2012年5月13日日曜日

Square

Prime numbers are also expressed as squares like ancient Babylonian. I found the pattern of prime numbers which were based on fractal. At first, any prime numbers are squared to find none prime numbers.

3^2=9

Then you pile a rectangle. 3*2=6. 9+6=15
You continue to pile rectangles. 15+6=21,21+6=27,27+6=33

You can expand prime numbers.

Then I put numbers in each squares and rectangles.

Any prime numbers which are squared are the sum of numbers in rectangles and squares.
For example, 7^2=9+6+6+10+4+14=49.
11^2=7^2+6+6+4+4+4+4+44=121.
Moreover, you can put the Pythagorean Theorem in it.
7^2=5^2+(√24)^2=25+24=49
11^2=7^2+(√72)^2=49+72=121

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