Mathematics

Quantum Physics depends on the reviewed format of simple harmonic oscillation, below. All simple harmonic oscillation, has only few constants and variables to consider. 1.1 A = amplitude 1.2 a = amplification 1.3 x = angle, in radians 1.4 h = phase shift, in radians Always take the beginning of the wave to be from the phase shift, rather than necessarily from the axis origin. Matinga’s Wave Function 1.5 A = a * sin ( x + h ) [ constant, amplification forced osc

Matinga's Network Law All networks are a portion of the unitary, universal network. All networks are arithmetically sequenced and divided by the number of networks to elicit the universal network. In some programming instances, it is prudent to express the divisor (number of networks) separately per individual network. Example 1.1 k = [ natural number ] 1.2 A = a [ i ] , 1.3 A = a [ i + 1 ] , 1.4 A = a [ i + 2 ] , . . . , 1.5 A = a [ i + n ] ,

Chaos Law The arithmetic 2 ^ 32 expression sequence of simple harmonic oscillations is Matinga Noise Floor. The variable can be extended further by adding any sequential harmonics of the original expression to the orginal expression. Matinga Noise Floor - In Chaos Law Real numbers proceed to expand or evolve at maximum clock speed for a duration of time. 'x' is the displacement or path length, while ω is the angular velocity, multiplied by time, 't' to evolve 'x' or the equiv

A manifold is any object's topology or qualitative relationship of inner-volumes or areas (2-dimensional volumes). Gaussian theory stipulates that the number of field lines or world lines entering [a manifold] must be the same as the number exiting the object or manifold. The Matinga component states that Gaussian theory must apply to inner manifolds or sub-manifolds, as well as the exterior or super-manifold. The universe is a supermanifold, containing a dense series of self

Matinga's Hyperdimensional Law extends Pythagoras' Theorem to any geometric sequence, rather than only powers of 2. The algorithm power averages a geometric dependent value after adding the geometric sequence of independent, geometric variables. It will plot a wave when transposed by the subtraction of one or more of the independent geometric variables, as well as the dependent geometric variable. Pythagoras' Theorem hyp, A = ( x [ 1 ] ^ 2 + x [ 2 ] ^ 2 ) ^ 1/2 Matinga's Hy

Facial recognition is best and most simply achieved by one three constant ratio. Two iris widths and their separation width are the constants of that ratio. The deployment of the technology offers global coverage of the human market. The animal stock, pet and wild animal identification markets are also extenstive. A similar technology could also be use to identify pairs of vehicle body markings or letter box or front door markings. "a [ i ]" and "a [ i + 2 ]" are horizontal i

Closed Systems Analysis Closed loop axes each has a finite scalar dimension. Infinite dimensions emerge from the notion of an absolutely expansive dimension, also presumably of the same topology as the finite dimensions. Dimensional loop revolution, achieving infinite revolutionary velocity is how the infinite dimension can be realised as a closed loop axis or dimension. When conserving the angular momentum for a given inertial reference frame, reducing the diameter will lowe

Kuona ( koo - orh - nah ) - 'to see' - is the world's only frequency matching or network assimilation algorithm. All forms of network intrusion can be mitigated by network encyption, such as the Xerqon Pty Ltd 'Quantum VPN'™, in this Centreweave Pty Ltd blog site. The network may be the carrier network (carrier wave) or the streaming object (content). Legacy software operates on carrier waves or networks - each of natural number frequency. // f = frequency, (1) x/2 * Pi

The Sine Power Law Add the ω constants and the mean of the phase shifts in the sine wave brackets. Example A = sin ( x [ 1 ] + h [ 1 ] ) * sin ( x [ 2 ] + h [ 2 ] ) * sin ( x [ 3 ] + h [ 3 ] ) * . . . * sin ( x [ n ] + h [ n ] ) , sin ( x [ 1 ] + x [ 2 ] + x [ 3 ] + . . . + x [ n ] + ( . . . + h [ 1 ] + h [ 2 ] + h [ 3 ] + . . . + h [ n ] ) / n ) © Sydney Matinga 2026

The programming solution to incrementation is represented below. It is based on the system clock, in all examples. "h" is the starting time. “n” is a natural number, and “a” is a real number constant. For the algorithm to function, do not attempt to simplify the independent expression any further. BODMAS or BEDMAS both dictate the sequence forced by brackets and powers ( high order multiplication). A = n [ i ] , ( clock() - h [ i + 1 ] )/2 * Pi * ( a [ i +

