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

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. :)

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

Now that is almost too much for my mind to absorb! :) Thank you for the link.

Anything for you, Bear! :)

One just never knows what they are going to find on Quilting Board!

Isn't math marvelous? :thumbup:

Yes, it is, Neesie. And I love your Dawkins' quote.

Thanks, Loisf! I find it fits so many situations, on so many levels! :D

On now this is really deep. :D

In a class years ago I had students make 4 rail fence blocks using four strips each:
one set of 4 blocks was cut at 3"x1" --- the 4 sewn into a 4-patch square
one set of 4 blocks was cut at 3 1/2" x 1 1/2" --- the 4 sewn into a 4-patch square
one set of 4 blocks was cut at 4 1/2 x 2" --- the 4 sewn into a 4-patch square

We then compared the four 4-patches and they were surprised at how much larger each slightly increased size was to what they had expected it to be. Have never forgotten the value of that lesson on them.:)

Jan in VA

This is why I love my EQ. I can change any block from a pattern that I have and instantly change the size.