Measuring rod
Encyclopedia
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 be flat boards. Some have markings at regular intervals. It is likely that the measuring rod was used before the line, chain or steel tapes used in modern measurement.

Ancient Sumer

The oldest preserved measuring rod is a copper
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...

-alloy
Alloy
An alloy is a mixture or metallic solid solution composed of two or more elements. Complete solid solution alloys give single solid phase microstructure, while partial solutions give two or more phases that may or may not be homogeneous in distribution, depending on thermal history...

 bar was found by the German
Germans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....

 Assyriologist
Assyriology
Assyriology is the archaeological, historical, and linguistic study of ancient Mesopotamia and the related cultures that used cuneiform writing. The field covers the Akkadian sister-cultures of Assyria and Babylonia, together with their cultural predecessor; Sumer...

 Eckhard Unger
Eckhard Unger
Eckhard Unger was a German assyriologist.In 1916, as curator of the Archeological Museum of Istanbul, he identified and described a copper-alloy object in the museum collection as an ell or measuring rod from Nippur...

 while excavating at Nippur
Nippur
Nippur was one of the most ancient of all the Sumerian cities. It was the special seat of the worship of the Sumerian god Enlil, the "Lord Wind," ruler of the cosmos subject to An alone...

 (pictured below). The bar dates from c. 2650 BC. and Unger claimed it was used as a measurement standard. This irregularly formed and irregularly marked graduated rule supposedly defined the Sumerian cubit as about 518.5 mm or 20.4 inches, although this does not agree with other evidence from the statues of Gudea
Gudea
Gudea was a ruler of the state of Lagash in Southern Mesopotamia who ruled ca. 2144 - 2124 BC. He probably did not come from the city, but had married Ninalla, daughter of the ruler Urbaba of Lagash, thus gaining entrance to the royal house of Lagash...

 from the same region, five centuries later.

Ancient East Asia

Measuring rods for different purposes and sizes (construction, tailoring and land survey) have been found from China and elsewhere dating to the early 2nd millennium B.C.E.

Ancient Egypt

Cubit-rods of wood or stone were used in Ancient Egypt. Fourteen of these were described and compared by Lepsius in 1865. Flinders Petrie reported on a rod that shows a length of 520.5 mm, a few millimetres less than the Egyptian cubit
Cubit
The cubit is a traditional unit of length, based on the length of the forearm. Cubits of various lengths were employed in many parts of the world in Antiquity, in the Middle Ages and into Early Modern Times....

. A slate measuring rod was also found, divided into fractions of a Royal Cubit and dating to the time of Akhenaten
Akhenaten
Akhenaten also spelled Echnaton,Ikhnaton,and Khuenaten;meaning "living spirit of Aten") known before the fifth year of his reign as Amenhotep IV , was a Pharaoh of the Eighteenth dynasty of Egypt who ruled for 17 years and died perhaps in 1336 BC or 1334 BC...

.

Further cubit rods have been found in the tombs of officials. Two examples are known from the tomb of Maya
Maya (Egyptian)
Maya was the Overseer of the Treasury during the reign of Pharaoh Tutankhamun, Ay and Horemheb of the eighteenth dynasty of Ancient Egypt. He was also an important official and was noted for restoring the burials of several earlier Pharaohs in the Royal Necropolis in the years following the deaths...

—the treasurer of Tutankhamun
Tutankhamun
Tutankhamun , Egyptian , ; approx. 1341 BC – 1323 BC) was an Egyptian pharaoh of the 18th dynasty , during the period of Egyptian history known as the New Kingdom...

—in Saqqara
Saqqara
Saqqara is a vast, ancient burial ground in Egypt, serving as the necropolis for the Ancient Egyptian capital, Memphis. Saqqara features numerous pyramids, including the world famous Step pyramid of Djoser, sometimes referred to as the Step Tomb due to its rectangular base, as well as a number of...

. Another was found in the tomb of Kha (TT8
TT8
TT8 or Theban Tomb 8 was the site of one of the greatest archaeological discoveries in ancient Egypt. This New Kingdom era tomb was one of the few tombs of Ancient Egypt's nobility to have survived intact down through the centuries - it was only discovered by Arthur Weigall and Ernesto Schiaparelli...

