## Collection 1: “Digital Numbers”

The first **Pyramid of Decimal Numbers **counts from 1 to 440 and reveals the *Top Right* to *Bottom Left* Diagonal of Square Numbers*.* with Last Digits 1 4 9 6 **5** 6 9 4 1. The series repeats with ‘mirror effect’ at 5.

It highlights *Multiples of 5 and 10*.

The difference between *cells* equals 1. But between *rows,* the intervals are growing in *even *and regular steps.

This **Pyramid of Digital Numbers** shows *vertical, horizontal* and *diagonal *differences between cells, rows and columns – a great improvement over the conventional Number Line, if we want to visualise relationships between Numbers.

This **Pyramid of Decimal Number Series **shows numbers ending with the Decimal Digits 0 1 2 3 4 5 6 7 8 9 and how they appear once, twice, thrice or four times as Horizontal Series in rows.

**Columns of Even Numbers**, the Roots of Square Numbers and the *Differences between Rows *in addition to the Diagonal of Square Numbers are on display here.

**Even Numbers** end with Last Digits 0 2 4 6 8.

**Columns of Odd Numbers** with Vertical Series lead inevitabily to the next image that unites the two complementary number qualities: *odd *and *even.*

**Odd Numbers** end with Last Digits 1 3 5 7 9.

**Decimal Numbers **have 0, 10, 20… as their ‘unique identifiers’. Here we see which positions these take, as we look only at Last Digits.

**5 is Half of 10. **Thus we see its multiples twice as often as the Last Digit 0.

How intriguing is the pattern 5 produces?

**0 and 5 together now!** Interesting ‘spearheads’ pointing ‘forward’ to the right, as if the Number Universe could only be one-directional, especially if we want to consider it as a 3D template to *model* physical realities!…

**Last Digits in Odd Columns **reveal yet more ‘whimsicalness’ of our Decimal Number System: repeated Vertical Series of 5 Last Digits in columns.

**Diagonals** show, mirrored at the central ‘Zero Column’, when the ends of Vertical Last Digit Series are seen together.

**Even Last Digits** reveal the same principle of Repeated Vertical Series of Last Digit patterns – diagonally staggered and *mirrored* by the central even column.

I cannot imagine who will retain and infer what from seeing these Vertical Series in a pyramid. But it was a pleasure designing and perfecting them!

Maths is beautiful – especially when *complementary *qualities come together to rise to a higher level concept:-

*odd*and*even*digits and numbers;*horizontal*and*vertical*series of digits or numbers;

resulting in *The Diagonal* as the next higher level concept:

- diagonal
*Square Numbers*and - diagonally staggered
*Limits of Vertical Series*.

The following sequence presents one digit at a time.

## Collection 3: Single “Last Digit Patterns”

## Coll. 4: Composite “Last Digit Patterns”

## Collection 5: “Digital Prime Diagonals”

## Collection 6: “Diagonal Sums”

## Collection 7: Primes as “Diagonal Sums”

## Coll. 8: Digital Matrices of SemiPrimes

## Collection 9: Factorisation of SemiPrimes

## Collection 10: “Digital Table” of Primes and SemiPrimes

## Collection 11: “Digital Tables” for “SemiPrime Series”

## Collection 12: Odd Products in “Number Planes”

## Collection 13: “Number Planes” for “Prime Axes”

^{0}) and “Prime Pairs” on “Horizontally Parallel Diagonals”