muḥammad ibn mūsā al.docx

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Muammad ibn Ms al-Khwrizm

Statue of Al-Khwrizm

Born c. 780

Died c. 850

Ethnicity Persian

Known for Treatises on algebra and Indian numerals

Influenced Abu Kamil

Ab Abdallh Muammad ibn Ms al-Khwrizm[note 1] (c. 780,Khwrizm[2][4][5]c. 850) was aPersian

[1][2][3]mathematician, astronomerand geographerduring the Abbasid Empire, a scholar in

the House of Wisdom in Baghdad. The word al-Khwarizmi is pronounced in classical Arabic as Al-

Khwarithmi hence the Latin transliteration.

In the twelfth century, Latin translations ofhis workon the Indian numerals introduced the decimal

positional number system to the Western world.[5]

His Compendious Book on Calculation by

Completion and Balancingpresented the first systematic solution oflinearand quadratic equationsin Arabic. In Renaissance Europe, he was considered the original inventor of algebra, although it is

now known that his work is based on older Indian or Greek sources.[6]

He revised Ptolemy'sGeographyand wrote on astronomy and astrology.

Some words reflect the importance of al-Khwarizmi's contributions to mathematics. "Algebra" is

derived from al-jabr, one of the two operations he used to solve quadratic equations.Algorismand

algorithm stem from Algoritmi, the Latin form of his name.[7]

His name is also the origin of(Spanish)guarismo

[8]and of(Portuguese)algarismo, both meaning digit.

Life

He was born in a Persian[1][2][3]

family, and his birthplace is given asChorasmia[9]

byIbn al-

Nadim.Few details of al-Khwrizm's life are known with certainty. His name may indicate that he camefrom Khwarezm (Khiva), then in Greater Khorasan, which occupied the eastern part of theGreater Iran, nowXorazm ProvinceinUzbekistan.Abu Rayhan Birunicalls the people ofKhwarizm "a branch of thePersiantree".[10]Al-Tabarigave his name as Muhammad ibn Musa al-Khwrizm al-Majousial-Katarbali ( ). The epithetal-Qutrubbulli could indicate he might instead havecome from Qutrubbul (Qatrabbul),

[11] aviticulture district nearBaghdad. However, Rashed

[12]