) in Thebes
Thebes, Egypt
Thebes is the Greek name for a city in Ancient Egypt located about 800 km south of the Mediterranean, on the east bank of the river Nile within the modern city of Luxor. The Theban Necropolis is situated nearby on the west bank of the Nile.-History:...

. These cubits are ca 52.5 cm long and are divided into seven palms, each palm is divided into four fingers and the fingers are further subdivided. Another wooden cubit rod was found in Theban tomb TT40
TT40
The Theban Tomb TT40 is located in Qurnet Murai, part of the Theban Necropolis, on the west bank of the Nile, opposite to Luxor. It is the burial place of the Ancient Egyptian Viceroy of Kush named Amenhotep called Huy , who lived during the end of the 18th during the reign of Tutankhamen.Huy was...

 (Huy) bearing the throne name of Tutankhamun (Nebkheperure).
Egyptian measuring rods also had marks for the Remen
Ancient Egyptian units of measurement
-Length:Units of length date back to at least the early dynastic period. In the Palermo stone for instance the level of the Nile river is recorded. During the reign of Pharaoh Djer the height of the river Nile was given as measuring 6 cubits and 1 palm...

 measurement of approximately 370mm, used in construction of the Pyramids.

Ancient Europe

An Oak
Oak
An oak is a tree or shrub in the genus Quercus , of which about 600 species exist. "Oak" may also appear in the names of species in related genera, notably Lithocarpus...

 rod from the Iron Age
Iron Age
The Iron Age is the archaeological period generally occurring after the Bronze Age, marked by the prevalent use of iron. The early period of the age is characterized by the widespread use of iron or steel. The adoption of such material coincided with other changes in society, including differing...

 fortified settlement at Borre Fen in Denmark
Denmark
Denmark is a Scandinavian country in Northern Europe. The countries of Denmark and Greenland, as well as the Faroe Islands, constitute the Kingdom of Denmark . It is the southernmost of the Nordic countries, southwest of Sweden and south of Norway, and bordered to the south by Germany. Denmark...

 mearure 53.15 inches (135 cm), with marks dividing it up into eight parts of 6.64 inches (16.9 cm), corresponding quite closely to half a Doric
Doric order
The Doric order was one of the three orders or organizational systems of ancient Greek or classical architecture; the other two canonical orders were the Ionic and the Corinthian.-History:...

 Pous
Pous
The pous was a unit of length used through much of the Iron Age in Europe and the Ancient Near East.A pous is a Greek foot. One stadion is always 600 podes,...

 (a Greek foot). A Hazel
Hazel
The hazels are a genus of deciduous trees and large shrubs native to the temperate northern hemisphere. The genus is usually placed in the birch family Betulaceae, though some botanists split the hazels into a separate family Corylaceae.They have simple, rounded leaves with double-serrate margins...

 measuring rod recovered from a Bronze Age
Bronze Age
The Bronze Age is a period characterized by the use of copper and its alloy bronze as the chief hard materials in the manufacture of some implements and weapons. Chronologically, it stands between the Stone Age and Iron Age...

 burial mound in Borum Eshøj, East Jutland by P. V. Glob in 1875 mearured 30.9 inches (78.5 cm) corresponding remarkably to the traditional Danish foot. The megalith
Megalith
A megalith is a large stone that has been used to construct a structure or monument, either alone or together with other stones. Megalithic describes structures made of such large stones, utilizing an interlocking system without the use of mortar or cement.The word 'megalith' comes from the Ancient...

ic structures of Great Britain
Great Britain
Great Britain or Britain is an island situated to the northwest of Continental Europe. It is the ninth largest island in the world, and the largest European island, as well as the largest of the British Isles...

 has been hypothesized to have been built by a "Megalithic Yard
Megalithic Yard
A Megalithic Yard is a unit of measurement, about , that some researchers believe was used in the construction of megalithic structures. The proposal was made by Alexander Thom as a result of his surveys of 600 megalithic sites in England, Scotland, Wales and Britanny...

