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Front page > Geometry based on Silver Ratio and Golden Ratio > Plane Filling with the Golden Rhombus and the Silver Square Rhombus
Geometry based on Silver Ratio and Golden Ratio

Plane Filling with the Golden Rhombus and the Silver Square Rhombus

The ratio  1 : \frac{1 + \sqrt{5}}{2}   is called the Golden Ratio and the ratio 1 : \sqrt{2}  is called the Silver Ratio. The square of the Silver Ratio is 1:2 and this ratio is called the Silver Square Ratio. On the other hand, a rhombus has a short diagonal and a long diagonal. If the length of these diagonals is in the Golden Ratio, the rhombus is called the Golden Rhombus and, if it is in the Silver Square Ratio, the rhombus is called the Silver Square Rhombus.

Plane filling with the Golden Rhombus and the Silver Square Rhombus

At the end of June, 2010, the author discovered that the combination of the Golden Rhombus and the Silver Square Rhombus enables the plane filling. This new finding is described in this paper.

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

Plane filling with the Golden Rhombus and the Silver Squared Rhombus Apr13 12

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