**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.**
**More Mathematical Recreations** |