Hexafoil

Ivory mirror case containing a hexafoil

A hexafoil is a traditional element of Gothic architecture,[1] created by overlapping six circular arcs to form a flower-like image.[2][3]

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.[4] 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.[5]

References

  1. Hartop, Christopher; Norton, Jonathan (2008), Geometry and the silversmith: the Domcha Collection, John Adamson, ISBN 9780952432289, The trefoil, quatrefoil, hexafoil and octofoil, essential elements of Gothic architecture, all figure in medieval silver.
  2. Passmore, Augustine C. (1904), Handbook of Technical Terms Used in Architecture and Building and Their Allied Trades and Subjects, Scott, Greenwood, and Company, p. 178, A geometrical figure used in tracery ; it is composed of six lobes or parts of circles joining each other.
  3. Rugoff, Milton (1976), The Britannica encyclopedia of American art: a special educational supplement to the Encyclopaedia Britannica, Encyclopaedia Britannica Educational Corp., p. 636, A geometrical figure with six lobes, used as the form of a silver platter or a wooden decorative panel.
  4. Spanton, John Humphrey (1895), Science and Art Drawing: Complete Geometrical Course ; Consisting of Plane and Solid Geometry, Orthographic and Isometric Projection, Projection of Shadow's the Principles of Map Projection, Graphic Arithmetic and Graphic Statics, Macmillan, p. 56.
  5. Betz, William; Webb, Harrison Emmett; Smith, Percey Franklyn (1912), Plane Geometry, Mathematical texts for school, Ginn, p. 321.


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