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Introduction
Introduction
We see it everywhere, from little chipped off pieces on the shore of beaches to the amazing reefs that it has built- coral. While this creature is widely known and often praised for its beauty in color and design, we hardly think about its odd structure. As with many things, it is something that is overlooked because of its commonality and the fact that we have just accepted that it is the shape it is. However, when we take a closer look, we see that there are no shapes like this that we can create in math class, and even in nature is not very widespread. In fact, these structures are "some of the most complicated mathematical models known to man". So let's take a deeper look.
Hyperbolic Geometry
Hyperbolic Geometry
When scientists first starting looking into the patterns and design of coral, they realized that it was a whole new level of complicated. The spirals and frills of coral were a confusing and complex pattern that they then called hyperbolic geometry. This was unlike anything they had encountered or looked into before. In fact, in a TED Talk about math behind the growth of coral, Margaret Wertheim said that scientists had symbolized math in such a way that they didn't even notice it in the nature around them- such as the sea slugs they were studying and the lettuce they were fed with.
Hyperbolic Geometry was discovered in 19th century by Diana Taimina, and then other scientists learned to model it in 1997. So, as they started doing research on this new type of modeling, they discovered that it could be imitated only by crotchet, and was nearly impossible on computers (though now I'm sure that's changed). The main principle behind it is that, while in other types of geometry given a line there can be exactly one through any given point that is parallel to that line, there can be an infinite number of lines that pass through the point and are still parallel to the line. This creates the frills that we see in these amazing specimens.
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Sources:
This page by Rebekah B. ('18)
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