Orion Research Institute for Metaphysics > > Logarithmic Spirals based on the Golden Ratio, Golden Square Ratio, Silver Ratio, and Silver Square Ratio

## Logarithmic Spirals based on the Golden Ratio, Golden Square Ratio, Silver Ratio, and Silver Square Ratio

At the end of June, 2010, the writer newly found out that the combination of the golden rhombus and the silver rhombus enables the plane filling. This fact shows that the Golden Ratio and the

Approximate construction of logarithmic spiral derived from the acute golden triangle

Silver  Square Ratio are closely related to each other．Earlier in 2009, the writer also discovered the mutually complementary relationship between the Golden Ratio and the Silver Ratio in the 3-dimensional space. Considering this point, this new plane filling seems to indicate that the Golden Ratio and the Silver Square Ratio are mutually complementary to each other in the 2-dimensional plane．

As already known, a logarithmic spiral is created from the golden rectangle whose side lengths are in the Golden Ratio. It is also created from the silver rectangle whose side lengths are in the Silver Ratio. Such known facts suggest that there could be other kinds of logarithmic spiral based on the Golden Ratio, Golden Square Ratio, Silver Ratio, and Silver Square Ratio. This paper describes the outcome of study on these possibilities.

For more details, please refer to the following PDF document.

Logarithmic spiral based on the Golden Ratio, Golden Squared Ratio, Silver Ratio, and Silver Squared Ratio Apr22 12

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