A ruler, sometimes called a rule, line gauge, or scale, is a device used in

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

and

technical drawing Technical drawing, drafting or drawing, is the act and Academic discipline, discipline of composing Plan (drawing), drawings that Visual communication, visually communicate how something functions or is constructed. Technical drawing is essent ...

, as well as the engineering and construction industries, to measure distances or draw straight lines.

Variants

Rulers have long been made from different materials and in multiple sizes. Some are wooden.

Plastics Plastics are a wide range of synthetic or semi-synthetic materials that use polymers as a main ingredient. Their plasticity makes it possible for plastics to be moulded, extruded or pressed into solid objects of various shapes. This adaptab ...

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. 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. Longer rulers, e.g., , are necessary in some cases. Rigid wooden or plastic yardsticks, 1 yard long, and

meter stick A meterstick, metrestick, or yardstick is either a straightedge or foldable ruler used to measure length, and is especially common in the construction industry. They are often made of wood or plastic, and often have metal or plastic joints so ...

s, 1

meter The metre ( British spelling) or meter ( American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pr ...

long, are also used. Classically, long

measuring rod A measuring rod is a tool used to physically measure lengths and survey areas of various sizes. Most measuring rods are round or square sectioned; however, they can also be flat boards. Some have markings at regular intervals. It is likely th ...

s were used for larger projects, now superseded by

tape measure A tape measure or measuring tape is a flexible ruler used to measure length or distance. It consists of a ribbon of cloth, plastic, fibre glass, or metal strip with linear measurement markings. It is a common measuring tool. Its design all ...

surveyor's wheel A surveyor's wheel, also called a clickwheel, hodometer, waywiser, trundle wheel, measuring wheel or perambulator is a device for measuring distance. Origin The origins of the surveyor's wheel are connected to the origins of the odometer. W ...

or laser

rangefinder A rangefinder (also rangefinding telemeter, depending on the context) is a device used to measure distances to remote objects. Originally optical devices used in surveying, they soon found applications in other fields, such as photography an ...

s. 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 Agate () is a common rock formation, consisting of chalcedony and quartz as its primary components, with a wide variety of colors. Agates are primarily formed within volcanic and metamorphic rocks. The ornamental use of agate was common in ...

, picas, and

points Point or points may refer to: Places * Point, Lewis, a peninsula in the Outer Hebrides, Scotland * Point, Texas, a city in Rains County, Texas, United States * Point, the NE tip and a ferry terminal of Lismore, Inner Hebrides, Scotland * Point ...

. 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 carpenter's rule, which folds down to a length of to easily fit in a pocket, and a 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., for a person's

waist The waist is the part of the abdomen between the rib cage and hips. On people with slim bodies, the waist is the narrowest part of the torso. ''Waistline'' refers to the horizontal line where the waist is narrowest, or to the general appear ...

measurement, as well as for linear measurement, e.g., for the inside leg length. It is rolled up when not in use, taking up little space. 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 a 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

In the

history of measurement The earliest recorded systems of weights and measures originate in the 3rd or 4th millennium BC. Even the very earliest civilizations needed measurement for purposes of agriculture, construction and trade. Early standard units might only have ap ...

many distance units have been used which were based on human body parts such as the

cubit The cubit is an ancient unit of length based on the distance from the elbow to the tip of the middle finger. It was primarily associated with the Sumerians, Egyptians, and Israelites. The term ''cubit'' is found in the Bible regarding ...

hand A hand is a prehensile, multi-fingered appendage located at the end of the forearm or forelimb of primates such as humans, chimpanzees, monkeys, and lemurs. A few other vertebrates such as the koala (which has two opposable thumbs on each " ...

and

foot The foot ( : feet) is an anatomical structure found in many vertebrates. It is the terminal portion of a limb which bears weight and allows locomotion. In many animals with feet, the foot is a separate organ at the terminal part of the leg mad ...

and these units varied in length by era and location. In the late 18th century the

metric system The metric system is a system of measurement that succeeded the decimalised system based on the metre that had been introduced in France in the 1790s. The historical development of these systems culminated in the definition of the Intern ...