suggests:
http://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-Hogendijk-2http://en.wikipedia.org/wiki/Indian_numeralshttp://en.wikipedia.org/wiki/Abu_Kamilhttp://en.wikipedia.org/wiki/Abu_Kamilhttp://en.wikipedia.org/wiki/Patronymic#Arabichttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-4http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-4http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-4http://en.wikipedia.org/wiki/Khwarezmhttp://en.wikipedia.org/wiki/Khwarezmhttp://en.wikipedia.org/wiki/Khwarezmhttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-5http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-5http://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-Hogendijk-2http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-Hogendijk-2http://en.wikipedia.org/wiki/Islamic_mathematicshttp://en.wikipedia.org/wiki/Islamic_astronomyhttp://en.wikipedia.org/wiki/Islamic_geographyhttp://en.wikipedia.org/wiki/Abbasid_Empirehttp://en.wikipedia.org/wiki/Scholarhttp://en.wikipedia.org/wiki/House_of_Wisdomhttp://en.wikipedia.org/wiki/Baghdadhttp://en.wikipedia.org/wiki/Latinhttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#Arithmetichttp://en.wikipedia.org/wiki/Indian_numeralshttp://en.wikipedia.org/wiki/Decimalhttp://en.wikipedia.org/wiki/Positional_notationhttp://en.wikipedia.org/wiki/Western_worldhttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-Struik_93-6http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-Struik_93-6http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-Struik_93-6http://en.wikipedia.org/wiki/Compendious_Book_on_Calculation_by_Completion_and_Balancinghttp://en.wikipedia.org/wiki/Compendious_Book_on_Calculation_by_Completion_and_Balancinghttp://en.wikipedia.org/wiki/Compendious_Book_on_Calculation_by_Completion_and_Balancinghttp://en.wikipedia.org/wiki/Linear_equationhttp://en.wikipedia.org/wiki/Quadratic_equationhttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-7http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-7http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-7http://en.wikipedia.org/wiki/Ptolemyhttp://en.wikipedia.org/wiki/Geography_%28Ptolemy%29http://en.wikipedia.org/wiki/Geography_%28Ptolemy%29http://en.wikipedia.org/wiki/Quadratic_equationshttp://en.wikipedia.org/wiki/Algorismhttp://en.wikipedia.org/wiki/Algorismhttp://en.wikipedia.org/wiki/Algorismhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Latinhttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-8http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-8http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-8http://en.wikipedia.org/wiki/Spanish_languagehttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-9http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-9http://en.wikipedia.org/wiki/Portuguese_languagehttp://en.wiktionary.org/wiki/pt:algarismohttp://en.wiktionary.org/wiki/pt:algarismohttp://en.wikipedia.org/wiki/Numerical_digithttp://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-Hogendijk-2http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-Hogendijk-2http://en.wikipedia.org/wiki/Chorasmiahttp://en.wikipedia.org/wiki/Chorasmiahttp://en.wikipedia.org/wiki/Chorasmiahttp://en.wikipedia.org/wiki/Chorasmiahttp://en.wikipedia.org/wiki/Ibn_al-Nadimhttp://en.wikipedia.org/wiki/Ibn_al-Nadimhttp://en.wikipedia.org/wiki/Ibn_al-Nadimhttp://en.wikipedia.org/wiki/Ibn_al-Nadimhttp://en.wikipedia.org/wiki/Khwarezmhttp://en.wikipedia.org/wiki/Khwarezmhttp://en.wikipedia.org/wiki/Greater_Khorasanhttp://en.wikipedia.org/wiki/Greater_Khorasanhttp://en.wikipedia.org/wiki/Greater_Iranhttp://en.wikipedia.org/wiki/Greater_Iranhttp://en.wikipedia.org/wiki/Xorazm_Provincehttp://en.wikipedia.org/wiki/Xorazm_Provincehttp://en.wikipedia.org/wiki/Xorazm_Provincehttp://en.wikipedia.org/wiki/Uzbekistanhttp://en.wikipedia.org/wiki/Uzbekistanhttp://en.wikipedia.org/wiki/Uzbekistanhttp://en.wikipedia.org/wiki/Abu_Rayhan_Birunihttp://en.wikipedia.org/wiki/Abu_Rayhan_Birunihttp://en.wikipedia.org/wiki/Abu_Rayhan_Birunihttp://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-11http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-11http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