Tuesday, July 10, 2012

A Quilty math lesson

Alright!  I know it's summer vacation, but when a quilting friend is in need, I can put my math-hat back on!  Linda (Living4Quilting) sent me an email asking for some math help.  This morning, I tinkered and played and figured it out WITH a conundrum.  Continue reading.....

Hi, Amy, I have a math/quilt problem I need help with and I thought of you.  I am working on a pattern that has been redrawn from a smaller version and some of the calculations are a little off.  I can cut bigger fabric and then sew it out and trim down but what a waste and also time consuming too.  I thought of you and hope you don't mind and can help me with this...

I'm making a block that is kinda like a square in a square but not.  The middle block has a four patch in it, in place of the plain middle block.  The outside triangles to go around the four patch is what I need help with. 
The middle block (4 patch comes out to be 2 1/2" unfinished)  
Okay.  I have LOADS of those!

The block with the outside corners will be 3 1/2" unfinished (3" finished).  

Here's my visual of the FINISHED block with the four patch laying on top.

Essentially, the FINISHED 3" block can be seen as 4 sections of 1.5" FINISHED corners.  Here is where I stopped reading her note and started playing......

If you follow the classic HST "add 7/8"rule" to the FINISHED block, the corner sections of the square-in-square block (which finish at 1.5") would need to be cut at 2 3/8"...

And then cut in half on diagonal

Fold along hypothenuse (long side) to find the center

match center fold with seam of 4-patch


repeat with other two corners.  And V'iola!  A 3.5"(unfinished) block, minus some perfect piecing. :D


For those of you who are Easy Angle users....... a 2" strip of fabric will give you the corner pieces.


And then.....With some CLOSE inspection!!!!!........
The realization!!!!!  2" inner finish with a 3" outer finish is MATHEMATICALLY IMPOSSIBLE (IF you want perfect points) - and THAT is the priority question!  Do you want perfect points?

HERE'S THE CONUNDRUM!!!! (and the math lesson)
To have a finished 3" block, the center CAN NOT be 2" finished 4-patch (and vice-versa) IF you want perfect points! :(

See how that segment is longer than 2"?  In fact, using the wonderful formula from our buddy Pythagorus, the math works out to be roughly 2.12".  

here is the rest of Linda's email....
The pattern called for 2 1/4" squares cut once on the diagonal. When sewn on, the square is too small.  It was recommended that we cut 2 3/4" squares then square everything up to 3 1/2" but we have to do like 128+ blocks for the quilt and that's alot of squaring up.  I got to thinking about how to come up with a better way to figure up the  size square I needed but couldn't find any info on it.  (If you know your middle square is a certain size, how do you find out what size squares to cut for the outside to come up with a new size for the block?)  I hope you can help me. If there is a formula, do you know it?  I hope you can understand all of my info, if not, let me know and I'll try to explain it better.  thanks for any help you can give me...hugs, Linda

So, PRIORITY OPTION A:  IF you want a 2" finished 4-patch in the center AND PERFECT POINTS, be prepared for "ugly" measurements!
The outer "corner" sections would need to finish at ~1.414".  

Therefore.....CUT SQUARES at a STRONG 2 1/4" (a bit larger than 2 1/4"), and then cut in half along the diagonal.  The finished block won't have "nice" measurements either;  finishing roughly at 2.83" (ewwwwww)  {{THIS is what you are finding, Linda.  Cutting the 2 1/4" will give you perfect points, but NOT the 3" finish you want}}

OR PRIORITY OPTION B:  IF you are perfectly fine with slight (.1") imperfect points using a 2" finished 4-patch and a 3" finished block (what I think Linda wants), follow directions listed at beginning of post.
I'm perfectly happy with slight imperfections to have an adorable 3" finished block.  :D
Still makes for a cute block when pieced together with others!  

I hope this helps, Linda!

And it looks like I have the start of another new quilt!  Name:  "Conundrum" 


Linda said...

Amy, thanks so much! A great math lesson. You always go above and beyond and I appreciate your help! I am angle challenged. I can do squares and rectangles and circles but angles throw me alot! Thanks for taking the time to help me.

Nancy said...

A2 + B2 = C2..... and then you lost me :o)

Linda said...

Hmm, I'm going home and play some more...

I love your post. I thought I was going crazy with this and I hate it when I can't figure something out. It's good to get such a detailed explanation. Thanks for putting your Math hat on for me!

Andee said...

You are brilliant!

Ellen said...

I am looking forward to seeing Conundrum - very cute block. It's wonderful that you took the time to solve the problem - a quilting friend indeed.

Math is definitely not my strong suit. Whenever I have a math problem I take it to my husband (engineer) and he figures everything out for me - thank goodness!