Thursday, November 4, 2010

Pyramid of squares of 2's

2 squared = 4    OR        4




22 squared = 484       OR       
(4) (8) (4)

                                                
222 squared = 49,284      OR  
(-) (1--2)(-)(-)
(4)(8)(-)(8)(4)
                                                     
2,222 squared =  4,937,284   OR 
(-)(-)(1-—-6)(-)(-)(-)
(-)(1  2)(-)(1  2)(-)(-)
(4)(8)(-)(-)(-)(-)(-)(8)(4)

                                                            
22,222 squared = 493,817,284    OR  
(-)(-)(-)(2——-0)(-)(-)(-)(-)
(-)(-)(1 6)(-)(-)(1 6)(-)(-)(-)
(-)(1  2) (-)(-)(-) (1  2) (-)(-)
(4)(8)(-)(-)(-)(-)(-)(-)(-)(8)(4)

                                       


222,222 squared = 49,382,617,284   OR 
(-)(-)(-)(-) (2—-4)(-)(-)(-)(-)(-)
(-)(-)(-) (2-0)(-)(2-0)(-)(-)(-)(-)
(-)(-) (1 6)(-)(-)(-)(1 6)(-)(-)(-)(-)
(-) (1  2) (-)(-)(-)(-) (1  2) (-)(-)(-)
(4)(8)(-)(-)(-)(-)(-)(-)(-)(-)(8)(4)


just like the pyramid/chiastic structure that appears in the process of squaring 1's

1 squared = 1
11 squared = 121
111 squared = 12321 ......

2's appear to have the same chiastic process however instead of sequential numbers they follow in fours...

four eight twelve sixteen twenty twenty-four twenty sixteen twelve eight four being the solution for 222,222 squared.

11 comments:

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