Hexafoil

A hexafoil is a traditional element of Gothic architecture, created by overlapping six circular arcs to form a flower-like image.

One common form of the hexafoil has a ring of six tangent circles circumscribed by a larger circle. It may be constructed by compass and straightedge, by drawing six circles at the centers of a regular hexagon, with diameter equal to the side of the hexagon. The inner circles of the hexafoil have radius 1/3 that of the outer circle containing them, from which it is possible to derive the area and perimeter of the figure as a mathematical exercise.

Hexafoil designs are known to have links to folk magic practices in various countries, including the United Kingdom and Australia, where a six leaf design with concentric circles have been found in homes and occasionally in public buildings.

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