Taken at the Phoenix Zoo in Spring 2001, this is a beautiful close-up of the icosahedron, where the interior structure of golden rectangles is clearly visible.  Notice that the interior structure and the icosahedron share the SAME vertices. The rectangles being "golden" means that the longer sides are ~1.618 times that of the shorter sides. This is a ratio very important in mathematics, seen in many places in nature, and emulated in art. If you are unfamiliar with the Golden Ratio, try looking it up on the web. One good site for this is Ron Knott's site. Go to google.com and type in "Ron Knott" and "golden ratio", just like that, with quotes. The Golden Ratio is closely related to the Fibonacci Numbers, where, starting with {0,1,...}, each "next" number in the sequence is got by adding the two previous numbers in the sequence. As the numbers in the sequence get bigger, the ratio between consequtive numbers gets closer and closer to the Golden Ratio, so that the next number= ~1.618 x number before it.

 

One of my very favorite pictures. The icosahedron is about the same size as the roses and fits in beautifully with them. This is a drawing where you really need the photograph, and it is only up because of the photograph.

 

I don't know what kind of roses these are. This was taken at the Phoenix zoo in April of 2001. The Sierpinski tetrahedron is a stage-2.

These rows show images taken while looking through the tetrahedrons in January 2004, three years after the February and March 2001 images shown above. I now use a digital camera and do not have prints to trace for coloring sheets.

In the far-left image, notice the bent edge of the tetrahedron along the edge of the picture, how it angles off. The line of the tetrahedron should be absolutely straight along the outside edge of the picture. This stage-4 structure was severely damaged in falls from trees while taking pictures at the Grand Canyon.

These images and the ones below were taken in April 2004 at the fenced rose garden next to the pelican exhibit at the Phoenix Zoo. Even though this isn't referred to as a Phoenix Zoo page exclusively, I have only placed photos here that were taken at the Zoo.

Hopefully, when visitors to this page look at the beautiful roses, the beautiful Sierpinski tetrahedra will get some attention, too! Isn't it a wonderful statement about them that they can look stunning next to roses?

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