-11http://en.wikipedia.org/wiki/Muhammad_ibn_Jarir_al-Tabarihttp://en.wikipedia.org/wiki/Muhammad_ibn_Jarir_al-Tabarihttp://en.wikipedia.org/w/index.php?title=Majousi&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Majousi&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Majousi&action=edit&redlink=1http://en.wikipedia.org/wiki/Epithethttp://en.wikipedia.org/wiki/Epithethttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-12http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-12http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-12http://en.wikipedia.org/wiki/Viticulturehttp://en.wikipedia.org/wiki/Viticulturehttp://en.wikipedia.org/wiki/Viticulturehttp://en.wikipedia.org/wiki/Baghdadhttp://en.wikipedia.org/wiki/Baghdadhttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-13http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-13http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-13http://en.wikipedia.org/wiki/File:Al-Chwarizmi.JPGhttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-13http://en.wikipedia.org/wiki/Baghdadhttp://en.wikipedia.org/wiki/Viticulturehttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-12http://en.wikipedia.org/wiki/Epithethttp://en.wikipedia.org/w/index.php?title=Majousi&action=edit&redlink=1http://en.wikipedia.org/wiki/Muhammad_ibn_Jarir_al-Tabarihttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-11http://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Abu_Rayhan_Birunihttp://en.wikipedia.org/wiki/Uzbekistanhttp://en.wikipedia.org/wiki/Xorazm_Provincehttp://en.wikipedia.org/wiki/Greater_Iranhttp://en.wikipedia.org/wiki/Greater_Khorasanhttp://en.wikipedia.org/wiki/Khwarezmhttp://en.wikipedia.org/wiki/Ibn_al-Nadimhttp://en.wikipedia.org/wiki/Ibn_al-Nadimhttp://en.wikipedia.org/wiki/Chorasmiahttp://en.wikipedia.org/wiki/Chorasmiahttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-Hogendijk-2http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-Hogendijk-2http://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Numerical_digithttp://en.wiktionary.org/wiki/pt:algarismohttp://en.wikipedia.org/wiki/Portuguese_languagehttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-9http://en.wikipedia.org/wiki/Spanish_languagehttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-8http://en.wikipedia.org/wiki/Latinhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Algorismhttp://en.wikipedia.org/wiki/Quadratic_equationshttp://en.wikipedia.org/wiki/Geography_%28Ptolemy%29http://en.wikipedia.org/wiki/Ptolemyhttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-7http://en.wikipedia.org/wiki/Quadratic_equationhttp://en.wikipedia.org/wiki/Linear_equationhttp://en.wikipedia.org/wiki/Compendious_Book_on_Calculation_by_Completion_and_Balancinghttp://en.wikipedia.org/wiki/Compendious_Book_on_Calculation_by_Completion_and_Balancinghttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-Struik_93-6http://en.wikipedia.org/wiki/Western_worldhttp://en.wikipedia.org/wiki/Positional_notationhttp://en.wikipedia.org/wiki/Decimalhttp://en.wikipedia.org/wiki/Indian_numeralshttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#Arithmetichttp://en.wikipedia.org/wiki/Latinhttp://en.wikipedia.org/wiki/Baghdadhttp://en.wikipedia.org/wiki/House_of_Wisdomhttp://en.wikipedia.org/wiki/Scholarhttp://en.wikipedia.org/wiki/Abbasid_Empirehttp://en.wikipedia.org/wiki/Islamic_geographyhttp://en.wikipedia.org/wiki/Islamic_astronomyhttp://en.wikipedia.org/wiki/Islamic_mathematicshttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-Hogendijk-2http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-Hogendijk-2http://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-5http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-5http://en.wikipedia.org/wiki/Khwarezmhttp://en.wikipedia.org/wiki/Khwarezmhttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-4http://en.wikipedia.org/wiki/Patronymic#Arabichttp://en.wikipedia.org/wiki/Abu_Kamilhttp://en.wikipedia.org/wiki/Indian_numeralshttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-Hogendijk-2http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-Hogendijk-2http://en.wikipedia.org/wiki/Persian_peoplehttp://en.wikipedia.org/wiki/Persian_people