", though some authorities believe these structures have been measured out by pacing. Several tentative Bronze age
Bronze Age
The Bronze Age is a period characterized by the use of copper and its alloy bronze as the chief hard materials in the manufacture of some implements and weapons. Chronologically, it stands between the Stone Age and Iron Age...

 bone fragments have been suggested as being parts of a measuring rod for this hypothetical measurement.

Roman Empire

Large public works and imperial expansion, particularly the large network of Roman roads and the many milecastle
Milecastle
A milecastle was a small fort , a rectangular fortification built during the period of the Roman Empire. They were placed at intervals of approximately one Roman mile along several major frontiers, for example Hadrian's Wall in Great Britain , hence the name.Along Hadrian's Wall, milecastles were...

s, made the measuring rod an indispensable part of both the military and civilian aspects of Roman life. Republican Rome
Roman Republic
The Roman Republic was the period of the ancient Roman civilization where the government operated as a republic. It began with the overthrow of the Roman monarchy, traditionally dated around 508 BC, and its replacement by a government headed by two consuls, elected annually by the citizens and...

 used several measures, including the various Greek feet measurements and the Oscan foot of 23,7 cm. Standardisation was introduced by Agrippa
Marcus Vipsanius Agrippa
Marcus Vipsanius Agrippa was a Roman statesman and general. He was a close friend, son-in-law, lieutenant and defense minister to Octavian, the future Emperor Caesar Augustus...

 in 29 BC, replacing all previous measurements by a Roman foot
Ancient Roman units of measurement
The ancient Roman units of measurement were built on the Hellenic system with Egyptian, Hebrew, and Mesopotamian influences. The Roman units were comparatively consistent and well documented.-Length:Notes...

 of 29.6 cm, which became the foot of Imperial Rome
Roman Empire
The Roman Empire was the post-Republican period of the ancient Roman civilization, characterised by an autocratic form of government and large territorial holdings in Europe and around the Mediterranean....

.

The Roman measuring rod was 10 Roman feet long, and hence called a decempeda, Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

 for ‘ten feet’. It was usually of square section caped at both ends by a metal shoe, and painted in alternating colours. Together with the groma
Groma surveying
The Groma or gruma was the principal Roman surveying instrument. It comprised a vertical staff with horizontal cross pieces mounted at right-angles on a bracket. Each cross piece had a plumb line hanging vertically at each end...

and Dioptra
Dioptra
A dioptra is a classical astronomical and surveying instrument, dating from the 3rd century BCE. The dioptra was a sighting tube or, alternatively, a rod with a sight at both ends, attached to a stand...

the decempeda formed the basic kit for the Roman surveyors
Gromatici
Gromatici , or agrimensores, was the name for land-surveyors amongst the ancient Romans...

. The measuring rod is frequently found depicted in roman art showing the surveyors at work. A shorter folding yardstick
Yardstick
A yardstick is a straightedge used to physically measure lengths of up to a yard high. Yardsticks are flat wooden boards with markings at regular intervals.-Construction:...

 one Roman foot long is known from excavations of a Roman fort in Niederburg
Niederburg
Niederburg is an Ortsgemeinde – a municipality belonging to a Verbandsgemeinde, a kind of collective municipality – in the Rhein-Hunsrück-Kreis in Rhineland-Palatinate, Germany...

, Germany.

Middle Ages

In the Middle Ages
Middle Ages
The Middle Ages is a periodization of European history from the 5th century to the 15th century. The Middle Ages follows the fall of the Western Roman Empire in 476 and precedes the Early Modern Era. It is the middle period of a three-period division of Western history: Classic, Medieval and Modern...

