Connecting the eight points of intersection of the circle and the sides of the square form an octagon.
Roof over the Hall of Abencerrajes @ Alhambra. source: SBE Builders, Sim Ayers
Interior view of the Hall of Abencerrajes @ Alhambra. source: SBE Builders, Sim Ayers
more:
http://sbebuilders.blogspot.com/2012/11/alhambra-granada-ad-quadratum-ground.html
Just about every medieval cathedral has an octagonal baptismal and the Alhambra in Granada Spain has several octagonal ground plans. The roof over the Hall of the Abencerrajes is unique because the roof actually follows the Ad Quadratum ground plan that is used to develop the octagonal ground plan. Squares rotated in the circle.
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Medieval vaulting geometry research, links, notes and keywords
Treatise On Those Parts of Geometry Needed by Craftsmen PDF files
A lesson in Applied Geometry and Euclidean Geometry
String Theory on Medieval Masons and Carpenters drawing an Ellipse
much more:
http://www.sbebuilders.com/tools/Medieval-Vaulting-Links.html
source: SBE Builders, Sim Ayers
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