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There is no need to be an expert on the period or a philologist to see that al-Tabari's second citationshould read Muhammad ibn Msa al-Khwrizmandal-Majsi al-Qutrubbulli, and that there aretwo people (al-Khwrizm and al-Majsi al-Qutrubbulli) between whom the letterwa[Arabic forthe article and] has been omitted in an early copy. This would not be worth mentioning if a seriesof errors concerning the personality of al-Khwrizm, occasionally even the origins of his

knowledge, had not been made. Recently,G. J. Toomer ... with naive confidence constructed anentire fantasy on the error which cannot be denied the merit of amusing the reader.Regarding al-Khwrizm's religion, Toomer writes:Another epithet given to him by al-abar, "al-Majs," would seem to indicate that he was an

adherent of the oldZoroastrianreligion. This would still have been possible at that time for a manof Iranian origin, but the pious preface to al-Khwrizm's Algebra shows that he was an orthodox

Muslim, so al-abar's epithet could mean no more than that his forebears, and perhaps he in his

youth, had been Zoroastrians.[1]

Ibn al-Nadm'sKitb al-Fihristincludes a short biography on al-Khwrizm, together with a list ofthe books he wrote. Al-Khwrizm accomplished most of his work in the period between 813 and

833. After theIslamic conquest of Persia, Baghdad became the centre of scientific studies andtrade, and many merchants and scientists from as far asChinaandIndiatraveled to this city, as did

Al-Khwrizm. He worked in Baghdad as a scholar at the House of Wisdom established byCaliph al-Mamn, where he studied the sciences and mathematics, which included thetranslation ofGreekandSanskritscientific manuscripts.D. M. Dunlop suggests that it may have been possible that Muammad ibn Ms al-Khwrizm

was in fact the same person asMuammad ibn Ms ibn Shkir, the eldest of the threeBanMs.[13][year missing]Contributions

A page from al-Khwrizm'sAlgebra

Al-Khwrizm's contributions to mathematics, geography, astronomy, and cartography

established the basis for innovation in algebra and trigonometry. His systematic approach tosolving linearandquadratic equations led to algebra, a word derived from the title of his 830book on the subject, "The Compendious Book on Calculation by Completion andBalancing" (al-Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala ).On the Calculation with Hindu Numerals written about 825, was principally responsible for

spreading the Indian system of numeration throughout the Middle Eastand Europe. It wastranslated into Latin asAlgoritmi de numero Indorum. Al-Khwrizm, rendered as (Latin)Algoritmi,

led to the term "algorithm".Some of his work was based on Persian and Babylonian astronomy, Indian numbers, and

Greekmathematics.Al-Khwrizm systematized and corrected Ptolemy's data for Africa and the Middle east.Another major book was Kitab surat al-ard ("The Image of the Earth"; translated as Geography),

presenting the coordinates of places based on those in the Geography of Ptolemybut withimproved values for theMediterranean Sea, Asia, and Africa.

He also wrote on mechanical devices like theastrolabeandsundial.

