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Golden Ratio. 王柏雄 B9202003 何宗祐 B9202010 吳士皓 B9202015 俞錫全 B9202036. Phi. The golden number 1.618…… One way to find Phi is to consider the solutions to the equation x = (1+ √5)/2 ~ 1.618... or x=(1- √5)/2 ~ -.618... and 1.618……is the golden number.

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Golden Ratio

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Golden ratio

Golden Ratio



Golden ratio


  • The golden number 1.618……

  • One way to find Phi is to consider the solutions to the equation

  • x = (1+√5)/2 ~ 1.618... or x=(1-√5)/2 ~ -.618...

  • and 1.618……is the golden number

Golden ratio

  • We consider the first root to be Phi. We can also express Phi by the following two series

Phi =                                                       or Phi =

Golden rectangle

Golden Rectangle

  • When we draw a rectangle that has sides A and B that are in proportion to the Golden Ratio

    Golden rectangle.

  • Golden Rectangle

    most pleasing rectangle to the eye.

Golden ratio

  • Assume that rectangle ABCD is a Golden Rectangle. Hence, AD/AB =AE/ED

  • But, FE = AE, and so FE/ED= Phi

  • Hence, rectangle FCDE is a Golden Rectangle

Golden ratio

  • If we connect the vertices of the regular pentagon, we can get two different Golden Triangles.

  • The blue and red one are all golden triangle.

Golden ratio

  • If we take the isosceles triangle that has the two base angles of 72 degrees and we bisect one of the base angles, we should see that we get another Golden triangle that is similar to the first (Figure 1).

  • we can get a set of Whirling Triangles (Figure 2).

Golden ratio and investment

Golden Ratio and Investment


Elliot’s Waves theory

Golden ratio

Above data can just be used for reference, the risk you have to take on your own if you invest in this way.

The use of golden section number in war

The Use of Golden Section Number in War

  • Strong and mysterious

  • By chance or bound to ?

  • Coincidence or regular pattern?

Golden ratio

The battle line

The compose of an army


Rate of destruction



  • If we draw a line from the center A to the edge E, it will intersect with B, C, D

  • Then we can find that

  • And it fit golden ratio!!!

Golden ratio

  • The ratio of the maple leaf’s width to it’s vein

  • The ratio of upper wings’ length to the lower one

  • They are all fit golden ratio

Are u a model

Are u a model?

  • Length from head to belly button = x

  • Length from belly button to the ground = y

  • If y/x = 1.618……

  • Congratulation!!! You can be a model.

Golden ratio

Thank you for your kind attention!

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