Increasing (or decreasing) a block size
06-25-2014, 07:53 AM
#1
Power Poster
Thread Starter
Join Date: May 2008
Location: MN
Posts: 24,522
Increasing (or decreasing) a block size
When I increase a block size from 6x6 to 12x12 -
doesn't it seem to be logical to say that I DOUBLE the size of the block?
But actually, the area of the block will be QUADRUPLED!
6x6 = 36
12x12 = 144
Or the other way around - when I decrease a block size from 12x12 to 6x6 -
it seems logical to me to say that I cut the size by half.
However, the area of the smaller block is only 1/4 the size of the larger block.
12x12 = 144
6x6 = 36
doesn't it seem to be logical to say that I DOUBLE the size of the block?
But actually, the area of the block will be QUADRUPLED!
6x6 = 36
12x12 = 144
Or the other way around - when I decrease a block size from 12x12 to 6x6 -
it seems logical to me to say that I cut the size by half.
However, the area of the smaller block is only 1/4 the size of the larger block.
12x12 = 144
6x6 = 36
06-25-2014, 08:09 AM
#2
Power Poster
Join Date: Feb 2009
Location: Northern Michigan
Posts: 12,861
Which is why it takes (4) 6 1/2" squares to make (1) 12" block...often people do not realize this until they try to just double everything, then wonder why it's not working. Glad you realized it. 
06-25-2014, 08:27 AM
#3
Super Member
Join Date: Jan 2009
Posts: 4,688
The doubling is of the square formed by the diagonals of the four inset squares. Socrates explained it best.
http://www.cut-the-knot.org/proofs/half_sq.shtml
http://www.cut-the-knot.org/proofs/half_sq.shtml
06-25-2014, 08:39 AM
#4
Power Poster
Thread Starter
Join Date: May 2008
Location: MN
Posts: 24,522
The doubling is of the square formed by the diagonals of the four inset squares. Socrates explained it best.
http://www.cut-the-knot.org/proofs/half_sq.shtml
http://www.cut-the-knot.org/proofs/half_sq.shtml
Now that is almost too much for my mind to absorb!
Thank you for the link.
06-25-2014, 11:31 AM
#10
Super Member
Join Date: Dec 2010
Location: MO (the Show Me state)
Posts: 2,947
On now this is really deep. 
The doubling is of the square formed by the diagonals of the four inset squares. Socrates explained it best.
http://www.cut-the-knot.org/proofs/half_sq.shtml
http://www.cut-the-knot.org/proofs/half_sq.shtml
Thread
Thread Starter
Forum
Replies
Last Post
