The Hidden Figure


The curvature continuous filet or squircle.


  • Why are the ios app icons shaped like they are?
  • Why are most dishes shaped as they are?
  • A simple tweak in design changing the look of it.
  • This week in Invisible History: "The balloon crossing the ocean." Domain: Air Travel.
  • Discuss the article here.

After late 2018 when I walked into the office I work, I learned a lot of things that a Mechanical Engineer must know. I learned about plastic design, sheet metal tooling, extrusion guidelines, design of castings and various others. In all the lessons, there is one particular thing I got to know which is something as invisible as it gets yet found everywhere: Fillets.

Fillets are something that is given to edges in mechanical design for aesthetics and safety. Fillets smoothen rough edges. There is a special type of fillets which I was introduced to while designing my first battery pack. These are called curvature-continuous fillets. It is mostly known by another name: Squircle. I can’t unsee it after I have the knowledge about it.

Let's get down to difference

As I said, once you notice the difference, it will be impossible for you to unsee it. In side-by-side comparison images, it is easy to see how the dynamic approach informs shapes and eliminates sharp transitions between flats and curves. A typical circular fillet usually shows the two edges generated at the tangential line where the circle contacts the line.

The round fillet (up corner) and squircle (bottom.) The curvature comb shows how complex the squircles are.

A squircle is a portmanteau of circle and square in English and mathematics (mathematical intermediate.) A squircle is usually preferred in the design as it avoids the tangential line where the circle contacts the line. It leaves a continuous crafted curvature and hence the name "curvature continuous fillet." In other words, no sharp transition from flats to curves.

Let not the sun go down on your Math

A general equation of a square and a rectangle is,1

x4 + y4 = r4 

x = X co-ordinate 
y = Y co-ordinate 
r = Radius of the circle.

This is the most basic equation for a squircle. There are more equations from Superellipse-based approach and Fern├índez–Guasti approach. But to understand the geometry, let's do a practical. Desmos is an excellent online graph generator. Plugin the basic equation as mentioned before but replace the 4 with any variable (e.g. variable can be a.)

The graph generated on Desmos. (x4+y4 = r4 with r=10)

Now in the scale slide the value of a to 4. You must see the graph making a squircle now. Slide the value of "a" to a higher value, and you will see that the radius of the fillet becomes smaller. We all know that when the value of "a" is 2, the shape of the graph is a circle. Now, as the value increases, the form turns more towards a square. The designers try to keep the value of this variable near 4 for a smooth intermediate between circle and square.

On the use

The most common example of squircles is the dinner plates. The plates in the past were supposed to be rectangular. The issue with rectangles or squares is that the area of the table occupied by it is more. Circles take the least space for a plate. But they are not very pleasing aesthetically. So squircles came to the rescue. It takes up less space as compared to square (but still hold enough food) and is aesthetically pleasing.2

Squircle dish
A soap dish with curvature continuous fillets.

Other examples are Nokia phones with their squircle-shaped touchpad buttons.3 Fiat extensively used squircles in the third generation of Panda. One of the most known examples is Apple phones. The app icon shapes and phone fillets are usually squircles.4 These are also used in Android Oreo phones.

Your turn now

Nowadays, squircles can be found everywhere, from aesthetics and safety to critical functions and space optimisation. I really think as a design engineer one must have a basic knowledge of this kind of fillet. About the math, I think we can pass that. :P So next time you see any phone or dish think about the fillet and the designing went behind it.

This week in Invisible History

I think the answer behind the last week’s history code was not that simple as only one person could guess the answer. Many came close but couldn’t get the exact name except Nikhil Chandratre (WhatsApp.) The last week’s code referred to the two specimens of Tyrannosaurus which were discovered in 1990 and 1987 respectively. Sue was discovered on 12th August 1990 by Sue Hendrickson an explorer and fossil collector. The dinosaur is named after her. This article5 from National Geography explains all the details about this discovery and the impact of it. It is a great read.

Sue’s skeleton

The clue for next week is something related to air travel. The clue is "The balloon crossing the ocean." You can write the answers to me in the comment section or on social media. I have left the links down below. If you give the right answer, your name will be mentioned in the next week’s article.

Reading about the fillet and how it affects the design was a shocker for me. Right now, as a Mechanical engineer, I use fillets daily. The thought that comes to my mind is that there are only a few things that would not change if one tries to design them from scratch to serve the purpose. Fillets are one of them. Squircles are the next improvements to it. I hope this article helped you to understand and appreciate the importance of these fillets and use them in your daily design. If you seek more inspiration, feel free to follow the blog on social media. I have included the links below.

See you next Saturday! Have a good one!

  1. Reddit:r/theinvisiblegenius
  2. Instagram: @theinvisiblegenius
  3. Twitter: @notnitinchopra

Reference links

  1. "Squircle -- from Wolfram MathWorld
  2. Squircle Plate | Kitchen
  3. Nokia 6700 – The little black dress of phones | Nokia Conversations - The official Nokia Blog
  4. The Hunt for the Squircle
  5. Dinosaur 13 and the Ghost of Tyrannosaurus Sue


  1. Nice Nitin. Great insight from you. I noticed it many a times but never dig much.
    Is this your personal blog?

    1. Hey Kolay!
      Thanks! I maintain this blog to publish article every Saturday. I won't call this a personal blog. I just want to learn and share what I learn. If you have any article ideas, do let me know. Or if you want to help out in other way, it will be awesome!

    2. Hey Abhishekh! I just saw your name on Linkedin. Thanks for your feedback!


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