Hirota Yano

Golden Ratio / Silver Ratio calculator

  • Round off to the fourth decimal place.
日本語 / English

Golden ratio (1:1.618)

Silver ratio (1:1.414)

Golden Ratio

1:1+521:{\dfrac {1+{\sqrt {5}}}{2}}

The approximate value is 1: 1.618, about 5: 8 or 8:13.

It seems Anyway beautiful ratio. It has been used for buildings and works of art since ancient times. Approximate values often appear in nature.

  • Artificial objects: Parthenon, Mona Lisa, Thirty-six Views of Mt. Fuji, Apple’s logo, etc.
  • Natural world: Nautilus shell spiral, sunflower seed spiral, typhoon and nebula vortex, etc.

The shape of this tool is a rectangle with a golden ratio of sides.

golden rectangle

φ=1+52φ={\dfrac {1+{\sqrt {5}}}{2}}

φ (phi) is the positive solution of x2−x−1=0x^{2}-x-1=0 and is called the golden number.

Silver Ratio

There are the following two silver ratios.

  1. 1:1+2{\textstyle 1:1+{\sqrt {2}}} - This is one of the precious metal ratios.
  2. 1:2{\textstyle 1:{\sqrt {2}}} - This is used for paper dimensions and so on.

This tool deals with the latter 1:2{\textstyle 1:{\sqrt {2}}} . For some reason, it is said that the Japanese prefer the silver ratio to the golden ratio, and it has been used in buildings for a long time.
e.g. Horyu-ji and Five-storied Pagoda, Choju-Giga, Tokyo Sky Tree, Doraemon, etc.

The shape of the tool is a rectangle of silver ratio. All rectangles have a silver ratio. This is the standard for paper such as A size and B size.

silver rectangle