Apple launches foldable phone iPhone Duo with a screen ratio of √2:1, a professor from National Taiwan Normal University explains mathematical design principles

Apple's 2026 autumn conference officially debuted on the 10th, Taiwan time. The most important highlight of this conference was the launch of the first foldable screen mobile phone "iPhone Duo". Assistant Professor of the Department of Electrical Engineering at National Taiwan Normal University, Lai Yiwei, pointed out the mathematical ingenuity hidden in the new phone. He said that he was later asked by his children, "What is the use of learning the root number?" and finally had a more technological answer: the screen ratio of iPhone Duo is the classic "√2:1".

Lai Yiwei posted on Facebook that Apple's official website emphasizes that the new phone's internal and external screen ratios are highly consistent in the folded and unfolded states, allowing display content to seamlessly fill the screen between different types. This design logic is exactly the same as the common paper specifications in daily life. Just like A4 paper becomes A5 after being folded in half, and two sheets are spliced ​​into A3, the length-to-width ratio remains unchanged.

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Lai Yiwei pointed out that for a rectangle with an aspect ratio of √2:1, the ratio becomes "√2/2:1" after the long side is folded in half. After being simplified and sorted, it becomes "1:√2". In essence, only the long and short sides are interchanged, and the overall geometric proportions remain the same. If you strictly check the screen resolution of iPhone Duo, you will find that it is not exactly √2, and there is still a small gap due to engineering compromise.

Lai Yiwei continued to point out that the mathematician who invented this ratio was called Lichtenberg. According to legend, he had been looking for a ratio of paper to make "proportional scaling" easier. If you think about it carefully, in an era without screens, this was really an important need.