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# Golden Mean And The Pentagon

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

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### Golden Mean And The Pentagon

1. 1. Golden Mean and the pentagon _ Stonemasonry technical skills at SkillsTech Australia
2. 2. <ul><li>Method </li></ul><ul><li>Construct a double square rectangle side: length = 1 : 2 [100mm : 200mm] </li></ul><ul><li>Using Pythagoras’ Theorem, prove that its diagonal has a length equivalent to [224mm] </li></ul><ul><li>Use the half diagonal to produce a Golden Rectangle side: length = 1: = 1: φ [100mm: 162mm] </li></ul><ul><li>Discuss the Golden Mean (a+b): a = a: b </li></ul><ul><li>Use the half diagonal to inscribe a pentagon in a circle with radius = 1. </li></ul>Golden Mean and the Pentagon
3. 3. Step 1: Draw vertical and horizontal centerlines at page centre right, intersecting at point A
4. 4. Step 2: Construct a circle centred at A with radius 1 [1 x 100mm]
5. 5. Step 3: Construct a double square with side 1 [1 x 100mm]
6. 6. Step 4: Join the diagonal of the double square from top right to bottom left, intersecting the horizontal line at point B
7. 7. Step 5: Centre compasses at point B and with radius BC = scribe semicircular arc BDE
8. 8. Step 6: Centre compasses at point C and with radius CE scribe an arc to intersect the circle at point F
9. 9. Step 7: Step off CF around the circle and join the points to form a pentagon
10. 10. Step 8: Construct the Golden Rectangle AC : AD = 1: so that (a+b) : a = a : b