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 2650 BCE and was found by the German Assyriologist

Eckhard Unger Eckhard Unger ( Landsberg an der Warthe, 11 April 1884 – 24 July 1966) was a German assyriologist. Unger who was the curator of the Istanbul museum described the remains of Balawat Gates that are still in the Istanbul Museum. Unger was fully ...

while excavating at the Sumerian city of Nippur (present day Iraq). Rulers made of

ivory Ivory is a hard, white material from the tusks (traditionally from elephants) and teeth of animals, that consists mainly of dentine, one of the physical structures of teeth and tusks. The chemical structure of the teeth and tusks of mammals ...

were in use by the

Indus Valley civilization The Indus Valley Civilisation (IVC), also known as the Indus Civilisation was a Bronze Age civilisation in the northwestern regions of South Asia, lasting from 3300 BCE to 1300 BCE, and in its mature form 2600 BCE to 1900 ...

period prior to 1500 BCE. Excavations at

Lothal Lothal () was one of the southernmost sites of the ancient Indus Valley civilisation, located in the Bhāl region of the modern state of Gujarāt. Construction of the city is believed to have begun around 2200 BCE. Archaeological Survey of ...

(2400 BCE) have yielded one such ruler calibrated to about .Whitelaw, p. 14. Ian Whitelaw holds that the

Mohenjo-Daro Mohenjo-daro (; sd, موئن جو دڙو'', ''meaning 'Mound of the Dead Men';Anton Ullrich invented the folding ruler in 1851. Frank Hunt later made the flexible ruler in 1902.

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 French curve is a template usually made from metal, wood or plastic composed of many different segments of the Euler spiral (aka the clothoid curve). It is used in manual drafting and in fashion design to draw smooth curves of varying radi ...

. A flexible device that 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 Lead is a chemical element with the Symbol (chemistry), symbol Pb (from the Latin ) and atomic number 82. It is a heavy metals, heavy metal that is density, denser than most common materials. Lead is Mohs scale of mineral hardness#Intermediate ...

rule used by

masons Mason may refer to: Occupations * Mason, brick mason, or bricklayer, a craftsman who lays bricks to construct brickwork, or who lays any combination of stones, bricks, cinder blocks, or similar pieces * Stone mason, a craftsman in the stone-cutt ...

that could be bent to the curves of a molding was known as a

lesbian rule A lesbian rule was historically a flexible mason's rule made of lead that could be bent to the curves of a molding, and used to measure or reproduce irregular curves. Lesbian rules were originally constructed of a pliable kind of lead found on ...

Philosophy

Ludwig Wittgenstein Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian- British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is cons ...

famously used rulers as an example in his discussion of

language games A language game (also called a cant, secret language, ludling, or argot) is a system of manipulating spoken words to render them incomprehensible to an untrained listener. Language games are used primarily by groups attempting to conceal their ...

in the ''

Philosophical Investigations ''Philosophical Investigations'' (german: Philosophische Untersuchungen) is a work by the philosopher Ludwig Wittgenstein, published posthumously in 1953. ''Philosophical Investigations'' is divided into two parts, consisting of what Wittgens ...

''. 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.

References

Bibliography

* Cherry, Dan. "Collector's guide to rules", ''Furniture & Cabinetmaking'', no. 259, July 2017
ISSN 1365-4292
pp. 52–6 * Rees, Jane and Mark (2010). ''The Rule Book: Measuring for the Trades''. Lakeville, MN: Astragal Press * Russell, David R.; with photography by James Austin and foreword by

David Linley David Albert Charles Armstrong-Jones, 2nd Earl of Snowdon (born 3 November 1961), styled as Viscount Linley until 2017 and known professionally as David Linley, is an English furniture maker, a former chairman of the auction house Christie's UK, ...

(2010). '' Antique Woodworking Tools: Their Craftsmanship from the Earliest Times to the Twentieth Century'', Cambridge: John Adamson , pp. 64–74 * Whitelaw, Ian (2007). ''A Measure of All Things: The Story of Man and Measurement''. Macmillan {{Authority control Length, distance, or range measuring devices Metalworking measuring instruments Stationery Stonemasonry tools Woodworking measuring instruments