, bars were used as standards of length when surveying
Surveying
See Also: Public Land Survey SystemSurveying or land surveying is the technique, profession, and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them...

 land.
These bars often used a unit of measure called a Rod (unit)
Rod (unit)
The rod is a unit of length equal to 5.5 yards, 5.0292 metres, 16.5 feet, or of a statute mile. A rod is the same length as a perch or a pole. In old English, the term lug is also used.-History:...

 of length
Length
In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...

 equal to 5.5 yard
Yard
A yard is a unit of length in several different systems including English units, Imperial units and United States customary units. It is equal to 3 feet or 36 inches...

s, 5.0292 metre
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

s, 16.5 feet, or of a statute mile. A rod is the same length as a perch
Perch (unit of measure)
A perch is as a unit of measurement used for length, area, and volume in a number of systems of measurement. Its name derives from the Ancient Roman unit, the pertica.-Origin:...

or a pole. In old English, the term lug is also used. The length is equal to the standardized length of the ox goad used for teams of eight oxen by medieval English ploughmen. The lengths of the perch (one rod unit) and chain
Chain (unit)
A chain is a unit of length; it measures 66 feet or 22 yards or 100 links . There are 10 chains in a furlong, and 80 chains in one statute mile. An acre is the area of 10 square chains...

(four rods) were standardized in 1607 by Edmund Gunter
Edmund Gunter
Edmund Gunter , English mathematician, of Welsh descent, was born in Hertfordshire in 1581.He was educated at Westminster School, and in 1599 was elected a student of Christ Church, Oxford. He took orders, became a preacher in 1614, and in 1615 proceeded to the degree of bachelor in divinity...

. The rod unit was still in use as a common unit of measurement in the mid-19th century, when Henry David Thoreau
Henry David Thoreau
Henry David Thoreau was an American author, poet, philosopher, abolitionist, naturalist, tax resister, development critic, surveyor, historian, and leading transcendentalist...

 used it frequently when describing distances in his work Walden
Walden
Walden is an American book written by noted Transcendentalist Henry David Thoreau...

.

Iconography

Two statues of Gudea of Lagash in the Louvre
Louvre
The Musée du Louvre – in English, the Louvre Museum or simply the Louvre – is one of the world's largest museums, the most visited art museum in the world and a historic monument. A central landmark of Paris, it is located on the Right Bank of the Seine in the 1st arrondissement...

 depict him sitting with a tablet on his lap, upon which are placed surveyors tools including a measuring rod.

Seal 154 recovered from Alalakh, now in the Biblioteque Nationale show a seated figure with a wedge shaped measuring rod.

The Tablet of Shamash
Tablet of Shamash
The Tablet of Shamash is a stone tablet recovered from the ancient Babylonian city of Sippar in southern Iraq in 1881. It is dated to the reign of King Nabu-apla-iddina ca. 888 – 855 BC.The tablet is long by wide and was recovered during the excavations by Hormuzd Rassam between 1878 to 1883...

 recovered from the ancient Babylon
Babylon
Babylon was an Akkadian city-state of ancient Mesopotamia, the remains of which are found in present-day Al Hillah, Babil Province, Iraq, about 85 kilometers south of Baghdad...

ian city of Sippar
Sippar
Sippar was an ancient Near Eastern city on the east bank of the Euphrates river, located at the site of modern Tell Abu Habbah in Iraq's Babil Governorate, some 60 km north of Babylon and 30 km southeast of Baghdad....

 and dated to the 9th century BC
9th century BC
The 9th century BC started the first day of 900 BC and ended the last day of 801 BC.- Overview :The 9th century BC was a period of great changes in civilizations. In Africa, Carthage is founded by the Phoenicians...

 shows Shamash
Shamash
Shamash was a native Mesopotamian deity and the sun god in the Akkadian, Assyrian and Babylonian pantheons. Shamash was the god of justice in Babylonia and Assyria, corresponding to Sumerian Utu...

, the Sun God awarding the measuring rod and coiled rope to newly trained surveyor
Surveying
See Also: Public Land Survey SystemSurveying or land surveying is the technique, profession, and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them...

s.

