I find completely useless
number theory fun. Amicable numbers
Who-hoo—and utterly useless!
In the spring of 2005, while I was spending a week with my grandmother,
I was playing with various functions and a knitting project.
quickly discovered that the difference between consecutive squares is
consecutive odd numbers. (For example, the first five squares
my pattern were 1, 4, 9, 16, and 25. The difference
4 and 1 is 3, between 9 and 4 is 5, between 16 and 9 is 7, and between
25 and 16 is 9—3, 5, 7, 9.)
When I came home, I told my then-boyfriend of my discovery and he said, "It
breaks down at bigger numbers." I argued with him until he
started proving it. I proved it by drawing squares on paper,
he proved it algebraically.
So now I'm interested in figuring out more patterns about exponents.
I'm sure I could do some research and find out that someone's
already done the work but...where's the fun in that?
2005-2006 Amanda Takes Off