Visualizing Math

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The Ratio of the Sides of a Sheet of Paper is √2

In the ISO paper size system, the height-to-width ratio of all pages is (purposely) the square root of two (1.4142 : 1). In other words, the width and the height of a page relate to each other like the side and the diagonal of a square. This aspect ratio is especially convenient for a paper size. If you put two such pages next to each other, or equivalently cut one parallel to its shorter side into two equal pieces, then the resulting page will have again the same width/height ratio.

Basically, the ratio between the two sides of your sheet of paper is the square root of two. This is so that you can fold (or cut) the paper in half and the two halves will each be mini versions of the whole sheet, with the exact same ratios. Some find this even more beautiful then the Golden Ratio! So, the next time you’re holding a standard sheet of paper, know that you’re holding some really cool math. I mean, that’s one of the most famous irrational numbers right there in your hands!

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