Arithmetical Operations

The results of arithmetical operations have different visual effects that are independent of prime numbers.

In summary:

  1. Sums: n + m
  2. Products: n x m
  3. Sums of Powers of 10 plus Digits: n x 10 + m
  4. Sums of Squares in Triangles: n2 + m2
    • Pythagoras’ a2 + b2 = c2
    • c = SQRT (a2 + b2) or as a new format:
  5. Sums of Squares in “OCTAGONS”
  6. Sums of Squares plus Roots: n2 + m

“Digital” Sums are as new a concept as “Octogonal” and “Multi-Dimensional” Sums – all thanks to the advent of software as ‘thinking aids’.

And here as ‘viewing aids’:

  1. DIAGONAL Sums“: n + m
The liberation of Numbers from the Number LINE into Number PLANES
illustrates Arithmetic Operations in new ways.

2. “ORTHOGONAL Products”: n x m

The Multiplication of Odd Numbers by Odd Numbers
creates Orthogonal Rows and Columns

3. “DIGITO-DECIMAL” or “DIGITAL” Sums: n x 10 + m

A “Prime Diamond” of Primes as Sums of n2 + m

4. Pythagoras’ Sums of Squares in Triangles: n2 + m2

A “Tapestry of Octagons” with “Core Diamonds” from Sums of Squares

5. Pythagoras’ Roots of Sums of Squares: SQRT (n2 + m2)

± Roots of Sums of Squares appear symmetrical to the Diagonal

6. “MULTI-DIMENSIONAL” Sums: n2 + m

NEXT: Diagonal Prime Numbers

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