# 4. “Arithmetical 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: