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Encyclopedia > Sexagesimal

The sexagesimal (base-sixty) is a numeral system with sixty as the base. It originated with the ancient Sumerians in the 2000s BC, and was transmitted to the Babylonians. Sexagesimal as used in ancient Mesopotamia was not a pure base 60 system, in the sense that they didn't have 60 individual digits for their place-value notation. Instead, their cuneiform digits used ten as a sub-base in the fashion of a sign-value notation: a digit was composed of a number of narrow wedge-shaped marks representing units up to nine (Y, YY, YYY, YYYY, ... YYYYYYYYY) and a number of wide wedge-shaped marks representing tens up to five (<, <<, <<<, <<<<, <<<<<); the value of the digit was the sum of the values of its component parts, which is similar to how the Maya expressed their vigesimal digits using five as a sub-base (see Maya numerals). The article on Babylonian numerals shows these cuneiform digits for 1 through 60. In this article places are represented in modern decimal, except where otherwise noted (for example, "10" means ten and "60" means sixty). A numeral is a symbol or group of symbols that represents a number. ... 60 (sixty) is the natural number following 59 and preceding 61. ... The radix (Latin for root), also called base, is the number of various unique symbols (or digits or numerals) a positional numeral system uses to represent numbers. ... Sumer (or Shumer, Sumeria, Shinar, native ki-en-gir) formed the southern part of Mesopotamia from the time of settlement by the Sumerians until the time of Babylonia. ... (4th millennium BC &#8211; 3rd millennium BC &#8211; 2nd millennium BC &#8211; other millennia) Events Foundation of the city of Mari (Syria) (29th century BC ) Creation of the Kingdom of Elam (Iraq) Germination of the Bristlecone pine tree Methuselah about 2700 BC, the oldest tree still living now Dynasty of... Babylonia, named for its capital city, Babylon, was an ancient state in the south part of Mesopotamia (in modern Iraq), combining the territories of Sumer and Akkad. ... Mesopotamia refers to the region now occupied by modern Iraq, eastern Syria, southeastern Turkey, and Southwest Iran. ... Digit may refer to: A finger or a toe Numerical digit, as used in mathematics or computer science Digit (unit), an ancient meterological unit Digit (magazine), an Indian information technology magazine This is a disambiguation page: a list of articles associated with the same title. ... Positional notation or place-value notation is a numeral system in which each position is related to the next by a constant multiplier called the base (or radix) of that numeral system. ... Ten can refer to: 10, a number AD 10, a year 10 BC, a year 10, a 1979 motion picture Ten, any one of a number of rock albums Network Ten, an Australian television network Trans-European Networks (TEN) Total Entertainment Network, an early-1990s attempt at an online server... In Computers Sign-value notation in computers is the use of the high-order bit (left end) of a binary word to represent the numeric sign: 0 for +, 1 for - followed by a binary number that is an absolute magnitude or a twos complement of an absolute magnitude. ... The word Maya or maya can refer to: // The Maya, a Native American peoples of southern Mexico and northern Central America Maya peoples, the contemporary indigenous peoples Maya civilization, their historical pre-Columbian civilization Mayan languages, the family of languages spoken by the Maya Maya people, an Australian Aboriginal group... The vigesimal or base-20 numeral system is based on twenty (in the same way in which the ordinary decimal numeral system is based on ten). ... 5 (five) is the natural number following 4 and preceding 6. ... Mayan numerals. ... Babylonian numerals were written in cuneiform, using a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record. ... 10 (ten) is an even natural number following 9 and preceding 11. ... 60 (sixty) is the natural number following 59 and preceding 61. ...

Contents

Sexagesimal in Babylonia

The Sumero-Babylonian version used a digit to represent "one" and another digit to represent "ten", and repeated the symbols in groups up to nine for units and five for tens, then used place-position shifting to the left for each power of sixty, with a larger space between one power of sixty and the next — this may be represented schematically here by using + and * thus: Look up one in Wiktionary, the free dictionary. ... 10 (ten) is an even natural number following 9 and preceding 11. ... For other senses of this word, see 9 (disambiguation). ... 5 (five) is a number, numeral, and glyph. ... 60 (sixty) is the natural number following 59 and preceding 61. ... Image File history File links GrayDot. ... Image File history File links BlackDot. ...

