# Pattern making: Concave and Convex Curves Update

Two weeks ago, I published a pattern making / sewing post about concave and convex curves and although I was not wrong (okay, mathematically speaking, I was wrong) I did not explain the subject fully and clearly. I thank a reader who commented on that post for bringing this to my attention. Below is the updated post.

I don’t remember what or when I was sewing. All I remember was staring at the unfinished garment on the form and seeing that something looked funky and not right.

“What’s wrong… what’s wrong?” I thought, stepping back to get a “monet” of the garment (monet is Cher Horowitz’s word for glancing at something from afar).

The garment was pulling in all sorts of directions at the seam and the seam allowance was not lying flat.

“You dweeb! It’s a concave curve!” I said to myself.

Problem solved.

Mathematically defined, a function is CONCAVE if every line segment joining two points does not lie ABOVE the graph and a function is CONVEX if every line segment joining two points does not lie BELOW the graph (click here for a diagram/illustration).

What’s interesting is that when I Googled ‘concave and convex curves’ and left out ‘mathematical’ in my search, the definitions were different. According to Google searches, a concave curve is a curve that is hollowed or rounded inward like the inside of a bowl and a convex curve is a curve that is rounded like the exterior of a sphere or a circle. An easier way to think of a concave and a convex curve is a concave curve is a valley and a convex curve is a mountain. Also, things that “vex” you tend to stick out and caves tend to be things that other things are stuck into (click here for diagram/illustration). This is the opposite of the mathematical definition of concave and convex curves!

But the mathematical and non-mathemical definitions don’t matter when concave and convex curves come into the world of sewing, particularly when pressing seam allowances. What matters is the relationship of lengths between the stitching line and edge.

For the sake of this post, I labeled the diagram above according to the mathematical definition of concave and convex curves.

For both concave and convex curves, there are two types – the only difference is that the stitching line and edge are transposed. The diagram gets even more confusing because curve #1 and curve #2 (and curve #3 and curve #4) are the same even though they’re supposedly different types of curves.

But throw all of that away and concentrate on the relationship of lengths between the stitching line and edge. For both types of concave and convex curves, there are two lines – the stitching line and the edge. If the edge is GREATER than the stitching line, then when the seam allowances are pressed back towards the stitching line, it will be too long in comparison to the stitching line and V NOTCHES SHOULD BE CUT so that the seam allowances lie flat. If the length of the edge is LESS than the stitching line, then when it is pressed back, it will be too short in comparison to the stitching line and CLIPS should be cut into the seam allowance so the seam allowances lie flat.

Does this make more or less sense? Do you understand why clipping and v notches are made?

## 4 Comments

## Kathy C.

Yes, this explanation makes much more sense to me. I didn’t understand the first post. Thanks for clearing that up.

## Natasha Estrada

The only thing I would add is overclipping and notching can distort the seam and weaken it as your removing fabric there which allows the area to collapse and bend which is exactly why it works in the first place. It’s like sculpture you can use your tools to manipulate your fabric. Knowledge is power and props to add Maddie for providing it.

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