The beauty of Apple products goes beyond technology, it’s also geometry


When we look at an Apple product, whether we’re talking about the latest iPhone 14 or just looking at an icon we have in the Dock, the grandeur of its proportions is evident. There is something beautiful about measurement that makes it simply alluring, elegant. These are, in many respects, Euler spirals.

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 hands, our heights are proportions. Nails Ratios that can be expressed mathematically, The best known is the golden ratio, which can be found in the distribution of sunflower seeds or in the branches of a tree, and also in La Gioconda. and or? Even in the Apple logo. But that is the subject of 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 is directly created by man. A straight line may look beautiful to us, but it is not natural, While curves are everywhere, let’s see where we’re looking. All kinds of curves, all kinds of spirals, and everything that nature put there.

The design model 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. What can also be called clothoid in Spanish, what is it? The transition curve is calledIn a few words, it looks like a curve, as it rotates its radius decreases, allowing it to connect two straight lines with great precision.

Euler curve in red. Circle in blue.

This has many applications, such as a highway or a railroad, because a vehicle traveling at constant speed will have a constant angular acceleration. in the apple Acts as a bridge between all the straight lines we see on all products. Examples are many, the curves of notches, the curves of similar products on their sides, the rounds of signs and buttons, etc.

Visually the difference is clear. We see here two straight lines (red) which form an Euler curve. In superposition we see a union by a quarter circle (in blue). We may like each other more than each other, but In our environment we usually see Euler curvesSo much so that its name clothoid comes from the Greek clothin (to turn), a reference to the shape of wool when it is rolled up on a loom.

The mystery of the Apple logo and its relationship to the Fibonacci sequence

Ultimately, aesthetics is the comparison. You 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 we recognize without necessarily understanding it. And that’s, quite simply, the reason behind the shape of our Apple products.

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