# A Study Of Notation #6  (still rough notes)

## Extending pi-and-Euler’s equations, and projective, Euclidean, and icosahedral geometries

Observation:  The number 6, often understood as three times two, is  the sixth doubling of the Planck numbers and within this system of numbers, geometries, and formulas.  The question is asked, “What happens within a notation if it is divisible by other notations? Does it have any special relation with Notation #2 and Notation #3?”

Planck unit doubles. Is it meaningful to say that 1.03×10-33 meters is X times larger than the Planck Length?  Does this notation help to stabilize all the different structures that have begun to emerge?  With an abundance of point-free vertices with which to make rather idealized constructions, what could possibly be going on at this juncture?

More to come:  16 December 2017

• Spheres:
• Projective geometries:
• Euclidean geometries:
• Simple doublings at Notation 4:
• Pentastars, tetrahedral rings, tetrahedral systems & the icosahedral phase:
• Simple doublings at Notation 6:

# Endnotes

ROLLOVER MATERIALS TO BE INCORPORATED OR DELETED:

Within the next prime-number notation are the grounds for another dimension of mathematics

Langlands, Barrows, Penrose, Rees, Wilczek (and so many others)  “How would this group envision a logical construction path and its modalities?

Observation:

Hypothesis:

Questions abound:

Explanation:

Diophantine geometry

“We use non-abelian fundamental groups to define a sequence of higher reciprocity maps on the adelic points of a variety over a number field satisfying certain conditions in Galois cohomology. The non-abelian reciprocity law then states that the global points are contained in the kernel of all the reciprocity maps.”

Hasse-Minkowski theorem

recab(F×) = 0.