Lichtenberg ratio
Encyclopedia
In paper size
s, the Lichtenberg ratio is the aspect ratio
of 1:√2. The term was proposed by Markus Kuhn in 2002.
This aspect ratio has the unique property that cutting any rectangular sheet of paper formed with the Lichtenberg ratio into two equal halves parallel to its shortest sides produces two smaller sheet of the same aspect ratio.
scientist Georg Christoph Lichtenberg
(in a letter to Johann Beckmann).
in 1922.
This has subsequently become the basis for the ISO 216
"A" series paper sizes.
Paper size
Many paper size standards conventions have existed at different times and in different countries. Today there is one widespread international ISO standard and a localised standard used in North America . The paper sizes affect writing paper, stationery, cards, and some printed documents...
s, the Lichtenberg ratio is the aspect ratio
Aspect ratio
The aspect ratio of a shape is the ratio of its longer dimension to its shorter dimension. It may be applied to two characteristic dimensions of a three-dimensional shape, such as the ratio of the longest and shortest axis, or for symmetrical objects that are described by just two measurements,...
of 1:√2. The term was proposed by Markus Kuhn in 2002.
This aspect ratio has the unique property that cutting any rectangular sheet of paper formed with the Lichtenberg ratio into two equal halves parallel to its shortest sides produces two smaller sheet of the same aspect ratio.
History
Writing paper in the ratio 1:√2, such that cutting it in half would preserve its proportions, was noted in 1786 by the GermanGermany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
scientist Georg Christoph Lichtenberg
Georg Christoph Lichtenberg
Georg Christoph Lichtenberg was a German scientist, satirist and Anglophile. As a scientist, he was the first to hold a professorship explicitly dedicated to experimental physics in Germany...
(in a letter to Johann Beckmann).
Usage
Early in the twentieth century, Dr Walter Porstmann noted the value of Lichtenberg's idea as a basis for a system of different paper sizes, which was first introduced as a DIN standard (DIN 476) in GermanyGermany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
in 1922.
This has subsequently become the basis for the ISO 216
ISO 216
ISO 216 specifies international standard paper sizes used in most countries in the world today. It defines the "A" and "B" series of paper sizes, including A4, the most commonly available size...
"A" series paper sizes.