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Many systems of weights and measures have existed throughout history. The definitions of some of these units were often vague and inaccurate, and although the roots of many of the units were the same, the actual value of a unit differed from country to country, or epoch to epoch. That fact should not lead to a conclusion that historical units of measure were inaccurate in general. Many units were defined to a high precision, and standards of measurement were in many cases excellent. As a case in point, the Great Pyramid of Giza was built to a precision of 15 mm over sides that are 235 m, over four and a half thousand years ago.1 The systems of antiquity
1.1 Main systems in antiquity
1.1.1 Mesopotamian system
Mesopotamia includes a number of cultures. The Sumerian number system uses a base 60 positional notation, and is the origin for the division of 60 for hours and angles.
1.1.1.1 Length
- kù – Cubit (Sumerian). Akkadian ammatu. The copper bar cubit of Nippur, the first known standard bar, defines the Sumerian cubit as about 518.5 mm, widely used in third millennium BC. It was split in 30 digits. The Babylonian (or Salamis) cubit was around 484 mm. For reference, the inner square of the Tower of Babel measured 120 by 120 cubits.
- foot – Defined as 264.6 mm by Sumerian ruler Gudea of Lagash around 2575 BC, this is the oldest preserved standard of length.
- digit – 1 / 16 foot or 1 / 30 cubit
- stadion – 148.5 m
- parasang – Babylonian league is 5.6 km
1.1.1.2 Area
- sar – Garden plot (Sumerian)
- iku – "Plot of land enclosed by a boundary dike/canal", 100 sar. Probably 120 ·120 cubit²
1.1.1.3 Volume
- log – 0.54 l
- homer – 720 log
1.1.1.4 Weight and monetary
- shekal – 8.36 g, introduced around 3000 BC
- mina – 60 shekal
1.1.1.5 Time
- year – The Sumerians used a 360 day year by 2100 BC.
- week – The Babylonians introduced the seven day week, due to the belief that seven brought bad luck, so they did not want to work the seventh day.
- hour – The 1212 twelve is the natural number following 11 and preceding 13. In mathematics Twelve is a composite number, its proper divisors being 1, 2, 3, 4 and 6. Twelve is also a highly composite number, the next one being 24. Twelve being the product of three and hour day and 12 hour night originates from Mesopotamia. The length of these hours changed through the year, being equally spaced over the time of light and dark, respectively.
1.1.2 Egyptian system
Much of the EgyptJumhuriyat Misr al-Arabiyah ( In Detail) Official language Arabic Capital Cairo Largest City Cairo President Hosni Mubarak Prime Minister Ahmed Nazif Area Total % water Ranked 29th 1,001,450 km² 0. 6% Population Total (2003) Density Ranked 15th 74,718,797ian system of measurement is based on the Mesopotamian. The Egyptian system in its turn formed the basis of the later Greek system. The Egyptians based their measurements on the Royal cubit, for which the pharaohThis article refers to the historical Pharaoh. For Pharaoh in the Book of Abraham, see Pharaoh (Book of Abraham). Pharaoh Standard Hebrew Paro Tiberian Hebrew Paroh is a title used to refer to the kings (of godly status) in ancient Egypt. See History of E devised a standard (master) cut in graniteGranite is a common and widely-occurring group of intrusive felsic igneous rocks that form at great depths and pressures under continents. Granite consists of orthoclase and plagioclase feldspars, quartz, hornblende, biotite, muscovite and minor accessory. From these standards, it is clear that accuracies in measurements of at least 1/16 yeba (1 mm) were possible. Note also the cubit and remen which has a ratio that constitutes an irrational numberIn mathematics, an irrational number is any real number that is not a rational number, i. one that cannot be written as a fraction a ''b with a and b integers, and b not zero. It can readily be shown that the irrational numbers are precisely those numbers. The Egyptian system was also noteworthy in having units for volume derived from the standard for length.
While the Royal cubit is a very well defined unit, uncertainty is connected to the units for land measurement, especially when the Greek stadion and schoinos units came in use.
The Egyptians were of fine geometers. They could not calculate the radix of two, but they could draw it. Discovering a good approximation in trigonometry: "Twenty times the radix of two, divided by 28, is very close to unit." So, they wanted to have a 28-digit cubit.
| By the theoretical value of the Mesopotanian 30-digit Nippur Cubit equal : 518 616 µm.
|
| The Egyptian Remen (pygon)
| equal
| 20 / 28
| Nippur Cubit (ell)
| =
| 37.044 cm
|
| The Old Egyptian Royal Cubit
| equal
| 20√2 / 28
| Nippur Cubit (ell)
| ~
| 52.388 cm
|
| The Egyptian Royal Cubit
| equal
| 20√2 / 28
| Old Royal Cubit
| =
| 52.920 cm
|
- The Egyptians geometers divided the Nippur Cubit into 28 digits instead of 30 (= ½ × 60 ! in Mesopotamia, inventor of sexagesimal calculation.) – Thus, Egyptians defined the later called "Roman digit".
- 20 (later called) Roman digits is the length the Egyptian construction Remen during the third millennium BC. – The 20-digit measure is called "pygon" in Greek language.
- Centuries later, they used a construction Remen with 20 digits token from the Old Royal Cubit. – Since, the foot of the new Royal Cubit (later called "Shaku" in Japan) and the (later called) Roman foot were related by the ratio: 100 to 98 exactly one.
Note, that the well-known "megalithic yard" (~ 83 cm) and the "Nippur cubit" are related by simple ratio 16 : 10. The theoretical "length of Roman barleycorn" is exactly 8 252 µm.
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