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# Topic: Sexagesimal

 Sexagesimal - Wikipedia, the free encyclopedia 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. en.wikipedia.org /wiki/Sexagesimal   (666 words)

 Sexagesimal Calendar / FAQ 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. www.sexagesimal.org /en_faq.php   (850 words)

 Autonomy » Community Standard Sexagesimal   (Site not responding. Last check: 2007-11-06) The Sumerians used a sexagesimal numerical system, which the Babylonians refined with a “positional” notation (”Positional Notation” is explained in the “Primer: Positional and Integer Base Notation.” The system all of us have grown up with is a decimal, or base-10, positional notation system). Digits were written in cuneiform characters reminiscent of a combination of different tally marks (modern efforts to use decimal numbers separated by commas or colons, and a period or semi-colon as a radix marker aren’t much better, and all fail to exploit the mnemonic advantages of a completely native sexagesimal notation). The Autonomous Community adopted an advanced sexagesimal system that included the advantages of the positional notation of our decimal system (including a radix marker separating positive and negative powers of 60), unique single-character representations of each digit 0-59, a nomenclature for naming numbers based on powers of 60, and a metric-60 nomenclature for unit prefixes. autonomyseries.com /sexagesimal-numerals   (844 words)

 Proposal Planning Toolkit: Colden Help   (Site not responding. Last check: 2007-11-06) Sexagesimal values are specified as "hh mm [ss[.ss]]" (that is, hours and minutes are required, seconds and fractions of seconds are optional). Sexagesimal values are specified as "sdd mm [ss[.ss]]". Sexagesimal values are specified as "hh mm [ss[.ss]]". asc.harvard.edu /toolkit/prop_help_colden.html   (728 words)

 Introduction The sexagesimal computation originated by making the metric system consistently sexagesimal; I shall show that this phenomenon explains the difficulties of Mesopotamian metrics and that by taking it into account the difficulties can be removed. This unfortunate remark, the value of which was formally denied by Lehmann-Haupt in his defense of the existence of Sumerian as a language, was seized by the racialists, and by the end of the nineteenth century it had developed into a general theory of a distinction between Semitic and non-Semitic mathematics. The tablets in their sexagesimal computations used as unit of landsurveying a double-cane of 12 cubits, called SAR or GAR, whereas buildings appear constructed by using a rod of 10 feet as in the rest of the ancient world. www.metrum.org /measures/meso_intro.htm   (7642 words)

 The First Place-Value Number System And so we come to the Babylonians, who were famous for their astrological observations and calculations, and who used a sexagesimal (base-60) numbering system (see also The invention of the abacus). sexagesimal system, which first appeared around 1900 to 1800 BC, is also credited as being the first known place-value number system, in which the value of a particular digit depends both on the digit itself and its position within the number. This was an extremely important development, because prior to place-value systems people were obliged to use different symbols to represent different powers of a base, and having unique symbols for ten, one-hundred, one thousand, and so forth makes even rudimentary calculations very difficult to perform (see also The Ancient Egyptians). www.maxmon.com /1900bc.htm   (315 words)

 Stereometric Texts The next sexagesimal submultiple is the saton of 10 normal single qa or 5 double qa, which is a cube with an edge of 10 fingers plus a discrepancy komma. Once a consistant system of sexagesimal computation was developed, the Mesopotamians were confronted with the problem of fitting the units of measure into a strictly sexagesimal system. In the tablet VAT 2596, there are two methods of fitting the units of volume into sexagesimal computation: one begins with the qa and has as submultiple 1/60 of qa or a sheqel; the other begins with 10 qa or a saton and has as submultiple 1/6 of qa. www.metrum.org /measures/stereometric.htm   (9564 words)

 sexagesimal Sexagesimal refers especially to the number system with base 60. Our degree of 60 minutes, minute of 60 seconds (in both time and angle measure), and hour of 60 minutes hark back to this ancient method of numeration. Quite why the Babylonians counted using sexagesimal isn't known, but 60 certainly has more factors than any other number of comparable size. www.daviddarling.info /encyclopedia/S/sexagesimal.html   (164 words)

