GEOMETRICAL DIMENSIONAL ANALYSIS
                              06 06 09

                     The Outlaw Map of Physics
True wherever and however written, the definitions and formulas of
the physics you thought you knew erect a 4D concept and factor map.

      Tutorial           Read the Article           References


            Unit Definitions Project a Lattice of Logic
The International System of Units (or SI) is a consistent, coherent
set: the mapping conventions project its members as a vector space.


                         Numbers Don't Lie
Fundamental constants portray the atomic units and the SI as a 4D
map, a 4D logarithm table, and a 4D structured natural unit system.


    ** The Gravitational Constant Has the Value 6.6917625e-11
Readjustment of the official Planck unit values combines with modern
experimental results to impel a specific value for the gravitational
constant and question the adequacy of the International System.

** Unlike 2002, CODATA 2006 adjustment excludes from probability
both the Fixler et al results and the near miss GDA value for [G],
(Rev Mod Phys, Vol 80, No 2, Apr-Jun 2008, table XXVII and fig 2),
but dimensional analysis still requires a [PM], [PL], and [PT] set
that correctly factors into [G] and other quantities and there still
exists a complete pattern of numerical coincidences among constants
in general if [G] has the same numerical value as [d]{[aa]^2}.

    Values table      Symbol key      Template1      Template2

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by NIST CODATA 2006 fundamental constants values, as "allascii.txt",
 seen 05/28/09 at http://physics.nist.gov , verify these excerpts:

                     If AUN = atomic unit of,
1/[2af] = AUN time,                 [2af] = AUN frequency,
[a0]= AUN length = Bohr radius,     [B0]= AUN Magnetic flux density,
[aa]= Fine structure constant,      [c ]= Speed of light in vacuum,
[d ]= Magnetic constant,            [i0]= AUN current,
[k ]= Electric constant,            [Ke]= 1/([4Pi][k]),
[Me]= AUN mass = mass of electron,  [Pf]= 1/[PT] = 1/(Planck time),
[PL]= Planck length                 [PM]= Planck Mass
[Q0]= AUN charge = electron charge, [RK]= von Klitzing constant,
[v0]= AUN velocity,       and       [w0]= Magnetic flux quantum,

                    then, as defined by the SI,

[Kilogram] = [Coulomb][Second][Tesla] :
mass is charge X time X magnetic flux density
   as in [Me] = [B0][Q0]/[2af],

[Kilogram] = [Farad][Meter^2][Tesla^2] :
mass is capacitance X length squared X magnetic flux density squared
   as in [Me] = ([B0]^2) x [Atomic unit of Polarizability],

[Kilogram] = [Weber^2][Farad]/[Meter^2] :
mass is magnetic flux squared X capacitance per length squared
   as in [Me] = ([w0]^2)/{([Pi]^2)[Ke][a0]},

[Kilogram] = [Coulomb^2][Henry]/[Meter^2] :
mass is charge squared X inductance per length squared
   as in [Me] = ([Q0]^2)[d]/{[4Pi][a0]([aa]^2)},

[Kilogram] = [Ampere^2][Ohm][Second^3]/[Meter^2] :
mass is current squared X resistance X time cubed per length squared
   as in [Me] = ([i0]^2)[RK]/{[2af]([v0]^2)[2Pi]},     and

[Kilogram] = [Coulomb^2][Second^2]/([Farad][Meter^2]) :
mass is ((charge X time per length) squared) per capacitance
   as in [Me] = ([Q0]^2)/[{[4Pi][k][a0]}{([aa][c])^2}].

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Compare maps and verify: the units of gravitational constant [G] are

 (Meter^3)/[(Kilogram)(Second^2)]   OR
 (Farad)(Meter)(Volt^2)/(Kilogram^2)   OR
 (Meter)/[(Farad)(Second^2)(Tesla^2)]   OR
 (Farad)(Meter)(Ohm)(Watt)/(Kilogram^2)   OR
 (Meter)(Weber^2)/[(Henry)(Kilogram^2)]   OR
 (Coulomb^2)(Meter)/[(Farad)(Kilogram^2)]   OR
 (Ampere^2)(Weber^2)/[(Kilogram^2)(Newton)]   OR
 (Ohm)(Meter^3)/[(Kilogram)(Henry)(Second)]   OR
 (Coulomb)(Meter^3)(Tesla)/[(Kilogram^2)(Second)]   OR
 (Newton)(Meter^2)/(Kilogram^2).

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