Is Math Really Involved With Everything? The Geometry of Starfish

Most people may not have seen a starfish in real life. For example, the closest thing I have seen in my life would probably be from biology lessons in which we learned about regeneration. However, they are all around us. We may come across star fish as their sculptures decorating our rooms, in documentaries, or most probably, hear about them just because of their shape! This really puts in perspective how there are tons of organisms residing in aquatic systems we have never heard about, yet most of us know starfish. Why? Of course, because of their curious shape. So, what is so important about these animals?


Although they live in salt waters and are called starfish, star fish – or also known as sea stars – look nothing like fish. Instead, they actually fall under a category named “echinoderm”. This term is used for some marine invertebrates and involves many classes which are separated by differences in skeletal structures (Britannica). Aside from that, these organisms interestingly have a water vascular system and radial symmetry. Most of them have a spiky appearance (Britannica).



Source: Nhobgood Nick Hobgood, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons


The shape of starfish is peculiar. Considering they have no means to see and cannot swim, they are mostly stuck on surfaces. While this could assist them in not drifting or defending themselves, it leaves them with their movement and locomotion dependent on their arms. With their arms, they are able to cover more area and do not have a sense of front and behind. Thus, having the same appendage in every direction allows them easier navigation (Auckland War Memorial Museum).


While they have no front or behind, they have a symmetry called “radial symmetry”. From the center point, multiple lines of symmetry can be drawn. And since most of them have five arms radiating from an indistinct disk (New World Encyclopedia), they possess pentameral symmetry. The shape that is similar to pentagram has a golden ratio. Considering that starfish with five arms are the most common, it is curious that the one exhibiting the golden ratio has persevered (“The Advantages of the Pentameral Symmetry of the Starfish.”). Moreover, their vital organs are located in their arms, thus they are able to regenerate lost appendages. Some species are even able to regenerate an entire body from an arm (National Geographic).

They possess a skeleton. This skeleton is made of calcite growths called ossicles. While calcite is not inherently strong and can be considered weak, even more so if it is porous, they are reinforced with its architectural design. The calcite are arranged like hexagons. This arrangement fortifies the calcite. In doing so, it also overrides the natural brittleness of calcite mineral. When zoomed in, the ossicles seem to be arranged similarly to the pattern of carbon atoms in a diamond. However, it is still a mystery how they were able to create this diamond-like lattice (“A Diamondlike Structure Gives Some Starfish Skeletons Their Strength.”).

Overall, starfish, with their shape, their water vascular system, the way they utilize their arms to navigate, and all other vast abilities, are incredibly exciting creatures to read about. There are various abilities they possess by the way they are shaped, which makes it truly fascinating to see their formation through the eyes of mathematics.


Works Cited


“Echinoderm.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., https://www.britannica.com/animal/echinoderm.


“Why the Starfish Is Star-Shaped.” Auckland War Memorial Museum, https://www.aucklandmuseum.com/discover/stories/blog/2015/why-the-starfish-is-star-shaped.


“Starfish.” New World Encyclopedia, https://www.newworldencyclopedia.org/entry/starfish.


Wu, Liang, et al. “The Advantages of the Pentameral Symmetry of the Starfish.” ArXiv.org, 21 Feb. 2012, https://arxiv.org/abs/1202.2219.


“Starfish (Sea Stars)” National Geographic, https://www.nationalgeographic.com/animals/invertebrates/facts/starfish-1.


Wilke, Carolyn. “A Diamondlike Structure Gives Some Starfish Skeletons Their Strength.” Science News, 10 Feb. 2022, https://www.sciencenews.org/article/starfish-skeleton-structure-diamond-strength-calcite.


Image Source: Nhobgood Nick Hobgood, CC BY-SA 3.0 <https://creativecommons.org/licenses/by-sa/3.0>, via Wikimedia Commons

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