The following is a VPN frequency coefficient. For regular IT, the VPN is divisor to the numerator x. That is such that the frequency coefficient is as follows a = ( ( n + 1 + h ) / n ) A Universal VPN which combines 2 or more amplitudes is unique or extremely rare in frequency distribution. The combination of both amplitudes or networks must be only shared between the two sets of networked network adaptors. Each device should operate on it o

The recording and retrieval of customer or partner passwords in IT systems is a legally indefensible position to sustain. It is obvious that passwords are being retained by security web platforms (databases). The leading web software will always inform you that a password has been repeated, when re-used for password resets. A legal enquiry would almost certainly reveal that the companies, which own or maintain the databases, have potential human access to the passwords which

Ideal tooling, made according to the design technology discussed, would best be constructed from carbides such as iron carbide for most applications or tungsten carbide for glass cutting. At the correct carbon to metal saturation or concentration, the subsequent, expected material is metal diamondoid. The following brief includes a mathematical function which will calculate and draft the shape of a pointed tip dremel, as above. It will also entail a helix, as indicated in the

Example 1 In the example, above, there are distinctively 7 valences or orbits or energy bands, represented by dotted lines (energy levels) and the 7 intersecting angles of Pi. The ratio comes a circumference of 22 to diameter of 7. Pauli's Principle is seen in the mirroring of the 7 series distrribution below the upper distribution. The bands each each have an orbital series which is self-similar in repeating a similar pattern once, for the filling of the period table, in Che

Matinga's Arc Laws First Law Matinga's Arc Law holds that a natural number harmonic or resultant of any angle, measured in metres, 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. Second Law Natural scalars or harmonics are measured as revolution, in radians. All straight lines are really segments of much larger arcs, like the apparently flat ground of the Earth. T

x = ω * t for a variable dimension, or for displacement evolution h = ω * T for a constant dimension, dimensional interval, or for constant displacement or total displacement Pythagoras Theorem c ^ 2 = a ^2 + b ^ 2 Formula For Circle (Conic Sections) r ^ 2 = x ^ 2 + y ^ 2 1 ^ 2 = x ^ 2 + y ^ 2 , Matinga Cyclical Functions (1) y ^ 2 = a ^ 2 - x ^ 2 , (2) a * sin ^ 2 ( x ) (3) A = ( 1 - x ^ 2 ) ^ (1/2) , (4) sin ( x ) (5) A = cos ( x ) , (6) sin (

Matinga's Function Laws Every formula can be expressed as an equation as every equation can be represented as an algorithm. They are ultimately univariable or simply functions. All algorithms represent a contiguous series of amplitudes as (1) heights or (2) vertical lengths representing the next dimension up from that of the heights. First Law (1) The heights of the function trace an infinitesimal path or wave function. Second Law (2) The lengths sweep an integral volume func

Scalar & Harmonic Law The mathematical variable for displacement represents every dependent scalar dimension or harmonic dimension, in physics. More About The Scalar The scalar is the ‘x’ IT variable, by virtue of that argument. The equation which relates the physics dimension is expressed following. It is the fundamental time evolution equation. θ, x = ω * t for a time evolving variable for sinusoidal functions. Numbers or scalars are measured in r

Free Licence Figure 1 Orthogonal Topology Law All spatial geometry is circular. In a circle or cycle, all radiality is parallelity, while radial axes are also harmonically othorgonal to other at each quarter cycle. Every factor of a product, including scalar factors, is orthogonal to all other factors in a product. Examples In Electrical Physics Gaussian theory combined with Orthogonality Law states, as extended Orthagonality Law, that field lines tangential to those enterin

n ∈ N Pi ∈ S S ∈ Q Example 1 S = 2 * ( 4 * ( n + 1 ) + 3 ) / (10 * n + 4) / 2 n = 1 returns the value 3 + 1/7 , 22/7 or Pi. Reference the conclusion with that of the article Proof of the True Value of the Pi Ratio. IT programming via iteration or estimation is what currently propagates the accepted Windows OS, Pi value. The value above is not estimation. It is the true, accurate and precise value of Pi. © Sydney Matinga 2026