Golden Ratio / Silver Ratio calculator

Golden Ratio

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.

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

Silver Ratio

There are the following two silver ratios.

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

This tool deals with the latter ${\textstyle 1:{\sqrt {2}}}$ . 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.