Titles of Collections

As a Table of Contents or Catalogue of Concepts – possibly best viewed in a second browser window – to accompany the Pattern Collections:

I. “DIGITAL PYRAMIDS”

  1. Pyramids of Decimal and “Digital” Numbers
  2. Pyramids of “Last Digit Series”
    • “Last Digits” form Vertical and Horizontal Series of 5 Digits
    • Diagonally, [Top Right to Bottom Left] we see Square Numbers] ending with Last Digits 0 1 4 9 6 5 6 9 4 1 0 with 5 acting as ‘mirror’
    • Symmetrically, we see “Squares – 1” with 5-Digit-Series that are mirrored by either 5 or 0 [Top Left to Bottom Right Diagonal]
  3. Single “Last Digit Patterns”
    • Fascinating, how every Digit reveals its own Pattern
  4. Composite “Last Digit Patterns”
    • Different ‘digital combinations’ form different Patterns
  5. Digital Prime Diagonals

II. “ARITHMETICAL MATRICES”

  1. “Diagonal Sums” of Odd and Even Summands
    • Sums can be visualised as Diagonals and on Parallel Diagonals
  2. Prime Numbers as “Diagonal Sums”
    • When Odd Numbers can do it, Primes can do it, too!
  3. “Digital Squares” of SemiPrimes
    • What do SemiPrimes show us in their Matrix of “Prime Products”?
  4. The “Sequential Factorisation” of SemiPrimes
    • A bit tricky to produce the Products first and then a sorted sequence as a LookUp Table – but I’ve moved from coding to designing code – so I have to do it ‘by hand’ – who will code it beautifully?

III. “DIGITAL TABLES”

  1. “Digital Tables” of Primes and SemiPrimes
    • Primes are Sums; SemiPrimes are Products; Together they form “Prime Pairs” when aligned by Leading and Last Digits
  2. “Digital Tables” for “SemiPrime Series”
    • Turning SemiPrimes products into a LookUp Table for humans or computers is greatly helped when we SEE the underlying patterns

IV. “ORTHOGONAL PYRAMIDS”

  1. Orthogonal Pyramids for Numbers as Counts
    • Vertical and Horizontal Pyramids doubled and mirrored
  2. Prime Numbers in Orthogonal Pyramids
    • Patterns of Non-Patterns or ‘regular irregularity’?
  3. Fourfold Pyramids for Primes and Non-Primes
    • Everything depends on Directions for Numbering

V. “NUMERICAL PLANES”

  1. Odd Products in “Symmetrical Number Planes”
    • Prime Numbers are a subset of Odd Numbers
    • When visualised in a Symmetrical Context, they show their beauty rather than their mystery…
  2. “Symmetrical Number Planes” for “Orthogonal Prime Axes”
    • What do we See when we highlight Prime Numbers along the Axes?
    • “Vertical Pairs” of Primes and SemiPrimes – Diagonally Staggered
    • revealing the Ortho-Diagonal Nature of “Digital Sums” n x 10 + m
  3. The OrthoDiagonal Nature of “Digital Sums”
    • A remarkable combination of “Parallel Diagonals” and “Vertical Pairs”
    • and an even more remarkable Pattern of mainly Primes
  4. “Digital Sums” in “Symmetrical Number Planes”
    • Who comes first: the Sums or the Pattern?

VI. SUMS and PRODUCTS

  1. “Diagonal Sums” of Last Digits of Odd and Even Summands in Orthogonal and Diagonal Chessboards:
    1. Odd + Odd = Even
      1. Odd + Even = Odd
    2. Even + Even = Even
      1. Even + Odd = Odd
  2. “Orthogonal Products” of Last Digits of Odd and Even Factors in Orthogonal and Diagonal Chessboards:
    1. Odd x Odd = Even
      1. Odd x Even = Even
    2. Even x Even = Even
      1. Even x Odd = Even
  3. OrthoDiagonal Symmetries in Number Planes
    • Numbers and their patterns as ‘digital footprints’ are distinctly beautiful!
  4. OrthoDiagonal Sums, Products and Primes
    • Diagonal Sums, Orthogonal Products and OrthoDiagonal Primes?
  5. “Symmetrical Number Planes” for “SemiPrime Factors”
    • The 4-fold Symmetry of a Number Plane is not only beautiful
    • Primes as Co-Factors create SemiPrimes as Products

VII. ROOTS and DIAGONALS: PYTHAGORAS through a DIGITAL LENS

  1. Pythagoras’ Sums of Squares in “Symmetrical Number Planes”
    • Patterns over Patterns… What do they tell us?

NEXT: “Digital Visualisations”

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