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The mysterious proportions of A4 paper: Do you know why its aspect ratio is √2?
In daily life, whether printing documents, writing letters or making manuals, A4 paper is one of the most widely used papers. However, this ordinary piece of paper hides an unusual secret: its ratio is √2. Why does this seemingly abstract number become the core of paper standard specifications? Not only is this really the design of the paper, but it also reflects a deeper wonder of mathematics.
"The ratio of the length to the width of A4 paper is √2, which means that you can fold an A4 paper in half and the two pieces will still be A5 size and maintain the same proportions."
The ISO 216 standard specifies international paper sizes, including the A, B and C series. A4, as one of the most popular sizes, has become a global standard, but only North America still uses its own paper sizes, such as "Letter" and "Legal". This difference makes the trend of A4 more diverse and global than other sizes.
"The emergence of ISO standards not only makes the use of paper more convenient, but also greatly improves the efficiency of the printing and design industry."
A Series papers are a unique design with all sizes sharing the same aspect ratio. This makes it possible to fold A0 size paper in half multiple times or cut it from a larger paper to A4, the resulting paper size still maintains the ratio of √2. Such characteristics are unique advantages for printing and folding designs.
In everyday applications, designers and printers can take advantage of this mathematical property to create beautiful and functional prints. Imagine that when you use A4 paper for comprehensive design or creation, whether it is folded or cut, the proportions of the paper can always ensure harmony between its parts. It’s a perfect blend from practicality to aesthetics.
“The advantage of using the √2 ratio was discovered by the German scientist Lichtenberg as early as the 18th century. He pointed out that paper like this can retain the advantage of proportion when folded or cut.”
With the development of standardization, the application scope of A4 is getting wider and wider. Whether it is school assignments or business reports, A4 paper is indispensable. However, the A4's popularity also has history behind it. Since the introduction of the DIN 476 standard in Germany in 1922, the influence of this design has rapidly expanded to all parts of the world. Especially after World War II, A4 paper has almost become a global standard.
But why is the aspect ratio of A4 paper so important in practice? There are many deeper considerations involved, involving the intersection of culture, technology and science. For designers, the advantage of A4 paper is that it can adapt to various types of design needs without worrying about its proportional imbalance.
“This proportional scaling feature allows designers no longer to stick to fixed sizes, but can flexibly change to meet various creative challenges.”
When discussing these issues, we might as well think back. During your work or creative process, have you ever found that the proportion of A4 provided you with unexpected inspiration and solutions? And does the mystery of A4 paper give you a new understanding of mathematics and design in daily life?
Therefore, this seemingly ordinary A4 paper actually carries countless wisdom and design philosophy, allowing us to feel this simple but profound beauty in our fast-paced life.