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Numeral systems by culture
Hindu-Arabic numerals
Western Arabic
Eastern Arabic
Indian family
Brahmi
East Asian numerals
Chinese
Japanese
Khmer
Korean
Thai
 
Alphabetic numerals
Abjad
Armenian
Cyrillic
Ge'ez
Hebrew
Ionian
Sanskrit
 
Other systems
Attic
Etruscan
Roman
Babylonian
Egyptian
Mayan
Numeral system topics
 
Positional systems by base
Decimal
2, 4, 8, 16, 32, 64, 128
3, 9, 12, 24, 30, 36, 60, more.   

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Image File history File links BlackDot. ... Image File history File links GrayDot. ... Image File history File links GrayDot. ... Image File history File links GrayDot. ... Image File history File links BlackDot. ... Image File history File links GrayDot. ... Image File history File links GrayDot. ... Image File history File links GrayDot. ... Image File history File links GrayDot. ... Image File history File links Blank300. ... Image File history File links GrayDot. ... Image File history File links Blank300. ... Image File history File links GrayDot. ... A numeral is a symbol or group of symbols that represents a number. ... The Hindu-Arabic numeral system (also called Algorism) is a positional decimal numeral system documented from the 9th century. ... Numerals sans-serif Arabic numerals, known formally as Hindu-Arabic numerals, and also known as Indian numerals, Hindu numerals, European numerals, and Western numerals, are the most common symbolic representation of numbers around the world. ... The Eastern Arabic numerals (also called Eastern Arabic numerals, Arabic-Indic numerals, Arabic Eastern Numerals) are the symbols (glyphs) used to represent the Hindu-Arabic numeral system in conjunction with the Arabic alphabet in Egypt, Iran, Pakistan and parts of India, and also in the no longer used Ottoman Turkish... India has produced many numeral systems. ... The Brahmi numerals are an indigenous Indian numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). ... Khmer numerals are the numerals used in the Khmer language of Cambodia. ... The Abjad numerals are a decimal numeral system which was used in the Arabic-speaking world prior to the use of the Hindu-Arabic numerals from the 8th century, and in parallel with the latter until Modern times. ... Cyrillic numerals was a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. ... Note: This article contains special characters. ... The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. ... Ionian numerals were used by the ancient Greeks, possibly before the 7th century BC. They are also known by the names Milesian numerals or Alexandrian numerals. ... The Sanskrit alphabetic numerals were created in about A.D. 510 by Āryabhaa. ... Attic numerals were used by ancient Greeks, possibly from the 7th century BC. They were also known as Herodianic numerals because they were first described in a 2nd century manuscript by Herodianus. ... The Etruscan numerals were used by the ancient Etruscans. ... The system of Roman numerals is a numeral system originating in ancient Rome, and was adapted from Etruscan numerals. ... Babylonian numerals were written in cuneiform, using a wedge-tipped reed stylus to make a mark on a soft clay tablet which would be exposed in the sun to harden to create a permanent record. ... Mayan numerals. ... This is a list of numeral system topics, by Wikipedia page. ... Positional notation is a system in which each position has a value represented by a unique symbol or character. ... In mathematics, the base or radix is the number of various unique symbols (digits), including zero, that a positional numeral system uses to represent numbers in a given counting system. ... The decimal (base ten or occasionally denary) numeral system has ten as its base. ... The binary numeral system (base 2 numerals) represents numeric values using two symbols, typically 0 and 1. ... Quaternary is the base four numeral system. ... The octal numeral system is the base-8 number system, and uses the digits 0 to 7. ... In mathematics and computer science, base-16, hexadecimal, or simply hex, is a numeral system with a radix or base of 16 usually written using the symbols 0–9 and A–F or a–f. ... Base32 is a derivation of Base64 with the following additional properties: The resulting character set is all uppercase, which can often be beneficial when using a case-sensitive filesystem. ... Base 64 is a positional numeral system using a base of 64. ... Uuencode is a form of binary to text encoding that originated as a Unix program for encoding binary data for transmission over the uucp mail system. ... Ternary or trinary is the base-3 numeral system. ... Nonary is a base 9 numeral system, typically using the digits 0-8, but not the digit 9. ... A duodecimal multiplication table The duodecimal (also known as base-12 or dozenal) system is a numeral system using twelve as its base. ... As there are 24 hours in a day a numbering system based upon 24, and as the base 12 is convenient here some examples of the base 24 (quadrovigesimal) system. ... Base 30 or trigesimal is a positional numeral system using 30 as the radix. ... Base 36 refers to a positional numeral system using 36 as the radix. ...

