Understanding the why of ISO 216:2007 paper sizes

Geometry Level 3

Starting with a sheet of paper with an area of $1 m^2$ , but not $(1 m)^2$ , by cutting a sheet in a straight line across the short dimension at the middle of the long edges, one gets the next smaller sheet size. The ratio of the long edge divided short edge remains the same. In the standard mentioned in the problem's title, the long edge of the original sheet can be expressed as $2^{\frac1n}$ rounded to the nearest millimeter. The answer is the value of $n$ .

The answer is 4.

1 solution

A Former Brilliant Member
Dec 22, 2018

The A series is being used in the problem. The area of each smaller sheet is one-half of the area of the previous sheet. Therefore, the edge sizes are descending by $\frac1{\sqrt2}$ . To get an initial area of $1 m^2$ with a long edge divided the short edge ratio of $\sqrt2$ , the initial long edge length needs to be $\sqrt{\sqrt2}$ meters or $2^\frac14$ meters. The answer is $4$ .

The B series starts with an area of $\sqrt2 m^2$ and a long edge length of $2^{\frac13}$ meters.

The C series starts with an area of $2^{\frac14} m^2$ and a long edge length of $2^{\frac38}$ meters.

Understanding the why of ISO 216:2007 paper sizes

The answer is 4.

1 solution

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