He assisted a project to determine the circumference of the Earth and in making a world map foral-Ma'mun, the caliph, overseeing 70 geographers.[14]
http://en.wiktionary.org/wiki/ar:wahttp://en.wiktionary.org/wiki/ar:wahttp://en.wiktionary.org/wiki/ar:wahttp://en.wikipedia.org/wiki/G._J._Toomerhttp://en.wikipedia.org/wiki/G._J._Toomerhttp://en.wikipedia.org/wiki/G._J._Toomerhttp://en.wikipedia.org/wiki/Zoroastrianhttp://en.wikipedia.org/wiki/Zoroastrianhttp://en.wikipedia.org/wiki/Zoroastrianhttp://en.wikipedia.org/wiki/Muslimhttp://en.wikipedia.org/wiki/Muslimhttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-toomer-1http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-toomer-1http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-toomer-1http://en.wikipedia.org/wiki/Ibn_al-Nad%C4%ABmhttp://en.wikipedia.org/wiki/Ibn_al-Nad%C4%ABmhttp://en.wikipedia.org/wiki/Ibn_al-Nad%C4%ABmhttp://en.wikipedia.org/wiki/Islamic_conquest_of_Persiahttp://en.wikipedia.org/wiki/Islamic_conquest_of_Persiahttp://en.wikipedia.org/wiki/Islamic_conquest_of_Persiahttp://en.wikipedia.org/wiki/Chinahttp://en.wikipedia.org/wiki/Chinahttp://en.wikipedia.org/wiki/Chinahttp://en.wikipedia.org/wiki/History_of_Indiahttp://en.wikipedia.org/wiki/History_of_Indiahttp://en.wikipedia.org/wiki/History_of_Indiahttp://en.wikipedia.org/wiki/House_of_Wisdomhttp://en.wikipedia.org/wiki/House_of_Wisdomhttp://en.wikipedia.org/wiki/Caliphhttp://en.wikipedia.org/wiki/Caliphhttp://en.wikipedia.org/wiki/Al-Ma%CA%BEm%C5%ABnhttp://en.wikipedia.org/wiki/Al-Ma%CA%BEm%C5%ABnhttp://en.wikipedia.org/wiki/Al-Ma%CA%BEm%C5%ABnhttp://en.wikipedia.org/wiki/Greek_languagehttp://en.wikipedia.org/wiki/Greek_languagehttp://en.wikipedia.org/wiki/Greek_languagehttp://en.wikipedia.org/wiki/Sanskrithttp://en.wikipedia.org/wiki/Sanskrithttp://en.wikipedia.org/wiki/Sanskrithttp://en.wikipedia.org/wiki/D._M._Dunlophttp://en.wikipedia.org/wiki/D._M._Dunlophttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_ibn_Sh%C4%81kirhttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_ibn_Sh%C4%81kirhttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_ibn_Sh%C4%81kirhttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_ibn_Sh%C4%81kirhttp://en.wikipedia.org/wiki/Ban%C5%AB_M%C5%ABs%C4%81http://en.wikipedia.org/wiki/Ban%C5%AB_M%C5%ABs%C4%81http://en.wikipedia.org/wiki/Ban%C5%AB_M%C5%ABs%C4%81http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-14http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-14http://en.wikipedia.org/wiki/Wikipedia:Citing_sourceshttp://en.wikipedia.org/wiki/Wikipedia:Citing_sourceshttp://en.wikipedia.org/wiki/Wikipedia:Citing_sourceshttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Geographyhttp://en.wikipedia.org/wiki/Geographyhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Cartographyhttp://en.wikipedia.org/wiki/Cartographyhttp://en.wikipedia.org/wiki/Algebrahttp://en.wikipedia.org/wiki/Algebrahttp://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Linear_equationhttp://en.wikipedia.org/wiki/Linear_equationhttp://en.wikipedia.org/wiki/Quadratic_equationhttp://en.wikipedia.org/wiki/Quadratic_equationhttp://en.wikipedia.org/wiki/Quadratic_equationhttp://en.wikipedia.org/wiki/The_Compendious_Book_on_Calculation_by_Completion_and_Balancinghttp://en.wikipedia.org/wiki/The_Compendious_Book_on_Calculation_by_Completion_and_Balancinghttp://en.wikipedia.org/wiki/The_Compendious_Book_on_Calculation_by_Completion_and_Balancinghttp://en.wikipedia.org/wiki/The_Compendious_Book_on_Calculation_by_Completion_and_Balancinghttp://en.wikipedia.org/wiki/Hindu-Arabic_numeral_systemhttp://en.wikipedia.org/wiki/Hindu-Arabic_numeral_systemhttp://en.wikipedia.org/wiki/Middle_Easthttp://en.wikipedia.org/wiki/Middle_Easthttp://en.