Because there was no symbol for zero with either the Sumerians or the earlier Babylonians, it is not always immediately obvious how a number should be interpreted, and the true value must sometimes be determined by the context; later Babylonian texts used a dot to represent zero. 0 (zero) is both a number — or, more precisely, a numeral representing a number — and a numerical digit. ...


It was later used in its more modern form by Arabs during the Umayyad caliphate. The Arabs (Arabic: عرب ) are an ethnic group found throughout the Middle East and North Africa. ... The Courtyard of the Umayyad Mosque in Damascus, one of the grandest architectural legacies of the Umayyads. ...


Usage

60 (sexagesimal) is the product of 3, 4, and 5. 3 is a divisor of 12 (duodecimal), 4 is a common divisor of 12 (duodecimal) and 20 (vigesimal), 5 is a common divisor of 10 (decimal) and 20 (vigesimal). 60 (sixty) is the natural number following 59 and preceding 61. ... This article discusses the number three. ... This article discusses the number Four. ... 5 (five) is a number, numeral, and glyph. ... In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder. ... 12 (twelve) is the natural number following 11 and preceding 13. ... A duodecimal multiplication table The duodecimal (also known as base-12 or dozenal) system is a numeral system using twelve as its base. ... In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder. ... 20 (twenty) is the natural number following 19 and preceding 21. ... The vigesimal or base-20 numeral system is based on twenty (in the same way in which the ordinary decimal numeral system is based on ten). ... The decimal (base ten or occasionally denary) numeral system has ten as its base. ...


Base-sixty has the advantage that its base has a large number of conveniently sized divisors {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}, facilitating calculations with vulgar fractions. Note that 60 is the smallest number divisible by every number from 1 to 6. In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder. ... Look up one in Wiktionary, the free dictionary. ... 2 (two) is a number, numeral, and glyph. ... This article discusses the number three. ... This article discusses the number Four. ... 5 (five) is a number, numeral, and glyph. ... Number 6, in this article, refers to the mathematical number. ... 10 (ten) is an even natural number following 9 and preceding 11. ... 12 (twelve) is the natural number following 11 and preceding 13. ... 15 (fifteen) is the natural number following 14 and preceding 16. ... 20 (twenty) is the natural number following 19 and preceding 21. ... 30 (thirty) is the natural number following 29 and preceding 31. ... In arithmetic, a vulgar fraction (or common fraction) consists of one integer divided by a non-zero integer. ...


Unlike most other numeral systems, sexagesimal is not used so much as a means of general computation or logic, but is used in measuring angles, geographic coordinates, and time. This article is about angles in geometry. ... Two distinct views exist on the meaning of time. ...


One hour of time is divided into 60 minutes, and one minute is divided into 60 seconds. Parts of seconds are measured using the decimal system, however. The hour (symbol: h) is a unit of time. ... A minute is a unit of time equal to 1/60th of an hour and to 60 seconds. ... The decimal (base ten or occasionally denary) numeral system has ten as its base. ...


Similarly, the fundamental unit of angular measure is the degree, of which there are 360 in a circle. There are 60 minutes of arc in a degree, and 60 seconds of arc in a minute. A degree (in full, a degree of arc, arc degree, or arcdegree), usually symbolized °, is a measurement of plane angle, representing 1/360 of a full rotation. ... 360(Three hundred sixty) is the natural number following 359 and preceding 361. ... It has been suggested that milliarcsecond be merged into this article or section. ...


In the Chinese calendar, a sexagenary cycle is commonly used. The Chinese calendar (Traditional Chinese: 農曆; Simplified Chinese: 农历; pinyin: nónglì) is a lunisolar calendar incorporating elements of a lunar calendar with those of a solar calendar. ... The Chinese sexagenary cycle (Chinese: ; pinyin: gānzhī) is a cyclic numeral system of 60 combinations of the two basic cycles, the ten Heavenly Stems (天干; tiāngān) and the twelve Earthly Branches (地支; dìzhī). These have been traditionally used as a means of numbering the years, not only in...


