Cutting out the pieces is one of my least favorite parts of the quiltmaking process, so I generally just slavishly follow the cutting directions and try to get it over with.

This week’s block is a diamond in a square in another square, and while I was cutting out the pieces, I noticed that the cutting instructions called for quarter-square triangles for the red triangles, and half-square triangles for the outer green triangles.

Half-square triangles are just what they sound like: you cut a square from one corner to the diagonally opposite corner, resulting in two triangles. Quarter-square triangles, unsurprisingly, are produced by making a second cut between the other two corners of the square (so your cuts look like an X), resulting in four triangles.

These two methods get you the exact same shape of triangles, and depending on the size of your starting square, the triangles from the two methods can even be the same size. In all my years of quilting, it had never occurred to me to wonder when you use one technique over the other. In this block, the two sets of triangles are serving the exact same function – they’re being attached to the sides of a diamond to turn it into a square. Why not cut both sets the same way?

The answer lies in the fabric bias.

Explaining exactly how fabric is made is somewhat outside the scope of this article, so I’ve got links at the bottom of the post to internet resources with all the gory details, but here is an extremely brief explanation of fabric construction and bias:

At its core, fabric is just a bunch of vertical threads and horizontal threads woven together in an interlaced pattern to give it structural integrity. The two directions that the threads are going are called grain lines. If you hold a piece of fabric on the top and the bottom and pull, you are basically pulling on both ends of all those vertical threads, and if you pull from the two sides, you’re pulling on both ends of the horizontal threads. One direction will probably have a little more give than the other, but neither one stretches very far, because the individual threads are not that stretchy, and you’re holding both ends of those threads.

However, if you’re pulling from one corner to the diagonally opposite corner of the piece of fabric, you’re not pulling on both ends of any (vertical or horizontal) threads, and there’s nothing to prevent the fabric from stretching. This diagonal is called the bias.

You can stretch the fabric a lot when you’re pulling on the bias. Go ahead and try it out, but use a small piece of fabric and one you don’t like that much, because it’s going to get stretched out like the knees on your favorite pair of leggings, and it won’t be usable for any sewing projects after that.

This stretchiness is a real concern for quilters, because nobody wants their quilt to look like baggy-kneed leggings. You have to be cautious when working with edges that are cut on the bias, so you don’t stretch out the pieces as you’re sewing them together.

When working with squares or rectangles, it’s relatively easy to avoid any bias edges. You just cut out those shapes so their sides are on a grain line (aligned with either the horizontal or vertical threads).

With right isosceles triangles, you don’t have that luxury. Either the two short sides, or the long side, must be on the diagonal. Which brings us back to the subject of half-square and quarter-square triangles. The difference between these two types of triangles is that half-square triangles have their bias on the one long side, and quarter-square triangles have their bias on the two short sides.

In a block like this diamond in a square in another square, these two types of triangles give you more flexibility to make sure that in the finished product, the grain line is going in the same direction on all the pieces. Most importantly, you want all the edges of the block to be aligned with the grain, so the edges don’t stretch out and look wavy.

You can see that in this finished block, the long sides of the red triangles run parallel to the sides of the block, so we want those long sides to be on the grain lines. This can be accomplished by cutting quarter-square triangles, which have the bias on the two short sides and the grain line on the long side.

For the outer green triangles, the short sides of the triangles run parallel to the sides (actually, they are the sides) of the block. Cutting half-square triangles gives us short sides that are on the grain lines.

Notice that the green triangles that make up the center square also have their short sides running parallel to the edges of the block. These were also cut as half-square triangles.

You can absolutely make your blocks without following the grain lines, but taking a little bit of extra time to pay attention to the grain can earn big dividends as far as the sturdiness and squareness of your finished block. I may be biased (ha ha!), but this extra effort is totally worth it to me.

As promised, here are a couple of articles that will give you more information about grain lines and bias:

1. http://www.generations-quilt-patterns.com/fabric-grain.html – this article from Generations Quilt Patterns gives a nice summary of bias and the two kinds of grain lines, plus when you’d want to use quilt pieces cut on each of them.
2. https://modernquilts.mqumag.com/grainline-and-quilting/ – if you really want to fall down an internet rabbit hole, this article from Modern Quilts Unlimited gets into the nitty-gritty of how fabric is made – there’s even a video of the fabric manufacturing process!