**Authors:** William Craig Byrdwell

A new series of equations for space, mass and the Periodic Table based on a common pattern is presented. Three equations for circular space represent the circumference (C), area (A), and volume (V) of a circle or sphere, which are mathematically equivalent to the conventional equations, specifically, C=2πr, A=πr^{2}, and V=4/3πr^{3}. The new equations incorporate a new understanding of pi, referred to as Whole PI to distinguish it from the classic understanding. A new symbol for Whole PI is presented and explained. Using Whole PI, the equations for the dimensions of space become 2PId^{p}/2p for the first dimension and PId^{p}/2p for the others. It is further shown that the second mass, helium, stands in relation to the first mass, hydrogen, the same as the second dimension of space stands in relation to the first dimension of space, specifically, H=2m^{p}/2p and He=m^{p}/2p, in which m equals the integer unit mass (m=1), the power signifies the atomic number (and therefore the number of electrons), and the denominator signifies the integer mass of the atom. Because of the similarity to the equations for dimensions of space, the elements may be referred to as dimensions of mass. Using the new equations, it is shown that the Periodic Table contains exactly ten dimensions of mass, and the other elements can be considered deconstructions of the ten dimensions of mass. This report shows a common pattern behind space and mass, and provides new insight into the anomalies in the Periodic Table.

**Comments:** 33 Pages. The version of this manuscript that contains the approximations for accurate monoisotopic masses (a.k.a. The 99.989% Solution) is "The Case for Whole PI and Alternative Equations for Space, Mass, and the Periodic Table", DOI: 10.13140/RG.2.1.3348.6968/2

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[v1] 2019-07-10 13:50:58

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