Questions, Problems, & Conjectures

about

SYMMETRY & GROUPS

From the 2006 ReSEARCH Group

Patterns from ReSEARCH Session 4: Patterns observed in Addition and Multiplication Tables for various mods

1. On the multiplication table for the 11 clock, in every column the # after increases by 1.


2. On the multiplication table for the 11 clock, in column 3 there is a pattern of differences.


3. In every table, the 1st row and 1st column are the same.


4. On the multiplication table for the 11 clock, you keep subtracting 3.


5. Look @ concentric squares – there are reflections along the diagonal.


6. There are column repeats for the multiplication table for the 6 clock: 6 times, 2 times, 3x, 2x, 6x.


7. There are diagonal patterns for addition.


8. In the multiplication tables for 1,6,10,14 the # in the middle of the diagonal is 1,3,5,7 respectively.