# Mexican Pyramid Squares the Circle

Mexican Pyramid Squares the Circle. First. What is “square the circle?” Squaring the circle is a problem proposed by ancient geometers. It is the challenge of constructing a square with the same area as a given circle.  You may only use a finite number of steps with compass and straightedge. In 1882, the task was proven to be impossible.  This was a consequence of the Lindemann–Weierstrass theorem.  But wait a minute. Lindemann and Weierstrass did not consider R. Buckminister Fuller’s theories in conjunction with the Mexican Pyramid of the Sun.

### Mexican Pyramid Really Spheres the Circle

So who was R. Buckminster Fuller?

## R. BUCKMINSTER FULLER, 1895 – 1983

The Estate of R. Buckminster Fuller:

Hailed as “one of the greatest minds of our times,” R. Buckminster Fuller was renowned for his comprehensive perspective on the world’s problems. For more than five decades, he developed pioneering solutions that reflected his commitment to the potential of innovative design to create technology that does “more with less”. Born in Milton, Massachusetts, on July 12, 1895, Richard Buckminster Fuller belonged to a family noted for producing strong individualists. They were inclined toward activism and public service. Fuller developed an early understanding of nature during family excursions to Bear Island, Maine.  He also became familiar with the principles of boat maintenance and construction. Below are a couple of internal links for further information.

### Comparing the Mexican Pyramid of the Sun and Fuller’s Formula for Packing of Spheres

Packing of spheres in successive layers falls under a formula. It was discovered by R. Buckminster Fuller. It’s the number of the particular layer being considered, squared x 10 + 2. You can pinpoint how many spheres successivelyen circle a central sphere. Here are the 1st five examples.

• For the 1st layer, 1² x 10 + 2 = 12 spheres.
• The 2nd layer we have 2² x 10 + 2 = 42.
• For the 3rd layer,  3² x 10 + 2 = 92.
• The 4th layer is 4² x 10 + 2 = 162.
• The 5th layer is 5² x 10 + 2 = 252.

Ancients looked at what things had in common by common numbers. This was regardless of unit of measure used. We can thus equate the packing of the 5th  layer of spheres with the measure of the Mexican Sun Pyramid.  Also, Plato’s Ideal City, in his Republic,  had 2520 rings. Is this line of thought just fun? Perhaps. But also, perhaps there is no such thing as mere co-incidence?