Stacy Getteson

Math in Patterns

Seashell's Spiral

The spiral of a seashell can be described as either equiangular or logarithmic, but it all can be explained by Fibonacci numbers. Fibonacci a mathematician discovered that in nature things occurred in a pattern. This pattern is 1,1,2,3,5,8,13,21, and so on. However, the equiangular spiral was officially discovered by Descartes in 1638. The spiral on a seashell is based on this pattern. The seashells that contain this spiral are usually on the nautilus shells and on the shell of a snail. There are many web sites that can be used to find out information about the spiral of a seashell. Each can be used to find different aspects about the shells. One can find out about the history or find pictures of the equiangular spiral.

At www.geom.umn.edu/~demo5337/s97b/spiral.html, there is a very good explanation on how to draw the spiral of the sea shell. It describes how to use a compass and draw an accurate picture of what the spirals pattern is and how it can be repeated. The web site is called Fibonacci in Nature.

Another web site explains why there are so many names for the same spiral. This is at www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#spiral. This page not only has information about the spiral of a shell, but explains about Fibonacci number=B9s in great detail. Although it is not important for the spiral, it is a good research web site.

At www.notam.uio.no/~oyvindha/loga.html, there are detailed pictures of several different types of mollusk shells. They all show how even though they are different shells, used for different things, they all contain the same equiangular spiral. This web site was small, but contained such great pictures that it is worth looking at. The name of the site is Logarithmic Spirals.

On the Equiangular Spiral page at http://www-groups.dcs.st-and.ac.uk/history/Curves/Equiangular.html, there is an in depth mathematical evaluation of the equiangular spiral. This explains how the pattern of the spiral is proven to work. The web site claims that the reason the seashells have the equiangular pattern is because the shell grows in proportion to the organism inside of it. Also, they state that every spiral on each sea shell is the same because they all start on the same point in space. This web site has a lot of useful information about the mathematical side of the seashell=B9s spiral.

The web site http://www.best.com/~xah/SpecialPlaneCurves_dir/EquiangularSpiral.-dir/equiangularSpiral.html, also called Equiangular Spiral gives a lot of useful information. This web site discusses the history of who discovered the spiral and when. They, like the other web sites, state that Descartes discovered the equiangular spiral in 1638. Also, the web site describes the mathematical point of view on where the spiral takes shape from. The spiral can be found on nautilus shells as well as several other types. The web site also gives formulas on how to find the equation of the spiral. The spiral that Descartes discovered is the equiangular spiral that is found on seashells. There are many web sites that have information about this subject, however the ones that I have listed provide the most useful information.