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GOLDEN RECTANGLE

A golden rectangle is a rectangle wherein the ratio of the its length to width is the golden ratio.  Because of this golden ratio, it has been known to be the rectangle of most aesthetic proportion.  The Parthenon has been known to be built based on this ratio. 

The golden rectangle has the property that it can be further subdivided into two portions: a square and a smaller golden rectangle, wherein the ratio of the area of the square to the smaller rectangle is the golden ratio.  Furthermore, the area of the original rectangle to the area of the square is also the golden ratio.

This smaller rectangle can similarly be subdivided into another set of smaller golden rectangle and smaller square.  And this process can be done repeatedly to produce smaller versions of squares and golden rectangles.

The golden rectangle is also related to other geometric figures.  It can be noted that the a spiral going thru vertices of the repeatedly formed golden rectangles formed an equiangular spiral.

An isocahedron, a 20 faced regular polygon and one of the 5 platonic solids, is also related to the golden rectangle.  The 12 vertices of an isocahedron can be grouped into three sets, where each set consists of 4 vertices which are vertices of a golden rectangle.  The 12 vertices also forms 3 congruent golden rectangles that are perpendicular to each other and intersect each other symmetrically.

A dodecahedron, a 12 faced regular polygon, is another one of the 5 platonic solids that is related to the golden rectangle.  The centers of the 12 faces of a dodecahedron may be grouped into three sets, where each set consists of 4 vertices which are vertices of a golden rectangle.  Similarly, those 12 vertices also forms 3 congruent golden rectangles that are perpendicular to each other and intersect each other symmetrically.

 

 

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