Beauty in Mathematics
July 12th, 2007 by SplineGuy
Symmetries are nice. I like seeing interesting patterns arrive even if they are not natural features of mathematics, but contrivances of our chosen numerical notation.
Here’s a good example. I wouldn’t call it beauty in mathematics as much as a beauty of numbers, or even elegant numerical relationships:
1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321
1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111
9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888
1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 111111! 1 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=12345678987654321
HT: O’ Grandad
kewl!
Where do you guys come up with this stuff?
I saw this guy on 20/20 tonight named Mike Byster that teaches math to kids for free. According to them, he’s a math expert that came up with a thing called “Brainetics”… Showing that you can multiply 2-four digit numbers in your head using his patterns and other neat tricks.
Very interesting how he showed to square numbers that end in 5…
25^2 (25×25)
Multiply the 2 by the next number up (2×3) up to get “6″
then muliply the fives, 5×5 = “25″
Put the 6 in front of the 25
The answer, 625!
Someone with deep pockets offered to help him produce a DVD and website which is coming out in November, I can’t wait!