A mathematical curiosity
This is probably an internet meme as old as AOL, but I only just discovered it today. And it’s truly remarkable. Or maybe it isn’t? Feel free to comment, if you know the short explanation.
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111=12345678987654321
You missed out 1 x 1 = 1.
I always said true beauty can only be found in tragedy, the female form and mathmatics, which I think you’ll agree makes me a particularly well-rounded individual.
Had Newton and Shakespeare had a daughter, you’d have found your soul-mate..
I hope the formatting works the way I want it to.
I don’t have a short explanation, just a fun way to think about this visually. Borrowing from Steven Strogatz http://opinionator.blogs.nytimes.com/2010/02/07/rock-groups/
1×1
.
2×2 or 2^2
. .
. .
10×10 or 10^2
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11 x 11 might look like a 10×10 with some more stuff:
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+ +
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That could be represented as:
the large square block + the left side + the right side + the bottom right part
so
10×10 + 1×10 + 10×1 + 1×1
or
100 + 20 + 1
Following that pattern 111×111 might be:
. . . — 94 more —- . . . + 11 dots
98 more
. . . — 94 more —- . . . + 11 dots
+
11 dots across + 11×11 square
100×100 + 11×100 + 100×11 + 11×11
10000 + 1100 + 1100 + 121
10000
1100
1100
+ 111
——-
1111×1111 becomes
1000000
111000
111000
12321