Golden Mean And The Pentagon
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Transcript of Golden Mean And The Pentagon
![Page 1: Golden Mean And The Pentagon](https://reader035.fdocument.org/reader035/viewer/2022062220/5557795ed8b42ad4278b4610/html5/thumbnails/1.jpg)
Golden Mean and the pentagon_
Stonemasonry technical skills
atSkillsTech Australia
![Page 2: Golden Mean And The Pentagon](https://reader035.fdocument.org/reader035/viewer/2022062220/5557795ed8b42ad4278b4610/html5/thumbnails/2.jpg)
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](https://reader035.fdocument.org/reader035/viewer/2022062220/5557795ed8b42ad4278b4610/html5/thumbnails/3.jpg)
Step 1: Draw vertical and horizontal centerlines at page centre right, intersecting at point A
![Page 4: Golden Mean And The Pentagon](https://reader035.fdocument.org/reader035/viewer/2022062220/5557795ed8b42ad4278b4610/html5/thumbnails/4.jpg)
Step 2: Construct a circle centred at A with radius 1 [1 x 100mm]
![Page 5: Golden Mean And The Pentagon](https://reader035.fdocument.org/reader035/viewer/2022062220/5557795ed8b42ad4278b4610/html5/thumbnails/5.jpg)
Step 3: Construct a double square with side 1 [1 x 100mm]
![Page 6: Golden Mean And The Pentagon](https://reader035.fdocument.org/reader035/viewer/2022062220/5557795ed8b42ad4278b4610/html5/thumbnails/6.jpg)
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](https://reader035.fdocument.org/reader035/viewer/2022062220/5557795ed8b42ad4278b4610/html5/thumbnails/7.jpg)
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](https://reader035.fdocument.org/reader035/viewer/2022062220/5557795ed8b42ad4278b4610/html5/thumbnails/8.jpg)
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](https://reader035.fdocument.org/reader035/viewer/2022062220/5557795ed8b42ad4278b4610/html5/thumbnails/9.jpg)
Step 7: Step off CF around the circle and join the points to form a pentagon
![Page 10: Golden Mean And The Pentagon](https://reader035.fdocument.org/reader035/viewer/2022062220/5557795ed8b42ad4278b4610/html5/thumbnails/10.jpg)
Step 8: Construct the Golden Rectangle AC : AD = 1: so that (a+b) : a = a : b
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