Not so Golden Seashell Spirals

I learned something this weekend...

I learned that if you are trying to draw that spiral in the nautical seashell you cannot do it by using the golden proportions. I am designing a tapestry with a nautical sea shell overlapping a golden spiral which spirals into a planet. I always thought the spiral in that shell was a golden spiral but turns out it is a logarithmic spiral. It does make a difference when trying to draw it.

I must have done four or five drawings of the spiral with my ruler and compass. I figured it was coming out poorly since I was not exact enough. When using a pencil with a ruler & compass the results are subject to error - sometimes significant. That was something I learned in my Coastal Navigation classes. If you want a good chance to get where you want to go don't be sloppy with the plotting pencil. This weekend, no matter how careful I was, my drawing always turned out poorly - the spiral would never spiral in enough.

Now I know I need to draw the seashell spiral logarithmically in order for it to spiral enough to look like a shell. If you can see the difference between the two spirals and learn more check out this article by John Sharp called Spirals and the Golden Section.

I will post a photo of my design when I finish the cartoon. It will be 32 wide - the loom is already warped. Not quite sure how long it will be - probably about 4 feet. But perhaps longer...