Buzz
Shapes are an integral part of the world we live in. Every living being and object we encounter is made up of shapes. Yet, these shapes are often something we overlook. For instance, did you know the shape of your eye? It closely resembles a sphere, although it isn't quite one.
That's why we've compiled this list of ten fascinating facts about shapes. It includes some of the most surprising and bizarre things about shapes you probably never knew—ranging from shapes we've discovered, created, and even misidentified.
10. A brand new shape was discovered
While it’s rare for the discovery of a new shape to make headlines, on July 27, 2018, scientists announced the identification of a completely new shape known as the scutoid.
The scutoid is an irregular 3D shape with eight faces, which we can best describe as a seven-sided pentagonal prism.
A pentagonal prism consists of seven faces—two pentagons at the top and bottom, and five rectangular sides. Now, imagine cutting off the top of one pentagon to create a hexagon. This cut extends into the neighboring rectangular faces, forming a small triangular face. This is the shape we call a scutoid.
Scutoids naturally appear in the curved regions of human organs, where epithelial cells adopt this shape to fit in, maintain stability, and conserve energy. Interestingly, these cells also take the form of prisms and fulcrums in other areas of the body and organs.
9. We created a brand new shape
When scientists aren't discovering new shapes, they’re inventing them. Take the hemihelix, a new shape crafted by Harvard scientists. In a classic case of serendipity, they created the shape accidentally while working on a project to develop helix-shaped rubber springs.
When it comes to helixes, the hemihelix is closely related. A helix is a spiral shape that moves upwards, and you’re probably familiar with helixes in things like springs, telephone cords, and spiral staircases.
You can easily make a hemihelix by manipulating flexible helix-shaped materials, like a telephone cord. Simply twist the cord until part of it stretches longer than the rest. As you keep twisting, the rest of the helix will become more curved and elongated, resulting in a hemihelix.
8. Pizza slices aren’t actually triangles
If there were one food to help teach shapes in a classroom, it would certainly be pizza. They’re baked as circles, cut into triangle shapes, and packed into square boxes. But why is it this way?
The answer is a bit more complex than you might think.
Pizzas are round because it’s the simplest way to bake dough into a pizza shape. They’re stored in square boxes because it’s the most efficient way to transport a round object. However, they aren’t cut into triangles, but rather into sectors.
A sector is a slice taken from the center of a circle to any point on its circumference (the curved edge of a circle). A pizza slice would be a triangle if all three sides were straight, but it’s actually a circular sector because two sides are straight and the third is curved.
7. Paper is not a rectangle
If you asked most people what shape a sheet of paper is, they’d say it’s a rectangle. But is a sheet of paper really a rectangle? The answer is no, and we’ll explain why.
Shapes are divided into 2-dimensional (2D) and 3-dimensional (3D) categories. 2D shapes have length and width (or breadth), while 3D shapes have length, width, and height (or depth).
Any shape we draw on paper is a 2D shape. These shapes have only length and width, even though we can use techniques like shading and lines to give the illusion of 3D. However, everything in the real world is three-dimensional, including the paper we draw on.
So why do so many people think paper is a 2D shape?
The answer lies in the key difference between 2D and 3D shapes. 2D shapes are flat, while 3D shapes have thickness. People often assume paper is flat, but in reality, it does have thickness. It may be small and barely noticeable, but it exists. Paper has length, width, and depth.
Now that we’ve clarified that, what kind of 3D shape is paper? Paper is a cuboid, which is the 3D version of a rectangle.
6. Shapes that resemble circles
If we asked you to name a perfectly round 2D shape, you'd probably mention circles, right? Circles are often seen as the only perfectly round 2D shapes.
Well, here’s a surprise: circles aren’t the only perfectly round 2D shapes out there. There are a few other 2D shapes that are just as perfectly round as circles. In fact, these shapes are so similar to circles that it’s nearly impossible to tell them apart.
One example is the 257-gon, a polygon with 257 sides. A polygon is any shape with at least three sides of equal length and angle. For instance, an equilateral triangle is a three-sided polygon, a square is four-sided, and a pentagon is five-sided.
But the 257-gon isn’t the only shape that can impersonate a circle. The 65537-gon is another example—it’s a polygon with 65,537 sides.
