## Saturday, November 10, 2012

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

Interior view of the Hall of  Abencerrajes @ Alhambra

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.

Developing the roof framing plan is pretty straight forward if you use polygon roof framing geometry. The hip rafter is base on a polygon with 4 sides and the valley rafter is based on a polygon with 8 sides.

Using the Rafter Tools for Android app select the Polygon Rafter Angles calculator and enter 4 for the Number of Sides of Polygon to calculate the angles for the hip rafter and use number of sides = 8 for the valley rafter slope angle. These angles can also be found on the Chappell Master Framing Square.

Octagon 8 Sides
2 - Squares Rotated in Circle

110.2128 = ( 144 × sin(45 ) ) ÷ sin(112.5)

Dodecagon - 12 sides
3 - Squares Rotated in Circle

Adjacent Radius = ( 144 × sin( 45 ) ) ÷ sin( 120)
117.5755 = ( 144 × sin( 45 ) ) ÷ sin( 120)

4 - Squares Rotated in Circle
Adjacent Radius = ( 144 × sin( 45 ) ) ÷ sin( 124.08620)
122.4619 = ( 144 × sin( 45 ) ) ÷ sin( 124.08620)