19 Piet Hein decided that this was the most beautiful shape possible for the roundabout. In an article he wrote afterward, he remarked that [1]: “To draw something freehand — such as the patchwork traffic circle they [other architects] tried in Stockholm — will not do. It isn't fixed, isn't definite like a circle or square. You don't know what it is. It isn't aesthetically satisfying. The super-ellipse solved the problem. It is neither round nor rectangular, but in between. Yet it is fixed, it is definite — it has a unity.” Between iOS 6 and iOS 7, the design team at Apple also decided to make use of this satisfying aesthetic. Up until then the shapes of the app icons in iOS had been squares with rounded corners (Figure 3) [6]. This is a problem for the same reason as the Stockholm roundabout: The transition from straight line to tightly curved circle is visually jarring even if we don’t notice it consciously. So, Apple’s designers based their new app icons on the Lamé curve. They adopted the curve where n = 26/5 or 5.2 with slight modifications [7], which results in a shape that has a smooth flow that is meant to feel more natural. (Note that the four sides of a superellipse are not straight lines, but curves, even if n equals to a relatively large number like 5.2.) Figure 4 Shapes of the previous (left) and new (right) logos of Xiaomi. Xiaomi may have thought along the same lines. In 2021, the electronics company also changed its logo from a rounded square to an obvious Lamé curve (Figure 4). Figure 2 Piet Hein’s solution to the roundabout at Stockholm. Figure 3 App icons in iOS 6 (square with rounded corners) and iOS 7+ (modified superellipse). Kenya Hara, the leading Japanese designer who oversaw the initiative, went through the same process as Piet Hein did and decided that n = 3 would look the most aesthetic [8]. But Piet Hein did something that Xiaomi didn’t. Piet Hein had a definite purpose in mind when he chose the superellipse. On the other hand, Xiaomi reportedly paid Hara two million yuan to change the shape of the logo and almost nothing else; the consensus on the Internet was that there was no real purpose to the redesign [9]. Xiaomi already had an iconic logo. Did the redesign really have a purpose? The answer was affirmative according to Hara; the new logo was said to be “an encapsulation of Xiaomi’s inner spirit” and “essentially a reflection of the concept ‘Alive [8].’” The Lamé curve strikes a balance between straight and curved, useful tool and purposeless curiosity. So does much of mathematics – it may be hiding out of sight; it may take 200 years to find an application; it may occasionally be mocked on the Internet, but somehow it is there, if you know where to look.
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