 Babylonier   (Site not responding. Last check: 2007-11-06) The Babylonians had a sexagesimal system and used the concept of place value to write numbers larger than 60. It is a shame the Babylonians did not consider these numbers further, since they would have yielded periodically repeating sexagesimal fractions that could have provoked investigation into infinite series. In sexagesimal notation this is (1;24,52,10) which in decimal is 1.41421296, and differs by about 0.0000006 from the true value. cs-exhibitions.uni-klu.ac.at /index.php?id=323   (1223 words)

 [No title] In the text of a program or expression run by table, compute or calc (and others) a number may be represented in sexagesimal notation. The sexagesimal number notation is supported in the printf function with a new format specifier "@". In addition to allowing sexagesimal notation the ASCII representation base of a number is tracked as an expression is evaluated. cfa-www.harvard.edu /~john/starbase/tawk.html   (857 words)

 CDLJ 2005:2 Two columns of sexagesimal numbers in place value notation are recorded on the obverse of YOS 4, 293, one (here called A) neatly in the first text case, the other one (here called B), in some disorder after the apparent end of the inscription. In Whiting 1984, the length of the given side of the square in A 5446 # 1 is expressed in sexagesimal numbers in place value notation as 27 59 59;58 20 ninda. Although Melville failed to realize it, the solution algorithm he proposes is closely related to a solution algorithm in terms of non-positional decimal numbers used in MEE 3, 74 (TM.75.G 1392), a metric division exercise from Ebla, nearly as old as the texts from Šuruppak (Friberg 1986). cdli.ucla.edu /pubs/cdlj/2005/cdlj2005_002.html   (9599 words)

 babylonian.htm mathematics number historical cuneiform writing sexagesimal scale principal position fractions Not to be overlooked is the fact that in the sexagesimal notation of integers the "principle of position" was employed. Their sexagesimal fractions were introduced into India and with these fractions probably passed the principle of local value and the restricted use of the zero. From that time sexagesimal fractions held almost full sway in Mtronomical and mathe­matical calculations until the sixteenth century, when they finally yielded their place to the decimal fractions. www.unb.ca /transpo/mynet/babylonian.htm   (1797 words)

 Old Babylonian Multiplication Tables Because the Mesopotamians used a sexagesimal (base 60) number system, you might expect that a multiplication table would have to list all the multiples from 1p, 2p,..., all the way up to 59p. Most of the principal numbers are regular sexagesimal numbers that also appear on the standard table of reciprocals. is the only three-place sexagesimal number which does occur as the principal number for a single multiplication table. it.stlawu.edu /~dmelvill/mesomath/multiply.html   (861 words)

 Babylonian Mathematics and Sexagesimal Notation Here the sexagesimal divisions continue past the "seconds" position, which is generally where modern and Babylonian base-60 notations diverge with the former inconsistently switching to tenths and hundredths of a second, etc. In the sexagesimal system, the extended use of reciprocals effectively reduces division and multiplication to a single operation, i.e., multiplication by numbers which are either larger or smaller than unity. This concept was maximized by Babylonian multiplication tables which extended from 1 through 19 with further entries for 20, 30, 40, and 50 to cover the entire range between 0 and 60. www.spirasolaris.ca /sbb1sup1.html   (2106 words)

 A generic floating-point datatype.   (Site not responding. Last check: 2007-11-06) A Sexagesimal number, optionally prefixed with a sign character. When a Sexagesimal variable is used as the dependent variable of a do-loop, the associated loop increment is also an Sexagesimal. This datatype is mainly used to specify do-loop increments when the loop variable is an unsigned floating point datatype that is also expressed in sexagesimal. www.astro.caltech.edu /~mcs/CBI/cbiscript/Sexagesimal.html   (83 words)

 Scientific/Engineering Functions Similarly a number in any other base can be converted to sexagesimal format by selecting the Angle mode. Arithmetic calculations can be carried out in Time mode, or the result or number entered can be converted to another format by selecting a different calculator mode. Similarly a number in any other base can be converted to sexagesimal format by selecting the Time mode. www.calculator.org /CalcHelpCD/science.htm   (876 words)

