Monday, December 31, 2012

Daisy Wheel Compass Geometry or Euclidean six point geometry

In the 10th century Persian mathematician Abul Wafa al-Buzjani at Baghdad wrote the treatise "On Those Parts of Geometry Needed by Craftsmen". Abul Wafa al-Buzjani writes about six point geometry and other types of geometry needed by craftsmen. You can see some of this geometry each time you step on your Persian rug and count the 3, 4, 5, 6, 7, 8, 10, 12, 16 or 24 point geometric shapes in the rug. Islamic geometry shows the influence that Euclid, Vitruvius, Archimedes had on Islamic mathematics after the late 8th century translation of Euclid's Elements into Arabic in Baghdad. Archimedes and Apollonius of Perga books on Conics, who named the conic section, ellipse, parabolas, hyperbolas , were also translated from Greek to Arabic and may be the reason for the medieval builders using conic and spherical geometry for their vaults instead of the Romanesque barrel vaults or groin vaults. Were medieval 
masons and carpenters, that used the daisy wheel geometry, influenced by the books from Baghdad?   Is the Elucidation of the 6 point geometry self evident ? 

Rotating the Euclidean six point  geometric drawing will result in a daisy wheel compass.
 It could have been used by carpenters to design hexagon or octagonal timber frames.

Trigon 3 sides Equilateral

Hexagon with 6 sides.

Square 4 sides.

Octagon 8 sides.

Dodecagon 12 sides.

Icosikaitetragon 24 sides

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