**Authors:** J. S. Markovitch

The fine structure constant is shown to arise naturally in the course of altering the symmetry
of two algebraic identities. Specifically, the symmetry of the
identity *M*^{2} = *M*^{2} is "broken" by making the
substitution *M* → *M* − *y* on its left side, and the
substitution *M*^{n} → *M*^{n} − *x*^{p} on
its right side, where *p* equals the order of the identity; these substitutions convert the above identity into
the equation (*M* − *y*)^{2} = *M*^{2} − *x*^{2}. These same
substitutions are also applied to the only slightly more complicated
identity (*M* / *N*)^{3} + *M*^{2} = (*M* / *N*)^{3} + *M*^{2} to
produce this second
equation (*M* − *y*)^{3} / *N*^{3} + (*M* − *y*)^{2} =
(*M*^{3} − *x*^{3}) / *N*^{3} + *M*^{2} − *x*^{3}.
These two equations are then shown to share a mathematical property relating to *dy*/*dx*, where, on the second
equation's right side this property helps define the special
case (*M*^{3} − *x*^{3}) / *N*^{3} + *M*^{2} −
*x*^{3} = (10^{3} − 0.1^{3}) / 3^{3} + 10^{2} − 0.1^{3} = 137.036,
which incorporates a value close to the experimental fine structure constant inverse.

**Comments:** 4 Pages.

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[v1] 8 Feb 2011

[v2] 14 May 2011

[v3] 14 Oct 2011

[v4] 2012-02-29 14:27:18

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