- Timeline of numerals and arithmetic
A

timeline of**numerals**andarithmetic **Before 2000 BC*** ca. 20,000 BC —

Nile Valley ,Ishango Bone : possibly the earliest reference toprime number s andEgyptian multiplication .

* ca.3400 BC —Mesopotamia , theSumerians invent the firstnumeral system , and a system of weights and measures.

* ca.3100 BC —Egypt , earliest known decimal system allows indefinite counting by way of introducing new symbols, [*http://www.math.buffalo.edu/mad/Ancient-Africa/mad_ancient_egyptpapyrus.html#berlin*] .

* ca.2800 BC —Indus Valley Civilization on theIndian subcontinent , earliest use of decimal ratios in a uniform system of ancient weights and measures, the smallest unit of measurement used is 1.704 millimetres and the smallest unit of mass used is 28 grams.

* ca.2000 BC —Mesopotamia , theBabylonians use a base-60 decimal system, and compute the first known approximate value of π at 3.125.**1st millennium BC*** ca

1000 BC —Vulgar fraction s used by theEgyptians .

* ca 8th century BC — theYajur Veda , one of the fourHindu Veda s, contains the earliest concept ofinfinity , and states that “if you remove a part from infinity or add a part to infinity, still what remains is infinity.”

* second half of 1st millennium BC — TheLo Shu Square , the unique normalmagic square of order three, was discovered inChina .

* ca.400 BC —Jain a mathematicians in India write the “Surya Prajinapti”, a mathematical text which classifies all numbers into three sets: enumerable, innumerable andinfinite . It also recognises five different types ofinfinity : infinite in one and two directions, infinite in area, infinite everywhere, and infinite perpetually.

*300s BC — Indian texts use theSanskrit word “Shunya” to refer to the concept of ‘void’ (zero.)

* ca.300 BC —Brahmi numeral s are conceived in India.

*300 BC —Mesopotamia , theBabylonians invent the earliest calculator, theabacus .

* ca.300 BC — Indian mathematicianPingala writes the “Chhandah-shastra”, which contains the first Indian use of zero as a digit (indicated by a dot) and also presents a description of abinary numeral system , along with the first use ofFibonacci numbers andPascal's triangle .

* ca.250 BC — lateOlmec s had already begun to use a true zero (a shell glyph) several centuries beforePtolemy in the New World. See0 (number) .

*150 BC — Jain mathematicians in India write the “Sthananga Sutra”, which contains work on the theory of numbers, arithmetical operations,geometry , operations withfractions , simple equations,cubic equations , quartic equations, andpermutations andcombinations .

*50 BC —Indian numerals , the firstpositional notation base-10 numeral system , begins developing in India.**1st millennium***

300 — the earliest known use of zero as a decimal digit is introduced byIndian mathematicians .

* ca.400 — the “Bakhshali manuscript” is written byJain a mathematicians, which describes a theory of the infinite containing different levels ofinfinity , shows an understanding of indices, as well aslogarithms tobase 2 , and computessquare roots of numbers as large as a million correct to at least 11 decimal places.

*550 —Hindu mathematicians give zero a numeral representation in thepositional notation Indian numeral system.

*628 —Brahmagupta writes the "Brahma-sphuta-siddhanta", where zero is clearly explained, and where the modernplace-value Indian numeral system is fully developed. It also gives rules for manipulating bothnegative and positive numbers , methods for computingsquare roots , methods of solving linear andquadratic equation s, and rules for summing series,Brahmagupta's identity , and theBrahmagupta theorem .

*940 —Abu'l-Wafa al-Buzjani extracts roots using the Indian numeral system.

*953 — Thearithmetic of theHindu-Arabic numeral system at first required the use of a dust board (a sort of handheldblackboard ) because “the methods required moving the numbers around in the calculation and rubbing some out as the calculation proceeded.”Al-Uqlidisi modified these methods forpen andpaper use. Eventually the advances enabled by thedecimal system led to its standard use throughout the region and the world.**1000–1500***ca.

1000 —Pope Sylvester II introduces theabacus using theHindu-Arabic numeral system to Europe.

*1030 —Ali Ahmad Nasawi writes a treatise on thedecimal andsexagesimal number systems. His arithmetic explains the division of fractions and the extraction of square and cubic roots (square root of 57,342; cubic root of 3, 652, 296) in an almost modern manner. [*MacTutor|id=Al-Nasawi|title=Abu l'Hasan Ali ibn Ahmad Al-Nasawi*]

*1100s —Indian numerals have been modified byArab mathematicians to form the modernHindu-Arabic numeral system (used universally in the modern world.)

*1100s — theHindu-Arabic numeral system reachesEurope through theArabs .

*1202 — Leonardo Fibonacci demonstrates the utility ofHindu-Arabic numerals in his "Book of the Abacus".

