Mathematics

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 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 l

Displacement or Angular 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 = 1 - x ^ 2 , (2) A = sin ^ 2 ( x ) (3) A = ( 1 - x ^ 2 ) ^ (1/2) , (4) A = sin ( x ) (5) A = cos ( x ) , (6) sin ( x + Pi/2 ) , (7) A = ( 1 - ( x - 1/4 ) ^ 2 ) ^ (1/2) (8) tan ( x ) = sin ( x ) / cos ( x ) (8) y ^ 2, A = x [1] ^ 2 + x [2] ^ 2 + x [3] ^

Schrodinger's Wave Function Matinga's Laws Of Functions 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 fucntion trace an infinitesimal path or wave function. Second Law (2) The lengt

The mathematical variable for displacement represents a dependent variable dimension, in physics. It 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. x = ω * t © Sydney Matinga 2026

Decay begins with a constant. The constant is translated to a cumulative dependent variable. In physics the first element in the sequence is a constant dimension. It is subject to a change of energy phase in reduce its magnitude. In Decaying orbits can be represented by the algorithm below. The algorithm is represented below. x = ω * t x is a variable. All other characters represent contestants. A = C * e ^ ( a [ 2 ] * -( x + h )/b ) ©

A unique insight is that for a fixed mass under sinusoidal acceleration, changing is angular phase will also change its acceleration to configure the 4 measured and agreed forces of physics. Let us observe the identities which govern their strengths. Quantum Scale Approximation Quantum amplitude is sin ( x ). Relativistic amplitude is 1/( sin ( x ) ), determined within the quantum particle. A [ R, 1 ] = a [ max ] * sin ( 0 ) , Electromagnetic Flux (real flux) , 1 / A [ M

(1) x = e ^ a is the equation for an Archimedean spiral. (2) x = h * e ^ a is the physics equation for discrete displacement in the spiral arc. (3) A = e ^ x , (4) x = e ^ n Both immediately preceding equations describe an accreting orbit. (4) represents a series of discrete, natural orbitals, similar to mosquito coil in configuration, beginning from the centre of the orbital. (3) represents the same orbit curve, contiguously, rather at full orbital interval

Time evolved, spatial displacement is calculated below. Scalars are in radians for modern physics and there are no units for them in classical physics. (1) A = ( a/2 ) * ( 1 - ( 2 * x /b ) ^ 2 ) ^ 1/2 (2) A = ( a/2 ) * ( 1 - ( 2 * ( 2 * Pi * f * t )/b ) ^ 2 ) ^ 1/2 (3) A = ( a/2 ) * ( 1 - ( 4 * Pi * f * t /b) ^ 2 ) ^ 1/2 (4) A = ( a/2 ) * ( 1 - ( 4 * Pi * ( 1 hz ) * t/b ) ^ 2 ) ^ 1/2 The ellips

Analysis θ = x, θ = ω * t Φ = h A = a * sin ( x + h ) A = a * sin ( ω * t + h ) ---> units of m Vectoring is both mathematics and then physics, once the time variable replaces part of the primary mathematical dependent variable, x. ω is a coefficient or constant. The vectoring indicated is linear vectoring. For a plane, the algorithm is A = a * ( a [ i ] * sin ( ω [ i ] * t + h [ i ] ) + a [ i + 1 ] * sin ( ω [ i + 1 ] * t + h [ i + 1 ] + Pi/2 rad) ) For a volume, si

The difference between mathematics and physics is that mathematics is time independent. In the world of complex application of mathematics the many convergent time dependent disciplines, including physics and economics, time already modelled into the corresponding mathematics simplifies application. The basic variables are indicated below. Mathematics has always been a latent discipline of physics and now it is salient. Constant dimensions are in uppercase - consistent with e

Human beings each have a different and unique electromagnetic glow, generated by their nervous system. Semiconductor sensors will detect that electromagnetic, Matinga noise floor and it is more perceivable if amplified and database filtered by a computer database. The algorithm for Matinga noise floor can be reviewed in the Xerqon blog article, Matinga Quantum Noise Floor Quantified. The immediate sensory device is a point radar antenna (see the Point Radar article in this bl

(1) y = C + x , (2) y = 3 * C + 4 * x ; (3) y = C + x , 3 * C + 4 * x ; Comma separated variable format (4) y = C + x , (5) y = 3 * C + 4 * x , from (4) + (5) (6) 2y = C + x + 3 * C + 4 * x (7) y = ( 4 * C + 5 * x )/2 Simultaneous equation format (8) y = ( a [ 1 ] * C + b [ 1 ] * x + a [2] * C + b [2] * x + a [3] * C + b [3] * x + . . . + a [ n ] * C + b [ n ] * x ) / n © Sydney Matinga 2026

A scientific law is established when a theory is tested by an existing law and found to be of greater value in analysis of nature when it delivers more complete answers than the previous law. A law also exists if a theory has been completed and is irrefutable in contemporary enquiry. A mathematical proof is an experiment to test whether a theorem validates as a Law. Peer review is best and most swiftly achieved via publishing in professional or independent media with opportun

A Priori is pronounced “ay-priory”. It translates to the intial conditions. In simple analysis, a priori must exist in both sides of a system for any communication to occur between the two. The qualities must be the same. The quantity may be different while they remain proportional to each other. A Priori In All Communication Anywhere where communication exist between two systems, they share the a priori which allows for the communication or active entanglement of that greate

Free Licence Diagram 1 Matinga Diagrams Versus Venn Diagrams The Language All Of Set Theorems, Sets describe algebraic expression or elements of algebra (language) as they relate to each other. Set theory is relational theory or database theory. All of algebra is related or relational. One element can be used to describe the other via a mathematical or algebraic relationship known as a formula. Repetition In Matinga Set Theorem In nuture when an element repeats, we cannot k

Matinga's Transposition Law All axes or curves described by an equation will be the same regardless of how the axis is transposed. Explanatory Examples Mathematics has reserved the term 'proof' for non-deviating arguments. The discipline is a subset of Physics, as it contains many of the same dimensions - as dependent dimensions, identified as dependent variables in mathematics. Mathematics is programming which is time-based, so it must join Physics whose fundamental dimensio

All mathematics is sequential. Labelling each sequential element with a event space designation is the beginning of fractal expression. The most convenient event space address to use is a numerical label or a timestamp by another definition. "n" is used rather than "x". "n" represents natural number sequences or natural events rather than "x" which represents contiguous real numbers. Example y = n , n = a [ 1 ] + a [ 2 ] + a [ 3 ] + . . . + a [ n ] , y [ n ] = a [ 1 ] + a

Free Licence Figure 1 Orthogonal Topology Law All spatial geometry is circular. In a circle or cycle, all radial field lines are orthogonal and simultaneously parallel to other. Examples In Electrical Physics Gaussian theory combined with Orthogonality Law states, as extended Orthagonality Law, that field lines tangential to those entering and exiting an enclosed surface (manifold) must be of equal number surrounding the enitre maninfold. In the closed segment area, "1", the

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