golden mean and the pentagon

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

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Examining the relationship between the number 1, the golden ratio 1 : φ and a pentagon

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Page 1: Golden Mean And The Pentagon

Golden Mean and the pentagon_

Stonemasonry technical skills

atSkillsTech Australia

Page 2: 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.

Golden Mean and the Pentagon

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Page 3: Golden Mean And The Pentagon

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

Page 4: Golden Mean And The Pentagon

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

Page 5: Golden Mean And The Pentagon

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

Page 6: Golden Mean And The Pentagon

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

Page 7: Golden Mean And The Pentagon

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

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Page 8: Golden Mean And The Pentagon

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

Page 9: Golden Mean And The Pentagon

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

Page 10: Golden Mean And The Pentagon

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

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