* ca.1400 —Ghiyath al-Kashi “contributed to the development ofdecimal fraction s not only for approximatingalgebraic number s, but also forreal number s such aspi . His contribution to decimal fractions is so major that for many years he was considered as their inventor. Although not the first to do so, al-Kashi gave an algorithm for calculating nth roots which is a special case of the methods given many centuries later by Ruffini and Horner.” He is also the first to use thedecimal point notation inarithmetic andArabic numerals . His works include "The Key of arithmetics, Discoveries in mathematics, The Decimal point", and "The benefits of the zero". The contents of the "Benefits of the Zero" are an introduction followed by five essays: “On whole number arithmetic”, “On fractional arithmetic”, “On astrology”, “On areas”, and “On finding the unknowns [unknown variables] ”. He also wrote the "Thesis on the sine and the chord" and "Thesis on finding the first degree sine".

*1400s —Ibn al-Banna andal-Qalasadi introduced symbolic notation for algebra and for mathematics in general.

*1427 —Al-Kashi completes "The Key to Arithmetic" containing work of great depth ondecimal fraction s. It applies arithmetical and algebraic methods to the solution of various problems, including several geometric ones.

*1478 — An anonymous author writes theTreviso Arithmetic .**17th century***

1614 -John Napier discusses Napierianlogarithm s in "Mirifici Logarithmorum Canonis Descriptio",

*1617 - Henry Briggs discusses decimal logarithms in "Logarithmorum Chilias Prima",

*1618 -John Napier publishes the first references to "e" in a work onlogarithms .**18th century***

1794 - Jurij Vega publishes "Thesaurus Logarithmorum Completus".**Calculation of Pi***

1706 -John Machin develops a quickly converging inverse-tangent series for π and computes π to 100 decimal places,

*1789 -Jurij Vega improves Machin's formula and computes π to 140 decimal places.

*1949 - John von Neumann computes π to 2,037 decimal places usingENIAC .

*1961 -Daniel Shanks andJohn Wrench compute π to 100,000 decimal places using an inverse-tangent identity and an IBM-7090 computer.

*1987 -Yasumasa Kanada , David Bailey,Jonathan Borwein , andPeter Borwein use iterative modular equation approximations to elliptic integrals and aNEC SX-2 supercomputer to compute π to 134 million decimal places.

*2002 -Yasumasa Kanada , Y. Ushiro,Hisayasu Kuroda ,Makoto Kudoh and a team of nine more compute π to 1241.1 billion digits using a Hitachi 64-nodesupercomputer .**See also***

Timeline of algorithms

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Timeline of mathematics**— A timeline of pure and applied mathematics history. Contents 1 Before 1000 BC 2 1st millennium BC 3 1st millennium AD 4 1000–1500 … Wikipedia**Timeline of Islamic science and engineering**— This timeline of Islamic science and engineering covers the general development of science and technology in the Islamic world during the Islamic Golden Age, usually dated from the 7th to 16th centuries.From the 17th century onwards, the advances … Wikipedia**Long and short scales**— The long and short scales are two of several different large number naming systems used throughout the world for integer powers of ten. Many countries, including most in continental Europe, use the long scale whereas most English speaking… … Wikipedia**List of mathematics articles (T)**— NOTOC T T duality T group T group (mathematics) T integration T norm T norm fuzzy logics T schema T square (fractal) T symmetry T table T theory T.C. Mits T1 space Table of bases Table of Clebsch Gordan coefficients Table of divisors Table of Lie … Wikipedia**History of mathematics**— A proof from Euclid s Elements, widely considered the most influential textbook of all time.[1] … Wikipedia**Algebra**— This article is about the branch of mathematics. For other uses, see Algebra (disambiguation). Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from… … Wikipedia**Roman Empire**— For other senses of the term, see Roman Empire (disambiguation). Imperium Romanum redirects here. For the video game, see Imperium Romanum (video game). Roman Empire Senatus Populusque Romanus (SPQR) The Senate and … Wikipedia**Islamic Golden Age**— The Islamic Golden Age, also sometimes known as the Islamic Renaissance, [Joel L. Kraemer (1992), Humanism in the Renaissance of Islam , p. 1 148, Brill Publishers, ISBN 9004072594.] was traditionally dated from the 8th century to the 13th… … Wikipedia**History of algebra**— Elementary algebra is the branch of mathematics that deals with solving for the operands of arithmetic equations. Modern or abstract algebra has its origins as an abstraction of elementary algebra. Historians know that the earliest mathematical… … Wikipedia**History of computing hardware**— Computing hardware is a platform for information processing (block diagram) The history of computing hardware is the record of the ongoing effort to make computer hardware faster, cheaper, and capable of storing more data. Computing hardware… … Wikipedia