multiples of the square root

of two [sqrt(2)] between two types of square: cardinal (flat) and diamond (pointed).

When a square’s diagonal touches opposite sides sides of a larger square, the two squares differ by sqrt(2) and a square becomes a diamond or visa versa. By repeating this effect a continuum can be generated to form the large patterns found in sacred buildings such as the Vedic Angkor Wat, Christian Gothic cathedrals, Islamic Dome of the Rock and even Stonehenge. The technique is therefore very ancient yet still used. Subjectively such buildings express a high degree of visual order by employing what is called a geometrical progression. Objectively, such patterns appear to convey cosmic principles known to ancient builders but largely forgotten recently.

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