#PrimeNumbers in #AmazingColourPatterns

4. Functional MATRICES

Complementary to the conventional Number Line, I have used these shapes for visualising decimal numbers:

  1. Decimal Pyramids that create
    • a left Diagonal of Squares and a right Diagonal of Squares – 1;
  2. Digital Tables that separate
    • Leading from Last Digits
    • and create spaces for “Vertical Prime Pairs” of Primes and SemiPrimes;
  3. Symmetrical Number Planes that reflect
    • the symmetries of complex numbers
    • and thus create the conceptual numerical link on 2D paper or screens to the physical metric world in 3D space;
  4. Functional Matrices to produce:-
    • Diagonal Sums
      • creating diagonally symmetrical sumsij and sumsji by adding summands from rowi to summands in columnj;
    • Orthogonal Products
      • creating orthogonally symmetrical productsij by multiplying factors from rowi with factors from columnj;
    • Products of SemiPrimes
      • creating orthogonally symmetrical matrices by multiplying Prime1 in rowi by Prime2 in columnj as SemiPrimesji and SemiPrimesij above and below the Top Left to Bottom Right Diagonal;
    • Factorial Tables of SemiPrimes
      • filling the gaps in the Digital Tables of Primes with SemiPrimes is achieved by following the series of results creating from multiplying Prime Factorsi with Prime Factorsj:

The matrices offer the full range of possible values from 1×1 to 109×109.

Next, we pick the SERIES of SemiPrimes, produced by the Prime Factors 7, 11 and 13:

And finally, altogether:

All the gaps are filled by Prime Factors producing SemiPrimes

NEXT: Diagonal Sums, Orthogonal Products, Matrix of SemiPrimes and Tables of Prime Factors