For those of you who thought my multiplication table and sum of the product table was cool (see extended entry) ... it looks like I may have discovered "arithmetic modulo 9". Google that if you like.
I'm glad someone else has discovered this already. Good old number theory.
PS - Apparently my "sums" table isn't exactly "modulo 9". Modulo 9 gets zeros instead of nines (i.e. 3-6-0-3-6-0 instead of my 3-6-9-3-5-9). This I have yet to wrap my head around.
Take a standard multiplication table:
1 2 3 4 5 6 7 8 9
1 1 2 3 4 5 6 7 8 9
2 2 4 6 8 10 12 14 16 18
3 3 6 9 12 15 18 21 24 37
4 4 8 12 16 20 24 28 32 36
5 5 10 15 20 25 30 35 40 45
6 6 12 18 24 30 36 42 48 54
7 7 14 21 28 35 42 49 56 63
8 8 16 24 32 40 48 56 64 72
9 9 18 27 36 45 54 63 72 81
To get the "sums" table, add the individual numbers from each product (answer in the multiplication table) until you get a single digit. For example, 4x8=32 so 3+2=5; or 7x8=56 so 5+6=11 and 1+1=2. It looks like this:
1 2 3 4 5 6 7 8 9
2 4 6 8 1 3 5 7 9
3 6 9 3 6 9 3 6 9
4 8 3 7 2 6 1 5 9
5 1 6 2 7 3 8 4 9
6 3 9 6 3 9 6 3 9
7 5 3 1 8 6 4 2 9
8 7 6 5 4 3 2 1 9
9 9 9 9 9 9 9 9 9
Horizontal/Vertical patterns
In the "1 row": increasing integers
In the "2 row": all even numbers, then all odd numbers (increasing)
In the "3 row": 3-6-9 and repeats
... "4 row": imagine 48, 37 ... (decreasing by 11)
... "5 row": imagine 51, 62 ... (increasing by 11)
... "6 row": 6-3-9 and repeats
... "7 row": all odd numbers, then all even numbers (increasing)
... "8 row": decreasing integers
Diagonal patterns as well
1 row: 1-4-9-7-7-9-4-1
2 row: 2-6-3-2-6-3-2
3 row: 3-8-6-6-8-3
4 row: 4-1-9-4-1-9
5 row: 5-3-3-5
etc
Ok, I haven't read your blog in awhile Jenn, and sorry, but all I can say about this post is *what the hell???!!* What got you thinking about math???? Don't you have any books to read? :)
I love your wierdness. You are so unpredictable.