Actually Applicable Application Problems and Brainteasers/Circle Skirt

Overview
Circle skirts are a popular fashion item, so for anyone who likes to make their own clothing designs, this type of math is definitely Actually Applicable.

The method described below is for a pull-on circle skirt cut from a single piece of fabric. Depending on your measurements, how long a skirt you want to make, and what fabric you have available, you might need to make and stitch together pieces of fabric that are actually half, a quarter, or etc., of the skirt. If you do that, please remember to leave seam allowances.

General Method

 * 1) Use a tape measure to measure the waist and hips of the person the skirt is meant for.
 * 2) You can use either inches or centimeters, or something else, as long as you are consistent.
 * 3) If you don't have a tape measure, use a string, then use a yardstick or ruler to measure the string.
 * 4) Cut a piece of elastic the length of your waist measurement. Sew its ends together without twisting it between and try the elastic on. If the elastic is fairly stretchy, you might need to shorten it by a few inches.
 * 5) Divide the hip measurement by 6.28. This is the hip radius.
 * 6) Subtract half an inch or one centimeter, or whatever you prefer, for a seam allowance.
 * 7) Usually seam allowances are added but this time subtracting will make the fabric reach up higher. You'll see!
 * 8) Draw a quarter-circle centered on the corner of a big piece of paper, with the radius you just calculated.
 * 9) I like to use the back of wrapping paper.
 * 10) If you don't have a drawing compass big enough, you can use a piece of string.
 * 11) Add the length you want the skirt to turn out, plus whatever hem allowance you prefer, to the radius of the quarter-circle you just drew. This is the hem radius.
 * 12) Draw a quarter-circle with the radius you just calculated centered at the corner.
 * 13) Cut out the pattern.
 * 14) Fold the fabric once horizontally and once vertically (so that it is in four layers), line the pattern up so that it is centered at the corner where the fabric's two folds cross. Adjust the fabric if necessary to make sure the pattern has four layers of fabric under it all over.
 * 15) Cut out the skirt, sew on the elastic, and sew up its hem.

Variations
If you will be adding a zipper instead of using elastic, use the waist measurement for the inner circle instead of the hip measurement.

Problems
Suppose you are a fashion designer and sketch patterns for these clients' orders. They don't have to be full-size, but do make sure you have all the needed numbers.


 * A client with a 34" waist and 40" hips wants a 20" skirt with a zipper.
 * A client with a 37" waist and 46" hips wants a 24" skirt with elastic.

Make Your Own Problem
Measure yourself or a family member, friend, stuffed animal, etc., and do the calculations to make an actual circle skirt. As an extension to the problem you can visit a fabric store, choose fabric you like, decide if actually making that skirt is in your budget, and if you wish, actually make it.