A similar scene with measuring rod and coiled rope is shown on the top part of the diorite
Diorite
Diorite is a grey to dark grey intermediate intrusive igneous rock composed principally of plagioclase feldspar , biotite, hornblende, and/or pyroxene. It may contain small amounts of quartz, microcline and olivine. Zircon, apatite, sphene, magnetite, ilmenite and sulfides occur as accessory...

 stele
Stele
A stele , also stela , is a stone or wooden slab, generally taller than it is wide, erected for funerals or commemorative purposes, most usually decorated with the names and titles of the deceased or living — inscribed, carved in relief , or painted onto the slab...

 above the Code of Hammurabi
Code of Hammurabi
The Code of Hammurabi is a well-preserved Babylonian law code, dating to ca. 1780 BC . It is one of the oldest deciphered writings of significant length in the world. The sixth Babylonian king, Hammurabi, enacted the code, and partial copies exist on a human-sized stone stele and various clay...

 in the Louvre
Louvre
The Musée du Louvre – in English, the Louvre Museum or simply the Louvre – is one of the world's largest museums, the most visited art museum in the world and a historic monument. A central landmark of Paris, it is located on the Right Bank of the Seine in the 1st arrondissement...

, Paris, dating to ca. 1700 BC.

The "measuring rod" or tally stick
Tally stick
A tally was an ancient memory aid device to record and document numbers, quantities, or even messages. Tally sticks first appear as notches carved on animal bones, in the Upper Paleolithic. A notable example is the Ishango Bone...

 is common in the iconography
Iconography
Iconography is the branch of art history which studies the identification, description, and the interpretation of the content of images. The word iconography literally means "image writing", and comes from the Greek "image" and "to write". A secondary meaning is the painting of icons in the...

 of Greek
Ancient Greece
Ancient Greece is a civilization belonging to a period of Greek history that lasted from the Archaic period of the 8th to 6th centuries BC to the end of antiquity. Immediately following this period was the beginning of the Early Middle Ages and the Byzantine era. Included in Ancient Greece is the...

 Goddess Nemesis
Nemesis (mythology)
In Greek mythology, Nemesis , also called Rhamnousia/Rhamnusia at her sanctuary at Rhamnous, north of Marathon, was the spirit of divine retribution against those who succumb to hubris . The Greeks personified vengeful fate as a remorseless goddess: the goddess of revenge...

.

The Graeco-Egyptian God Serapis
Serapis
Serapis or Sarapis is a Graeco-Egyptian name of God. Serapis was devised during the 3rd century BC on the orders of Ptolemy I of Egypt as a means to unify the Greeks and Egyptians in his realm. The god was depicted as Greek in appearance, but with Egyptian trappings, and combined iconography...

 is also depicted in images and on coins with a measuring rod in hand and a vessel on his head.

The most elaborate depiction is found on the Ur-Nammu
Ur-Nammu
Ur-Nammu founded the Sumerian 3rd dynasty of Ur, in southern Mesopotamia, following several centuries of Akkadian and Gutian rule...

-stela, where the winding of the cords has been detailed by the sculptor. This has also been described as a "staff and a chaplet of beads".

Mythology

The myth of Inanna
Inanna
Inanna, also spelled Inana is the Sumerian goddess of sexual love, fertility, and warfare....

's descent to the nether world describes how the goddess dresses and prepares herself:

Lachesis
Lachesis (mythology)
In Greek mythology, Lachesis was the second of the Three Fates, or Moirae, also known as the Triple Moon Goddesses or the Lunar Dieties. Each phase of the moon representing each of the fates - Clotho, Lachesis and Atropos...

 in Greek mythology
Greek mythology
Greek mythology is the body of myths and legends belonging to the ancient Greeks, concerning their gods and heroes, the nature of the world, and the origins and significance of their own cult and ritual practices. They were a part of religion in ancient Greece...

 was one of the three Moirae
Moirae
The Moirae, Moerae or Moirai , in Greek mythology, were the white-robed incarnations of destiny . Their number became fixed at three...

 (or fates) and "allotter" (or drawer of lots). She measured the thread of life allotted to each person with her measuring rod. Her Roman equivalent was Decima
Decima (mythology)
In Roman mythology, Decima was one of the Parcae, or the Fates. She measured the thread of life with her rod. She was also revered as the goddess of childbirth. Her Greek equivalent was Lachesis....