 Hindu Cosmological Time Cycles The structural correspondence with the longer time intervals established by the three mean motions of the Sun proves that the Indian sexagesimal division of the day is an intrinsic part of the original system. We have shown that cycles of sixty days and sixty years as well as the sexagesimal number system are derived from the interaction between the first and second mean motions of the Sun intrinsic to Hindu cosmological time cycles. The ancient Egyptians are known to have counted the cycle of the third mean motion of the Sun separately, using the heliacal rising of Sirius to mark the beginning of their sidereal year. mysite.verizon.net /bonniehill/pages.aux/astrology/hindu.cycles.html   (5808 words)

 [No title] He discusses theories about the = reasons for and origin of the Sumerian sexagesimal system of counting = (and duodecimal systems of other people) as discussed by Francois = Thureau-Dangin in 1932.=20 Of the theories that were mentioned, ideas based on mathematics were the = oldest, going back to the fourth century. He discusses theories = about the reasons for and origin of the Sumerian sexagesimal system of = counting (and duodecimal systems of other people) as discussed by = Francois Thureau-Dangin in 1932.=20 Of the theories that were mentioned, ideas based on mathematics were = the oldest, going back to the fourth century. I don't have references but I thought one of the = main theories=20 about the sexagesimal system was that it evolved out of the need to = calculate a=20 two-month food supply for workers. oi.uchicago.edu /OI/ANE/ANE-DIGEST/2000/v2000.n302   (3049 words)

 Invention of Zero At a time that is unclear to scholars, though it was most likely at the beginning of the second millennium B.C., the idea of a place-value notation was conceived for the first time by the mathematicians and astronomers of Babylon. Since the Babylonian sexagesimal place-value system was decimal and additive within each order of units, it had ambiguities that often caused errors. Probably because they were aware of this difficulty, scribes sometimes left a blank space to indicate transition from one sexagesimal order to the next. www.andrews.edu /~calkins/math/biograph/biozero.htm   (1269 words)

 Ptolemy's Trig Class Every branch of mathematics begins somewhere, and for Ptolemy it began with a circle that had a radius of 60 parts, or units. Ptolemy's mathematics is based on a sexagesimal system or a base 60 system (as opposed to our base 10 system). Thinking in this way, using a sexagesimal system, Ptolemy's 60 unit circle is the same as our unit circle today - a circle with radius of 1 unit - the foundation of our trigonometric functions we see in today's mathematics textbooks. www.bsu.edu /web/cvjones/AlgBridge/ptolemy.htm   (745 words)

 HEASARC: Object Names/Coordinates Help The coordinates may be either decimal degrees or in sexagesimal format. As shown above, many of the above formats may be used in any coordinate system; however, the units of the longitude coordinate may depend upon the coordinate system if the syntax does not explicitly identify the units. For Galactic and Ecliptic sexagesimal formats, the longitude must be given in degrees. starchild.gsfc.nasa.gov /Tools/name_or_coordinates_help.html   (312 words)

 Some Computer Programs for Research in the History of Ancient and Medieval Astronomy The sexagesimal calculator SCTR and the calendar conversion program CALH display on the screen at any time a complete overview of all available operations and include brief manuals. The parameter database can be sorted using the "Greek" representation of the sexagesimal values (e.g., 365;14,48 for Ptolemy's length of the solar year) or a purely sexagesimal one (6,5,14,48 for the same value). Conversions between the two systems can be performed with a single keystroke and sexagesimal numbers can be shown in various forms (purely sexagesimal, in signs and degrees, with decimal integer part). user.uni-frankfurt.de /~dalen/programs.htm   (1923 words)

 Dr. Dobb's | Dr. Dobb's Math Power Newsletter - December 2003 | January 28, 2004 "Sexagesimal" means base 60, being the relationship of hours or degrees to minutes and seconds of either genre. In this implementation, PC time is read in decimal hours, then a decimal hour shift is specified by the user, to be added or subtracted by the program, and the result is presented in sexagesimal format. The overall effect is to add a decimal number N to a sexagesimal number. www.ddj.com /184405515   (3065 words)

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