Mamma mia! I used a lot of math to draft the Vionnet skirt I mentioned in my previous post. Here is my journey in creating what looks like just a simple skirt. Ha!

This is a rendering of the skirt from a bird’s eye perspective.

Looks simple enough. Kirke described it as a barrel-cut skirt. Looking at the pattern pieces, you can tell that the back yoke is 1/2 a circle, while the front yoke is 3/4 of a circle. Hmm…that’s interesting.

When comparing the pattern pieces in the two books, I noticed a discrepancy. Kirke’s illustration shows the side seam line where the front yoke and back yoke are attached together (E and F) as being on grain.

The Bunka pattern shows the back yoke side seam as slightly off grain.

I deducted that Vionnet would have likely had the side seams, where a closure is necessary, to be cut on-grain and not on the bias.

I decided to draft the hip yokes myself instead of relying on the Bunka pattern book. This way I could ensure that the edges where the front and back meet at the side seams would be on-grain, and I could take into consideration my daughter’s actual waist measurement. Oddly, I rather enjoyed the math challenges that drafting this skirt presented. I also think it helped me better understand Vionnet’s thought process as well.

Recall from your high school days that the calculation for the circumference of a circle is C = 2πr. In order to draft the pattern pieces for a circular skirt, you need to know the circumference of your waist measurement. I used my daughter’s waist circumference or 26 inches (Circle A). But, the conundrum of this Vionnet pattern is that the back yoke is TWO quadrants of a full circle (typical), while the front yoke is THREE quadrants of a circle. I can’t use the same circumference for both the front and the back yokes because the waist would be too big. This meant I had to figure a different circumference and radius for the front yoke pattern piece (Circle B) in order to draft it.

Determining circumference of Circle B (Front yoke):
Front + Back = 26
3/4*B + 1/2*A = 26
3/4*B + 13  = 26
3/4*B = 26 -13
B = 13*4/3
B = 17.33 inches

Determining radius of Circle B (Front yoke)
C = 2πr
17.33 = (6.283)r
2.75 = r

Determining radius of Circle A (Back yoke)
C = 2πr
26 = (6.283)r
4.14 = r

See what I mean by a lot of math. Of course, the fun doesn’t end here. Now it is time to plot this on paper to create the pattern. You will need a ruler, large sheet of paper, and pencil.

Back Yoke Drafting instructions:
1. Draw a vertical line and then a horizontal line perpendicular to it. 
2. Measure out to the right from the center of these intersected lines the distance of the radius
for the back yoke (4.14 or 4 inches)
3. Measure out to the left from the center point the distance of the radius (4 inches)
4. Keep plotting this distance from the center point and in between
the other two points until you have a semi-circle. 
5. Connect the dots.
6. From this new curved line, plot the distance from you waist 
to your hip line (I used 8 inches). Connect the dots of this curved
line.
7. Add seam allowances at all the edges. I used one inch.

I followed similar steps to plot the front yoke. This is a drawing of what the pieces should look like.

Usually, I make a full muslin (toile) for the garments I sew, but I only made a muslin of the hip yokes and waistband in order to fit my daughter. The rest of the skirt is based on this fit, and I did not want to waste 7 yards of muslin fabric. Now, I understand one of the reasons why Vionnet used a half-scale dress form when draping her designs and testing her garments.

The toile of the hip yoke was a success and fit my daughter well at the waist. But, when I cut the hip yoke pattern in the silk, it did not fit. It was HUGE! What went wrong?

Well, it is something I should have known would happen – it stretched. Vionnet knew all about this (Kirke 87). When garments hang on the bias, especially a circular cut garment, it stretches and there is distortion, also known as hang-out. The best way to control it is to the force the distortion from the beginning. So I decided to follow a method similar to what Vionnet would have done.

I hung the yoke on a dress form and weighted it with grommet tape. I will let the piece hang for about a week and then re-cut the pattern from the stretched fabric. I guess I could have accounted for the stretch by reducing the waist circumference by 1 to 2 inches in the calculation, which I have seen pattern books advise, but hanging out the fabric before cutting is probably best, since stretch can vary for materials . For example, my muslin did not stretch much but the silk stretched by more than 2 inches.

By the way, the authors of Bias Cut Blueprints, Julianne Bramson and Susan Lenahan, do an excellent job of describing all things bias and hang-out. (Check out their book and their website Fashion in Harmony).

Another mark of cleverness I noted about Vionnet after making this yoke, is that it is actually a spiral.

When I mentioned this to my husband, he said “Oh yeah, the Fibonacci sequence.” What?? Into another rabbit hole I went.

I won’t get into the mathematics of it, which is cool, but basically spirals occur all around us in the natural world – nautilus shells, weather, leave pattern growth, galaxies, DNA double helix to name a few.

Leonardo Fibonacci was a mathematician in the 13th century who studied natural occurrences in nature and developed a number sequence whereby the ratio between each successive number in the sequence approximated and got closer and closer to the Golden Ratio, also known as the never-ending, never-repeating number, or phi (1.6180339887… ). The mathematician, Euclid, documented the ratio around 300 B.C. but Fibonacci did much to expand people’s understanding and usefulness of this magic number. Understanding the Fibonacci sequence allows one to draft the logarithmic spiral. The Golden Ratio has intrigued artists and scientists alike with its harmonious qualities and and is considered by some the “perfect” proportion.

Vionnet, the geometrician, was definitely familiar with this mathematical and natural phenomenon. In fact, in Kirke’s book on Vionnet she discusses dynamic symmetry, proportion, the spiral and how Vionnet related it to the human body (pages 115 -117). I didn’t fully appreciate this until I started doing the geometry myself. It’s truly fascinating!

I should also mention that Sandra Ericson wrote a good article, The Golden Rule of Proportions in Threads Magazine (March 2009, p 37-41) about these same principles of design. She explains how to apply the golden ratio to your own body type when designing clothes.

Speaking of proportion and balance, the yoke is too long on my daughter. To be honest, my daughter wasn’t around when I was drafting the pattern, so I used my waist to hip measurement. Wrong. We aren’t the same proportion and I didn’t consider the best silhouette for her regardless of the measurement, which Ericson’s article helps one analyze. Vionnet and other good designers are very in tune to this principle and I’m learning how important it is as well.

I now understand why Vionnet was such a genius! I will keep you posted on the details of constructing the rest of the skirt, once it’s done “hanging-out”. In the meantime, go do your math homework!

For instructions on drafting the rest of the skirt see The Golden Skirt: Drafting the Pattern.

Sources:
“Before You Hem a Bias Garment, Let the Fabric ‘Hang Out.’” Threads, 20 June 2018, www.threadsmagazine.com/2014/02/20/before-you-hem-a-bias-garment-let-the-fabric-hang-out.
Fashion in Harmony, www.fashioninharmony.com/pages/fabricsbiascut.htm.
Kirke, Betty. Madeleine Vionnet. Chronicle Books, 1991.
Bramson, Julianne, and Susan Lenahan. Bias Cut Blueprints: a Geometric Method for Clothing Design and Construction. Fashion in Harmony, 2015.
Ericson, Sandra. “The Golden Rule of Proportions.” Taunton's Threads, Mar. 2009 pp. 36-41.
Vionnet, Bunka Fashion College, 2002
Math is Fun, https://www.mathsisfun.com/numbers/fibonacci-sequence.html
Livio, Mario. The Golden Ratio. Broadway Books, 2002.