Hexagon Quilt Math

 I'm making a baby quilt! Baby quilts could quite possibly be my absolute favorite craft. I mean babies: ADORABLE, quilts: BEAUTIFUL, baby quilts: PERFECT.  

I had a vision for this one.  A vision of hexagons and triangles.  But no pattern.  Which is cool, because I hate patterns. But I knew that the hexagons and triangles needed to be perfectly regular on all sides, and at every angle, and I knew I couldn't free hand that.  

So I sat down and tried to problem solve some sort of geometry equation that would help me with this challenge.  It turned out I didn't remember enough from my 9th grade geometry class. 

Lots of math comes next.  Most people don't think math is pretty, so I'll inject some gorgeous fabric shots to keep it appealing.

 

After doing some brief internet research I learned more about hexagons, and came up with a plan for making one that's perfect... 

I learned that every regular polygon (or hexagon) has two circles related to them, an inner and an outer.  The outer circle is called the circumcircle, and is the one that could help me. The radius of this circle is the distance between the center point of the hexagon, and one of the corners.

So, step one was to make my own compass:

 I used a pencil, a pen, some twine, scissors and a measuring tape. 

 I tied the twine to the pencil, and decided on a 4 inch radius.  I cut it a little long, and then tied the pen at the 4 inch mark. 

I figure we're in need of another beautiful fabric break.   Ahhh....

Ok.  Back to the math.  I used the pencil to make the center point, and swung the pen around it, drawing a circle on some tag board (I wanted something sturdy that I could cut around).

As it turns out, a regular hexagon has side lengths equal to the radius.  So the next thing I did was stretch the pencil and the pen apart on the line circumference and draw dots that were the same distance apart as the twine. Then I drew straight lines between each dot.

 Pretty, pretty, pretty.

Now for the triangle: I knew the triangle had to be equilateral, and that each side is the same length I've been using, so I started with an edge of the hexagon, and used the twine to pick a third point.  I had to try a few different ones before finding one that was exactly 4 inches apart on each side.  

Now wait.  I thought I had figured it all out. So I cut.  Bad idea.  This isn't exactly right. Don't cut yet.  I'll show you. 

I cut all my beautiful fabrics. (wrong)

Unfortunately I planned for the triangle sides and the hexagon sides to be exactly the same size.  And once seam allowance was accounted for,  I had triangles with bases much smaller than the sides of the hexagons. Big gaps mean that the hexagons all overlap each other by an inch on each side.  I only wanted them to kiss at the corners. GRRR.  How'd that happen?

OK. Look at the angles on these two shapes, when laid together to make a seam. Draw an imaginary seam line straight across the top, about an 1/8 of an inch down. See how the triangle's side gets shorter as you come down towards the point?  Now look at the hexagon.  Because the hexagon's angles go out rather than in, the hexagon's side length just keeps getting bigger. UGH.  One got bigger, one got smaller, and I got MAD.

Let's call it a learning experience.  I re-cut all my hexagons, cutting a half an inch off of each side.  Now the triangle has longer sides, but at the seam line, they have the exact same length.

And when I sew them together they make beautiful straight lines.

More later!