Complementary to the conventional Number Line, I have used these shapes for visualising decimal numbers:
- Decimal Pyramids that create
- a left Diagonal of Squares and a right Diagonal of Squares – 1;
- Digital Tables that separate
- Leading from Last Digits
- and create spaces for “Vertical Prime Pairs” of Primes and SemiPrimes;
- 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;
- 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:
- Diagonal Sums







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:

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