# 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