# ISO standard A4 paper is commonly used throughout most of the world, except in the United States...

## Question:

ISO standard A4 paper is commonly used throughout most of the world, except in the United States and Canada. Its dimensions are 210 by 297 mm. This is not a golden rectangle, but the aspect ratio is close to another familiar irrational mathematical quantity. What is that quantity? If you fold a piece of A4 paper in half, what is the aspect ratio of each of the halves?

## Aspect Ratio of a Rectangle

The aspect ratio describes the proportion between the lengths of a geometric shape. It may be expressed in the form a:b, in fraction form, or in decimal form.

For a rectangle, the aspect ratio is the ratio of it width to it height.

The aspect ratio is the ratio of the width to the height. For the case of A4 paper, the aspect ratio is

{eq}\dfrac{297 \text{ mm}}{210 \text{ mm}} = \dfrac{99}{70} \approx \boxed{1.414285714} {/eq}

This is very close to {eq}\sqrt{2} \approx 1.414213562 {/eq}

Folding an A4 paper in half means halving its width while maintaining its height. Therefore, the aspect ratio of each half is

{eq}\dfrac{\frac{297}{2} \text{ mm}}{210 \text{ mm}} = \dfrac{99}{140} \approx \boxed{0.7071428571} {/eq}