5. Points are circles
Logic suggests that a collection of points and lines can only form a shape if they create a distinct figure, meaning the lines must all connect, enclosing the space inside them. This implies that a point or a line cannot be considered a shape, and the simplest shape is a triangle, consisting of three sides or lines.
But what if we told you that a point can be considered a shape, similar to a circle? Would you believe that? It’s actually true! To understand why a point can be regarded as a circle, we first need to understand what defines a circle.
Circles don’t conform to the usual definition of shapes. Although they have a boundary, a surface, and a curved line, they lack sides. They don’t have length or width, but instead have a radius, which is a line extending from the center to any point along the curve.
So, what is the smallest radius a circle can have? It’s zero inches (or centimeters, or any unit of measure). If we draw a circle with a zero-inch radius, we would essentially have a point. And what do we call that point? It’s still a circle, naturally.
Mathematicians refer to this point as a “degenerate circle.” The term degenerate means it doesn’t follow the usual rules that apply to other circles.
4. Spheres don't actually exist
There’s an ongoing debate in mathematics about whether true spheres exist in nature. You might be thinking, ‘but surely spheres exist!’ Aren’t planets, moons, and stars all spherical?
To answer this, we must first define what a sphere is. A shape is called a sphere if the distance from its center to any point on its surface is exactly the same all the way around. But do the planets, stars, or moons have a consistent distance from their center to their surface? The answer is no, they don’t.
Due to their rotational speed and the various internal and external forces acting on them, every planet, star, and moon is slightly flattened at the poles and bulges at the equator. This means the distance from their center to the surface is longer at the equator and shorter at the poles.
As a result, these celestial bodies are not perfect spheres. So, what shape are they? They are oblate spheroids. While they may appear spherical, they are not truly spheres.
3. 4D shapes are mind-bending
We all know about 2D shapes like squares and 3D shapes like cubes, but have you ever considered 4D shapes like tesseracts?
A tesseract is to a cube what a cube is to a square. To visualize it, think of a cube: It has six square faces. Now, imagine that each of those square faces is actually a cube. That’s a tesseract – essentially, six cubes inside a larger cube.
4D shapes, like tesseracts, are purely hypothetical and exist only in the realm of scientific imagination. Even if they did exist, it’s unclear whether we would be capable of perceiving them. But who knows? If we can imagine and understand 2D shapes that don’t physically exist, perhaps we might one day be able to grasp the concept of 4D shapes. But again, it’s all uncertain.
2. Triangular tires are real
Have you ever attempted to drive a car with square wheels? Mythbusters once experimented with this, and let’s just say it wasn’t the smoothest ride for either the driver or the vehicle. There's a reason why tires and wheels are round.
But is it possible to make wheels and tires with shapes other than circles? The answer is yes, and one option is using Reuleaux triangles. These shapes resemble triangles, but with curved edges instead of straight lines.
To create a Reuleaux triangle, start with an equilateral triangle. Next, draw three circles of the same radius from each of the triangle’s three angles. The result is a Reuleaux triangle, made up of the original triangle and three curved segments outside its sides.
The Reuleaux triangle mimics the functionality of a circle, especially when you need something that works better in certain situations or when ergonomics matter. For example, if you needed a rotor to function in a confined space, like a square, you'd use a Reuleaux triangle instead of a circle.
Reuleaux triangles are also a key feature in modern pencils, as they provide a better grip. In fact, they could potentially be used for bicycle wheels, and maybe even car tires. With a few modifications, you could replace your regular circular bicycle wheels with Reuleaux triangle wheels, and they would work just fine.
1. Squircles are not rounded squares
You might not be familiar with the term 'squircle,' but chances are you’ve seen one. You probably mistook it for a square. Squircles are a blend of squares and circles, essentially squares with rounded edges.
That said, a squircle isn’t the same as a rounded square, although they may look alike. A rounded square still retains some sharpness at its corners, though less pronounced. On the other hand, squircles have entirely smooth, circular edges.
Apple is known for incorporating squircles into its design, which is one reason their products are so visually appealing. The edges of iPhones are inspired by the soft curves of squircles. Even the app icons on iPhones used to be rounded squares before iOS 7, but now they are squircles.