(the 'Tenth').

Varuna
Varuna
In Vedic religion, Varuna is a god of the sky, of water and of the celestial ocean, as well as a god of law and of the underworld...

 in the Rigveda
Rigveda
The Rigveda is an ancient Indian sacred collection of Vedic Sanskrit hymns...

, is described as using the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 as a measuring rod to lay out space in a creation myth. W. R. Lethaby has commented on how the measurers were seen as solar deities and noted how Vishnu
Vishnu
Vishnu is the Supreme god in the Vaishnavite tradition of Hinduism. Smarta followers of Adi Shankara, among others, venerate Vishnu as one of the five primary forms of God....

 "measured the regions of the Earth".

Bible

Measuring rods or reeds are mentioned many times in the Bible
Bible
The Bible refers to any one of the collections of the primary religious texts of Judaism and Christianity. There is no common version of the Bible, as the individual books , their contents and their order vary among denominations...

.

A measuring rod and line are seen in a vision of Yahweh
Yahweh
Yahweh is the name of God in the Bible, the God of Abraham, Isaac, Jacob, Jews and Christians.The word Yahweh is a modern scholarly convention for the Hebrew , transcribed into Roman letters as YHWH and known as the Tetragrammaton, for which the original pronunciation is unknown...

 in Ezekiel
Ezekiel
Ezekiel , "God will strengthen" , is the central protagonist of the Book of Ezekiel in the Hebrew Bible. In Judaism, Christianity and Islam, Ezekiel is acknowledged as a Hebrew prophet...

 40:2-3:
Another example is Revelation
Revelation
In religion and theology, revelation is the revealing or disclosing, through active or passive communication with a supernatural or a divine entity...

 11:1:
The measuring rod also appears in connection with foundation stone rites in Revelation
Revelation
In religion and theology, revelation is the revealing or disclosing, through active or passive communication with a supernatural or a divine entity...

 20:14-15:

See also

  • Ancient Egyptian units of measurement
    Ancient Egyptian units of measurement
    -Length:Units of length date back to at least the early dynastic period. In the Palermo stone for instance the level of the Nile river is recorded. During the reign of Pharaoh Djer the height of the river Nile was given as measuring 6 cubits and 1 palm...

  • Ancient Greek units of measurement
    Ancient Greek units of measurement
    Ancient Greek units of measurement would later create the foundation of Egyptian, and formed the basis of the later Roman system.Generally speaking, standards of measurement within the ancient Greek world varied according to location and epoch. Systems of ancient weights and measures evolved as...

  • Ancient Mesopotamian units of measurement
    Ancient Mesopotamian units of measurement
    Ancient Mesopotamian units of measurement originated in the loosely organized city-states of Early Dynastic Sumer. The units themselves grew out of the tradition of counting tokens used by the Neolithic cultural complex of the Near East. The counting tokens were used to keep accounts of personal...

  • Levelling rod
  • Rod (unit)
    Rod (unit)
    The rod is a unit of length equal to 5.5 yards, 5.0292 metres, 16.5 feet, or of a statute mile. A rod is the same length as a perch or a pole. In old English, the term lug is also used.-History:...

  • Rod-and-ring symbol
    Rod-and-ring symbol
    The Rod and ring symbol is a symbol that is depicted on Mesopotamian stelas, cylinder seals and reliefs. It is held by a god or goddess and in most cases is being offered to a king who is standing, often making a sacrifice, or otherwise showing respect...

  • Ruler
    Ruler
    A ruler, sometimes called a rule or line gauge, is an instrument used in geometry, technical drawing, printing and engineering/building to measure distances and/or to rule straight lines...

  • Shen ring
    Shen ring
    A shen ring is a circle with a line at a tangent to it, which was represented in hieroglyphs as a stylised loop of a rope. The word shen itself means, in ancient Egyptian, encircle, while the shen ring represented eternal protection...

  • Surveying
    Surveying
    See Also: Public Land Survey SystemSurveying or land surveying is the technique, profession, and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them...

  • Units of measurement
    Units of measurement
    A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...

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