The Prime Cuboctahedron – Order from Chaos

The Prime Cuboctohedron

“…despite their simple definition and role as the building blocks of the natural numbers, the prime numbers grow like weeds among the natural numbers, seeming to obey no other law than that of chance, and nobody can predict where the next one will sprout.”  -Don Zagier 1975 There is structure to the prime numbers. Divine order from apparent chaos. Prime numbers, or numbers that are divisible by only themselves and one, don’t grow like weeds among the other numbers. A very simple pattern emerges when the numbers are laid out in multiples of six. The cuboctahedron, or vector equilibrium, is the most simple geometric form that is in balance with the space it occupies, in perfect equilibrium on all sides. Organizing numbers one to infinity in a radial pattern on its twelve points creates a 2-Dimensional cross emerging from the most harmonious 3-Dimensional form.…

Continue reading

Palindromic Squares

Palindromic Squares

A palindrome is a word, phrase, or number which reads the same backward or forward.  The squares of 10, 11, 12, and 13 fit the bill.  It breaks down after that since 15 squared is 225, and 51 squared is 2601. Why only these 4 or arguably 3 numbers? Does this give credence to the notion that base 10 is an innate numerical matrix to our reality? Did we invent the decimal system or did we observe patterns in the numbers themselves and organize them according to nature? What is it about ten that makes numbers so easily scalable and calculable? I found this gem in a book by Marty Leeds.  I added the ten squared to it.  It works of course if you put two zeros before the one on the right side.  It’s weird how this works for 10, 11, 12, and 13.…

Continue reading

Square the Circle with Earth and Moon

Square the Circle with Earth and Moon

When we compare the size of Earth and Moon strange geometric synchronicities appear. The most fascinating of all is the ancient philosophical concept of ‘squaring the circle‘, that is drawing a square with the same area as that of the circle. You can also ‘square the circle’ with equal perimeters, which is what the Earth-Moon system do, to a very high degree of accuracy (99.97%). The Earth and Moon’s diameters can be described as a simple ratio, 11:3, when comparing one to another. It turns out that this ratio is the solution to ‘squaring the circle’ (of equal perimeter).   The Moon describes a circle that has the same circumference as the square’s perimeter that surrounds Earth. This fact was discovered or rediscovered by the late and great John Michell. The magic number found in these geometries is 273, or more specifically 2732.  I…

Continue reading