Golden Mean and the pentagon _ Stonemasonry technical skills at SkillsTech Australia

Method Construct a double square rectangle side: length = 1 : 2 [100mm : 200mm] Using Pythagoras’ Theorem, prove that its diagonal has a length equivalent to [224mm] Use the half diagonal to produce a Golden Rectangle side: length = 1: = 1: φ [100mm: 162mm] Discuss the Golden Mean (a+b): a = a: b Use the half diagonal to inscribe a pentagon in a circle with radius = 1. Golden Mean and the Pentagon

Method

Construct a double square rectangle side: length = 1 : 2 [100mm : 200mm]

Using Pythagoras’ Theorem, prove that its diagonal has a length equivalent to [224mm]

Use the half diagonal to produce a Golden Rectangle side: length = 1: = 1: φ [100mm: 162mm]

Discuss the Golden Mean (a+b): a = a: b

Use the half diagonal to inscribe a pentagon in a circle with radius = 1.

Step 1: Draw vertical and horizontal centerlines at page centre right, intersecting at point A

Step 2: Construct a circle centred at A with radius 1 [1 x 100mm]

Step 3: Construct a double square with side 1 [1 x 100mm]

Step 4: Join the diagonal of the double square from top right to bottom left, intersecting the horizontal line at point B

Step 5: Centre compasses at point B and with radius BC = scribe semicircular arc BDE

Step 6: Centre compasses at point C and with radius CE scribe an arc to intersect the circle at point F

Step 7: Step off CF around the circle and join the points to form a pentagon

Step 8: Construct the Golden Rectangle AC : AD = 1: so that (a+b) : a = a : b