When we look at an Apple product, whether we are talking about the latest iPhone 14 or simply looking at an icon that we have in the Dock, the elegance of its proportions is evident. There is something aesthetic about the measurements that makes it simply appealing, Elegant. That something, in many cases, is the Euler spiral.
A mathematical form that we unconsciously recognize
Let’s take a philosophical stance for a moment. Beauty is practically encoded in our genes. If we look at nature, there are proportions. If we look at our own hands, our size, there are proportions. Nail proportions that can be expressed mathematically. The best known is the golden ratio, it is what can be found in the distribution of the seeds of a sunflower or in the branches of a tree and also in La Gioconda. Or more? Also in the Apple logo. But that’s a subject for another article.
We are talking here about curved lines and straight lines. There are very few straight lines in nature. If we look at our environment, everything that is righteous has generally been created by man. A straight line may seem elegant to us, but it is not natural. While curves are everywhere, let’s look where we’re looking. Curves of all kinds, spirals of all kinds, and everything nature puts into it.
Design template of an iOS icon, with its proportions.
Good design is as much an art as it is a math. At Apple they are fully aware of this and that is why all products have a very specific curve, where they need it. An Euler spiral. The one that in Spanish we can also call clothoid is what is known as the transition curve. In a few words we will say that it is a curve which, while turning, reduces its radius, which allows it to join two straight lines with great precision.
Euler curve in red. Circle in blue.
It has many applications, such as highways or railways, because a vehicle traveling at constant speed will have a constant angular acceleration. at Apple serves as a bridge between all the straight lines we see
Visually the difference is clear. We see here two straight lines (red) forming an Euler curve. In superposition we see a union by a quarter circle (in blue). We may personally appreciate one more than the other, but in our environment we usually see Euler curves. So much so that its name Clothoid comes from the Greek klothein (to turn), in reference to the shape of the wool when it is rolled up on the loom.
Ultimately, aesthetics is the comparison. Yes the comparison is directly marked by custom. The habit of seeing these mathematical objects in our daily lives and then seeing them in Apple products is something that, without necessarily realizing it, we recognize. And that, if simply put, is the reason behind the shape of our Apple products.