wikipedia.org/wiki/Europehttp://en.wikipedia.org/wiki/Europehttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Iranhttp://en.wikipedia.org/wiki/Iranhttp://en.wikipedia.org/wiki/Babylonianhttp://en.wikipedia.org/wiki/Babylonianhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Indian_numeralshttp://en.wikipedia.org/wiki/Indian_numeralshttp://en.wikipedia.org/wiki/Ancient_Greecehttp://en.wikipedia.org/wiki/Ancient_Greecehttp://en.wikipedia.org/wiki/Ptolemyhttp://en.wikipedia.org/wiki/Ptolemyhttp://en.wikipedia.org/wiki/Africahttp://en.wikipedia.org/wiki/Africahttp://en.wikipedia.org/wiki/Middle_easthttp://en.wikipedia.org/wiki/Middle_easthttp://en.wikipedia.org/wiki/Ptolemyhttp://en.wikipedia.org/wiki/Ptolemyhttp://en.wikipedia.org/wiki/Mediterranean_Seahttp://en.wikipedia.org/wiki/Mediterranean_Seahttp://en.wikipedia.org/wiki/Mediterranean_Seahttp://en.wikipedia.org/wiki/Astrolabehttp://en.wikipedia.org/wiki/Astrolabehttp://en.wikipedia.org/wiki/Astrolabehttp://en.wikipedia.org/wiki/Sundialhttp://en.wikipedia.org/wiki/Sundialhttp://en.wikipedia.org/wiki/Sundialhttp://en.wikipedia.org/wiki/Al-Ma%27munhttp://en.wikipedia.org/wiki/Al-Ma%27munhttp://en.wikipedia.org/wiki/Al-Ma%27munhttp://en.wikipedia.org/wiki/Al-Ma%27munhttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-15http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-15http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-15http://en.wikipedia.org/wiki/File:Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpghttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-15http://en.wikipedia.org/wiki/Al-Ma%27munhttp://en.wikipedia.org/wiki/Al-Ma%27munhttp://en.wikipedia.org/wiki/Sundialhttp://en.wikipedia.org/wiki/Astrolabehttp://en.wikipedia.org/wiki/Mediterranean_Seahttp://en.wikipedia.org/wiki/Ptolemyhttp://en.wikipedia.org/wiki/Middle_easthttp://en.wikipedia.org/wiki/Africahttp://en.wikipedia.org/wiki/Ptolemyhttp://en.wikipedia.org/wiki/Ancient_Greecehttp://en.wikipedia.org/wiki/Indian_numeralshttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Babylonianhttp://en.wikipedia.org/wiki/Iranhttp://en.wikipedia.org/wiki/Algorithmhttp://en.wikipedia.org/wiki/Europehttp://en.wikipedia.org/wiki/Middle_Easthttp://en.wikipedia.org/wiki/Hindu-Arabic_numeral_systemhttp://en.wikipedia.org/wiki/The_Compendious_Book_on_Calculation_by_Completion_and_Balancinghttp://en.wikipedia.org/wiki/The_Compendious_Book_on_Calculation_by_Completion_and_Balancinghttp://en.wikipedia.org/wiki/Quadratic_equationhttp://en.wikipedia.org/wiki/Linear_equationhttp://en.wikipedia.org/wiki/Trigonometryhttp://en.wikipedia.org/wiki/Algebrahttp://en.wikipedia.org/wiki/Cartographyhttp://en.wikipedia.org/wiki/Astronomyhttp://en.wikipedia.org/wiki/Geographyhttp://en.wikipedia.org/wiki/Mathematicshttp://en.wikipedia.org/wiki/Wikipedia:Citing_sourceshttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-14http://en.wikipedia.org/wiki/Ban%C5%AB_M%C5%ABs%C4%81http://en.wikipedia.org/wiki/Ban%C5%AB_M%C5%ABs%C4%81http://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_ibn_Sh%C4%81kirhttp://en.wikipedia.org/wiki/D._M._Dunlophttp://en.wikipedia.org/wiki/Sanskrithttp://en.wikipedia.org/wiki/Greek_languagehttp://en.wikipedia.org/wiki/Al-Ma%CA%BEm%C5%ABnhttp://en.wikipedia.org/wiki/Caliphhttp://en.wikipedia.org/wiki/House_of_Wisdomhttp://en.wikipedia.org/wiki/History_of_Indiahttp://en.wikipedia.org/wiki/Chinahttp://en.wikipedia.org/wiki/Islamic_conquest_of_Persiahttp://en.wikipedia.org/wiki/Ibn_al-Nad%C4%ABmhttp://en.wikipedia.org/wiki/Mu%E1%B8%A5ammad_ibn_M%C5%ABs%C4%81_al-Khw%C4%81rizm%C4%AB#cite_note-toomer-1http://en.wikipedia.org/wiki/Muslimhttp://en.wikipedia.org/wiki/Zoroastrianhttp://en.wikipedia.org/wiki/G._J._Toomerhttp://en.wiktionary.org/wiki/ar:wa


