Shapes Shapes

I have a problem with some shapes. For example, not really a fan of the square. It has never done anything to me, I just don’t feel much affinity towards it. It’s kinda terrible in engineering, it always needs other trusts supporting it, and it is just kind of ugly. Other shapes, however, (the calabi-Yau manifold, scutoid, vesica piscis, the reuleaux triangle) are cool. My personal favorite is the torus, which there is already a past post on, but hopefully, you will be able to find your own favorite shape too.

Let’s start with the scutoid.

This shape is formed by connecting two parallel polygons into a verticle column. You can see that one surface has 5 sides while the other surface has five. The scutoid then twists around to join each of these corners. Just like in the sphere packing video, this shape maximizes exposed surface area and volume. Imagine you start with many lumps of dough in a closed space. When that dough rises, it naturally twists around each other and molds into different shapes. When biological sells are left to grow and expand in a similar nature, these scutoid are formed. They are part of epithelia or continuous sheets of cells. Such examples would be in the skin or organ tissues. What is also cool is that not all “cell packings“naturally form into the shapes of a scutoid. For example, past posts talk about the arrangements of biology parts into the Fibonacci sequence. Honeycombs and some fruits are instead found in a hexagonal shape. This suggests that the scutoid has benefits when used in sheets of cells. One such is that is flexible. Because all the cells formed around each other, they can move with each other pretty efficiently. It might also have to do with how all of the cells originated, all of them expanding at once instead of adding new cells after certain periods of time. What I think is cool about this shape is that it is considered relatively new. It was only in 2018 that researchers discovered this shape and gave it a name, which means you could be one of the first few to choose this as your own favorite shape.

Pros of this shape: It is pretty useful overall. It is also sturdy and abundant in nature.

Cons of this shape: It has gotten more popular since 2018, so it may no longer be a unique favorite shape.

Moving on to the Vesica Piscis:

This is less of a stand-alone shape and more the result of two other shapes. The vesica Piscis is the intersection between two same-radius circles. Each circle intersects the other circle’s radius. This “shape“ might seem un-useful on its own, but Euclid in his Elements lays out how to use this shape to form an equilateral triangle. If you horizontally divide the vesica piscis in half and connect each side to the intersection of the two circles, you will be left with two equilateral triangles and four circle sectors.

This shape can be found most obviously in Venn diagrams, but it is also used in many different cultures through the eras. For example, the Christian “fish“ uses the vesica piscis with the addition of a triangle. It is also used in different religious artworks. The shape itself is popular in cathedrals and roof structures. This paper illustrates more in detail this shape’s connection to architecture.

Pros of this shape: Cool connections to architecture and a good historical staple.

Cons: Not aesthetically pleasing by itself.

Finally, the Reuleaux Triangle

Great. Another triangle thing. This shape can again be formed by the intersection of circles. If you draw three circles of equal size, the intersection at their centers, this shape will appear. Another way to construct this shape is to first start with the equilateral triangle. Then, place a compass on each corner and draw the corresponding arc. After all three arcs are drawn, the Reuleaux triangle will remain.

What I think is cool about this shape, is that if inscribed into a square, rotating the triangle will smoothly move the square. This is useful in engineering with you need to turn circular motion into lateral motion. I think that one strange use of this shape is in a fire hydrants valve nut which secures the fire hydrant. Some countries also use this shape for currency.

Pros of this shape: Easy to construct and useful in engineering.

Cons of this shape: A little bland for a favorite shape.

Maybe you don’t like any of these shapes which is totally fine. Personally, I will stick to the torus for my favorite, but the scutoid might be a close second. Hopefully, you too can find your own shape and advocate for it when faced with challenges.