Matinga's Arc Law - Trigonometry

Matinga's Arc Law

Matinga's Arc Law holds that a natural number harmonic of any angle or natural number power series of any angle will always intersect the same phase angle. The law is true for circular arcs as well as for Archimedean spiral arcs.

Image 1

Prologue

In Image 1, the outer circle or arc is congruent with the unit circle.

The inner, closed arc or the fundamental circle or fundamental arc θ [o] is concentrically parallel to the the unit circle. It is half the arc length or half of the θ variable - i.e. it is θ/2. For θ [o], origin angle, or fundamental angle, the arc length is Pi rad. The diameter is 1 m - equivalent to 1 radian.

Example 1

In electrical physics the fundamental, natural frequency or rotational frequency, ω, is Pi rad/s. The resultant frequency or fundamental linear frequency is then 1 Hz. ( ω [ o ] = 2 * Pi * f [ o ]. ) The fundamental displacements - natural and resultant types are quantum displacements.

All references of fundamental dimensional constants in quantum physics will be measured from those known constants. They are the lowest electrical rotational or angular displacements in nature. They occur without applied force. That is the true angle or arc, θ, and the resultant angle known distance or diameter, d.

Pi rad, in electrical physics, is rounded to the interger or digit of 3, for practicality in information technology. It is the fundamental constant in every natural order of magnitude of electromagnetic frequency. The fundamental count in IT begins with the value of 3, and then 3 is then subtracted to obtain the value of 0.

There are 2 ^ 32 frequency harmonics in silicon, consistent with electronic, Matinga Noise Floor. (Germanium may elicit a different set of harmonics. It will prove to be a valuable test of Matinga Noise Floor Constance or variability in natural substrates.) Microsoft assigns one harmonic value or digital value to create a full count in its Operating System database.

Conclusion With Example

One version of Pi rad as an arc exhibits the maximum arc angle for the one full revolution. Any other arc length, represented on the unit circle may be displaced as a segment of any other concentrically parallel arc - even of non-full-revolutionary angle of the unit circuit or unit arc. That may displace or evolve as any arc proportion, including one revolution of any given arc.

As one full rotation of any angle will produce the same phase, no matter how many full revolutions occur, the following is true. An example is shown.

Example 2

n = [ natural numbers ] ;

n * ( θ rad ) ~ θ rad ,

( θ rad ) ^ n ~ θ rad ;

Φ = θ rad ,

n * ( θ rad ) ;

Φ = θ rad,

( θ rad ) ^ n ;

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