Golden Ratio in an Irregular Pentagon, Construction I

The following construction has be devised by Bui Quang Tuan:


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'.

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at, download and install Java VM and enjoy the applet.

What if applet does not run?

Some properties of so constructed pentagon ABCDE are discussed elsewhere. There is an additional construction of pentagons of this kind.

|Activities| |Contact| |Front page| |Contents| |Geometry|

Copyright © 1996-2018 Alexander Bogomolny