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fun with geometry

January 7, 2013

When an idea for a garment starts unfurling in my mind, I’m often at a loss for how to capture the nuances well enough that I can perhaps act on them later. For years now, I’ve been wanting to create a so-called sketchbook, suitable for a fiber artist. What’s held me back is, I want my ‘sketches’ to be 3-D, but then how do they fit in a 2-D book? A box might be better, but then I would need a series of boxes, and we’re quickly talking about oodles of storage space.

I’m spontaneous and impatient–I want to just jump right in, creating on the fly, when I have an idea. But often my ideas are complicated enough that it seems sensible to first establish if they are actually plausible. If there is some glaring defect, I’d like to work through that before I cut into my lovely fabrics. I’ve been creating very rough prototypes, using paper as if it were fabric. But since I create best on a body, I need a scaled-down ‘body’ for the prototypes.

As I was thinking, “what do I have that’s the right height and has a shape similar to my dress form?”, I remembered a likely soda bottle I had on hand. (I collect old glass bottles with interesting shapes and/or colors.) Wegmans, our local supermarket, sells “Frizzante European soda” in several flavors, and I had saved 2 in the 330 mL size.

Their shape is a lot like what’s called a “pear shape” of a woman’s body: smallish ‘chest’, and wider ‘hips and stomach’.

They’re not ideal because they don’t have ‘shoulders’, but for a very rough 3-D sketch, they actually kind of work!


I love math and geometry, but before now, they were never part of my garment design process. Once I had this bottle, though, I asked myself, “what is the actual scale of the bottle, compared to my dress form?”

I quickly measured the height of the dress form’s torso, then the height of the bottle: 32” vs. 8”. That suggested a scale of 4:1. That didn’t seem right! Oh yeah, volume! I could have used calculus, if I wanted to be super exact, but an estimate using geometry sufficed.

A quick check of Wikipedia showed equations for both volume and circumference of a cylinder, enough to get me started.

V = hr^2 * [pi]

C =  2r * [pi]


But wait! Both the bottle and the dress form have at least 3 places I could measure circumference. Which one(s) do I use?

I decided to measure both the ‘bust’ and the ‘hips’, and average them.

So I would measure circumference to solve for the radius, which I would then use in the equation for deriving volume.


Before I got around to doing all of this, Spouse spied a much bigger (1 L) bottle of Frizzante soda at Wegmans, and I bought it, to use with larger prototypes.

Comparing the smaller bottle to the larger (which I did not do until right now), the 330 mL ≈ 1/3 of 1 L, so their volumes should be approximately 1:3. But how do they compare to the dress form?

Variable Small bottle Large bottle Dress form
Height, h 8 inches 12 inches 32 inches
Avg. circumference, C 8 inches 11 inches 39 inches
Radius, r 1.27 inches 1.75 inches 6.2 inches
r^2 1.62 inches 3.06 inches 38.5 inches
Volume, V 40.7 inches^3 115.5 inches^3 3873.2 inches^3

See the 2 bottles and the dress form here:

volume comparison

volume comparison

Therefore, the scale of the small bottle to the dress form ≈ 1:95 and the scale of the large bottle to the dress form ≈ 1:33.5, or 2:67.

(The small bottle to the large bottle ≈ 1:2.84, which may be that much less than 1:3 because of rounding errors.)

So that takes care of one question—how do my bottles proportionally compare to my dress form?

For the second question—how can I store 3-D sketches in a 2-D book?—I also think I have an answer. I’m going to try paper clipping them on one side of the page, with maybe a pencil drawing on the other side. Although now that I think about it, maybe I should photograph the prototypes draped on the bottles, and affix hard copies of those photos into my sketchbook, so I preserve some of the dimensionality.

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