Fractions

The sexagesimal system is quite good for forming fractions:

 1/2 = 0.30 1/3 = 0.20 1/4 = 0.15 1/5 = 0.12 1/6 = 0.10 1/8 = 0.07:30 1/9 = 0.06:40 1/10 = 0.06 1/12 = 0.05 1/15 = 0.04 1/16 = 0.03:45 1/18 = 0.03:20 1/20 = 0.03 1/30 = 0.02 1/40 = 0.01:30 1/50 = 0.01:12 1/1:00 = 0.01 (1/60 in decimal) 

but is not very good for simple repeating fractions, because both the neighbors of 60 (i.e. 59 and 61) are prime numbers. In mathematics, a prime number (or a prime) is a natural number that has exactly two (distinct) natural number divisors, which are 1 and the prime number itself. ...

 1/7 = 0.08:34:17:08:34:17: recurring 

Examples

1.414212... ≈ 30547/21600 = 1.24:51:10 (sexagesimal = 1 + 24/60 + 51/602 + 10/603), a constant used by Babylonian mathematicians in the Old Babylonian Period (1900 BC - 1650 BC), the actual value for sqrt{2} is 1.24:51:10:07:46:06:04:44...,
365.24579... = 6:05.14:44:51 ( = 6×60 + 5 + 14/60 + 44/602 + 51/603),

(Note that the average length of a year in the Gregorian calendar is exactly 6:05.14:33 in sexagesimal notation.) In mathematics, diagonal has a geometric meaning, and a derived meaning as used in square tables and matrix terminology. ... In mathematics, a square root of a number x is a number whose square (the result of multiplying the number by itself) is x. ... In plane (Euclidean) geometry, a square is a polygon with four equal sides, four right angles, and parallel opposite sides. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... (Redirected from 1900 BC) (20th century BC - 19th century BC - 18th century BC - other centuries) (3rd millennium BC - 2nd millennium BC - 1st millennium BC) Events Hittite empire in Anatolia 1829 - 1818 BC -- Egyptian-Nubian war 1818 BC -- Egyptian Campaign in Palestine 1813 BC -- Amorite Conquest of Northern Mesopotamia 1806 BC... (Redirected from 1650 BC) Centuries: 18th century BC - 17th century BC - 15th century BC Decades: 1690s BC 1680s BC 1670s BC 1660s BC - 1650s BC - 1640s BC 1630s BC 1620s BC 1610s BC 1600s BC Events and trends Egypt: Start of Seventeenth Dynasty Significant people Categories: 1650s BC ... A tropical year is the length of time that the Sun, as viewed from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere). ... Chaldea, the Chaldees of the KJV Old Testament, was a Hellenistic designation for a part of Babylonia. ... Hipparchus. ... The Gregorian calendar is the calendar that is used nearly everywhere in the world. ...

3.141666... ≈ 377/120 = 3.8:30 ( = 3 + 8/60 + 30/602 ).

When a circles diameter is 1, its circumference is π. The mathematical constant π is an irrational real number, approximately equal to 3. ... An artists rendition of Claudius Ptolemaeus This article is about the geographer and astronomer Ptolemy. ...

See also

Latitude, usually denoted symbolically by the Greek letter φ, gives the location of a place on Earth north or south of the Equator. ... Wikibooks has a book on the topic of Trigonometry Trigonometry (from the Greek trigonon = three angles and metron = measure [1]) is a branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 degrees (right triangles). ...

References

  • Georges Ifrah. The Universal History of Numbers: From Prehistory to the Invention of the Computer, Wiley, 1999. ISBN 0-471-37568-3
  • Hans J. Nissen, P. Damerow, R. Englund, Archaic Bookkeeping, University of Chicago Press, 1993, ISBN 0-226-58659-6.

External link

  • Extensive page on Base-sixty

  Results from FactBites:
 
Sexagesimal - Wikipedia, the free encyclopedia (666 words)
The sexagesimal (base-sixty) is a numeral system with sixty as the base.
Sexagesimal as used in ancient Mesopotamia was not a pure base 60 system, in the sense that they didn't have 60 individual digits for their place-value notation.
Unlike most other numeral systems, sexagesimal is not used so much as a means of general computation or logic, but is used in measuring angles, geographic coordinates, and time.
Sexagesimal Calendar / FAQ (850 words)
We will leave an old and uncomfortable house where there are not two rooms at the same level and where there are so many nooks and corners that you never know exactly where you are, for a new, spacious, comfortable and welcoming house into which each will be able to move with one's own furniture.
Adopting the sexagesimal calendar calls for an adaptation of the local employment law.
In the sexagesimal calendar the years are notated with three digits.
  More results at FactBites »

 
 

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