# Ruler

"Carpenter's rule" redirects here. For the mathematical unfolding problem, see Carpenter's rule problem.
A variety of rulers
A 2-meter carpenter's rule
Retractable flexible rule or tape measure
A closeup of a steel rule

A ruler, sometimes called a rule or line gauge, is an instrument used in geometry, technical drawing, printing, engineering and building to measure distances or to rule straight lines. The ruler is a straightedge which may also contain calibrated lines to measure distances.[1]

## Types

Gilded Bronze Ruler - 1 chi = 23.1 cm. Western Han (206 BCE - CE 8). Hanzhong City, China
Bronze ruler. Han dynasty, 206 BCE to CE 220. Excavated in Zichang County, China
A flexible ruler unstretched.
A flexible ruler stretched.

Rulers have long been made of different materials and in a wide range of sizes. Some are wooden. Plastics have also been used since they were invented; they can be molded with length markings instead of being scribed. Metal is used for more durable rulers for use in the workshop; sometimes a metal edge is embedded into a wooden desk ruler to preserve the edge when used for straight-line cutting. 12 inches or 30 cm in length is useful for a ruler to be kept on a desk to help in drawing. Shorter rulers are convenient for keeping in a pocket.[2] Longer rulers, e.g., 18 inches (45 cm) are necessary in some cases. Rigid wooden or plastic yardsticks, 1 yard long and meter sticks, 1 meter long, are also used. Classically, long measuring rods were used for larger projects, now superseded by tape measure or laser rangefinders.

Desk rulers are used for three main purposes: to measure, to aid in drawing straight lines and as a straight guide for cutting and scoring with a blade. Practical rulers have distance markings along their edges.

A line gauge is a type of ruler used in the printing industry. These may be made from a variety of materials, typically metal or clear plastic. Units of measurement on a basic line gauge usually include inches, agate, picas, and points. More detailed line gauges may contain sample widths of lines, samples of common type in several point sizes, etc.

Measuring instruments similar in function to rulers are made portable by folding (carpenter's folding rule) or retracting into a coil (metal tape measure) when not in use. When extended for use they are straight, like a ruler. The illustrations on this page show a 2-meter carpenter's rule which folds down to a length of 24 cm to easily fit in a pocket, and a 5-meter-long tape which retracts into a small housing.

A flexible length measuring instrument which is not necessarily straight in use is the tailor's fabric tape measure, a length of tape calibrated in inches and centimeters. It is used to measure around a solid body, e.g., a person's waist measurement, as well as linear measurement, e.g., inside leg. It is rolled up when not in use, taking up little space.

A contraction rule is made having larger divisions than standard measures to allow for shrinkage of a metal casting. They may also be known as a shrinkage or shrink rule.[3]

A ruler software program can be used to measure pixels on a computer screen or mobile phone. These programs are also known as screen rulers.

## Ruler applications in geometry

In geometry, a ruler without any marks on it (a straightedge) may be used only for drawing straight lines between points. A straightedge is also used to help draw accurate graphs and tables.

A ruler and compass construction refers to constructions using an unmarked ruler and a compass. It is possible to bisect an angle into two equal parts with ruler and compass. It can be proved, though, that it is impossible to divide an angle into three equal parts using only a compass and straightedge — the problem of angle trisection. However, should two marks be allowed on the ruler, the problem becomes solvable.

## History

A wooden carpenter's rule and other tools found on board the 16th century carrack Mary Rose

In the history of measurement many distance units have been used which were based on human body parts such as the cubit, hand and foot and these units varied in length by era and location.[4] In the late 18th century the metric system came into use and has been adopted to varying degrees in almost all countries in the world. The oldest preserved measuring rod is a copper-alloy bar that dates from c. 2650 BC and was found by the German Assyriologist Eckhard Unger while excavating at Nippur. Rulers made of Ivory were in use by the Indus Valley Civilization period prior to 1500 BC.[5] Excavations at Lothal (2400 BC) have yielded one such ruler calibrated to about 116 inch (1.6 millimetres).[5] Ian Whitelaw holds that the Mohenjo-Daro ruler is divided into units corresponding to 1.32 inches (33.5 millimetres) and these are marked out in decimal subdivisions with amazing accuracy, to within 0.005 inches (0.13 millimetres). Ancient bricks found throughout the region have dimensions that correspond to these units.[6]

Anton Ullrich invented the folding ruler in 1851. Frank Hunt later made the flexible ruler in 1902.[7]

## Curved and flexible rulers

The equivalent of a ruler for drawing or reproducing a smooth curve, where it takes the form of a rigid template, is known as a French curve. A flexible device which can be bent to the desired shape is known as a flat spline, or (in its more modern incarnation) a flexible curve. Historically, a flexible lead rule used by masons that could be bent to the curves of a molding was known as a lesbian rule.[8]

## Philosophy

Ludwig Wittgenstein famously used rulers as an example in his discussion of language games in the Philosophical Investigations. He pointed out that the standard meter bar in Paris was the criterion against which all other rulers were determined to be one meter long, but that there was no analytical way to demonstrate that the standard meter bar itself was one meter long. It could only be asserted as one meter as part of a language game.

## Sticking to the ruler's marks

When using a ruler use the smallest mark as the first estimated digit. For example, if a ruler's smallest mark is cm, and 4.5 cm is read, it is 4.5 (±0.1) or range 4.4 to 4.6 cm.

The overall length of a ruler may not be accurate within the degree of the smallest mark and the marks may be imperfectly spaced within each unit. With both of these errors in mind, reading between the marks (to 4.55) does not increase one's confidence in the overall reading and may make it worse.

## References

1. Dictionary.com definition
2. contraction rule Retrieved May 15, 2013
3. Klein, Herbert A.. The science of measurement: a historical survey. Reprint, unabridged, corr. republ. der Ausg. New York, Simon & Schuster, 1974. ed. New York, NY: Dover, 1988. Print.
4. Whitelaw, p. 14.
5. Whitelaw, p. 15.
6. "Flexible Ruler Invented by Frank G. Hunt". National Museum of National History. Retrieved 7 June 2016.
7. "lesbian, adj. and n.". Oxford English Dictionary (3rd ed.). Oxford University Press. September 2005. (Subscription or UK public library membership required.) (subscription required)

## Bibliography

• Whitelaw, Ian (2007). A Measure of All Things: The Story of Man and Measurement. Macmillan. ISBN 0-312-37026-1.