Golden Ratio in an Irregular Pentagon, Construction I
The following construction has be devised by Bui Quang Tuan:
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Let X, Y, Z be collinear, Y between X and Z, such that XY/YZ = φ, the golden ratio. Construct
- A reflection of Y in X,
- Choose any point D not on the line XYZ,
- C reflection of D in Z,
- C' the intersection of CY and AD,
- D' the intersection of DY and AC,
- B reflection of D in midpoint of YD',
- E = reflection of C in midpoint of YC'.
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Some properties of so constructed pentagon ABCDE are discussed elsewhere. There is an additional construction of pentagons of this kind.
Copyright © 1996-2010 Alexander Bogomolny
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