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When, in the 12th century, his works spread to Europe through Latin translations, it had a

profound impact on the advance of mathematics inEurope. He introduced Arabic numerals into theLatin West, based on a place-value decimal system developed from Indian sources.

[15]

Carl Friedrich Gauss

From Wikipedia, the free encyclopedia

Jump to:navigation,search"Gauss" redirects here. For things named after Carl Friedrich Gauss, see List of things namedafter Carl Friedrich Gauss. For other persons or things named Gauss, see Gauss

(disambiguation).

Carl Friedrich Gauss

Carl Friedrich Gauss (17771855), painted by

Christian Albrecht Jensen

Born

30 April 1777

Braunschweig, Duchy ofBrunswick-Wolfenbttel,Holy Roman Empire

Died

23 February 1855 (aged 77)

Gttingen, Kingdom of

Hanover

Residence Kingdom of Hanover

Nationality German

Fields Mathematicsandphysics

Institutions University of Gttingen

Alma mater University of Helmstedt

Doctoral

advisorJohann Friedrich Pfaff
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Other

academic advisors

Johann Christian MartinBartels

Doctoral students

Christoph GudermannChristian Ludwig GerlingRichard Dedekind

Johann ListingBernhard RiemannChristian PetersMoritz Cantor

Othernotable students

Johann EnckePeter Gustav LejeuneDirichletGotthold Eisenstein

Carl Wolfgang Benjamin

Goldschmidt

Gustav KirchhoffErnst KummerAugust Ferdinand MbiusL. C. Schnrlein

Julius Weisbach

Known for See full list

InfluencedSophie Germain

Ferdinand Minding

Notable awards Copley Medal(1838)

Johann Carl Friedrich Gauss (/as/; German: Gau, pronounced [as]( listen); Latin:Carolus Fridericus Gauss) (30 April 177723 February 1855) was a Germanmathematician

andphysical scientistwho contributed significantly to many fields, including number theory,algebra, statistics, analysis,differential geometry, geodesy, geophysics, electrostatics,

astronomyandoptics.Sometimes referred to as thePrinceps mathematicorum

[1](Latin, "the Prince of Mathematicians" or

"the foremost of mathematicians") and "greatest mathematician since antiquity", Gauss had a

remarkable influence in many fields of mathematics and science and is ranked as one of history's

most influential mathematicians.[2]

He referred to mathematics as "the queen of sciences".[3]

Early years (17771798)
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Statue of Gauss at his birthplace,BraunschweigCarl Friedrich Gauss was born on 30 April 1777 inBraunschweig(Brunswick), in theDuchy ofBraunschweig-Wolfenbttel, now part of Lower Saxony, Germany, as the son of poorworking-class parents.

[4] Indeed, his mother was illiterate and never recorded the date of his birth,

remembering only that he had been born on a Wednesday, eight days before the Feast of the

Ascension, which itself occurs 40 days afterEaster. Gauss would later solve this puzzle about his

birthdate in the context offinding the date of Easter, deriving methods to compute the date inboth past and future years.

[5] He was christened and confirmed in a church near the school he

attended as a child.[6]

Gauss was achild prodigy. There are many anecdotes about his precocity while a toddler, and hemade his first ground-breaking mathematical discoveries while still a teenager. He completed

Disquisitiones Arithmeticae, hismagnum opus, in 1798 at the age of 21, though it was notpublished until 1801. This work was fundamental in consolidating number theory as a discipline and

has shaped the field to the present day.

Gauss's intellectual abilities attracted the attention of theDuke of Braunschweig,[2]who sent him

to the Collegium Carolinum (now Technische Universitt Braunschweig), which he attendedfrom 1792 to 1795, and to theUniversity of Gttingenfrom 1795 to 1798. While at university,

Gauss independently rediscovered several important theorems;[7]

his breakthrough occurred in 1796

when he showed that any regularpolygonwith a number of sides which is aFermat prime(and,consequently, those polygons with any number of sides which is the product of distinct Fermat

primes and apowerof 2) can be constructed bycompass and straightedge. This was a majordiscovery in an important field of mathematics; construction problems had occupied mathematicians

since the days of the Ancient Greeks, and the discovery ultimately led Gauss to choosemathematics instead ofphilologyas a career. Gauss was so pleased by this result that he requested

that a regularheptadecagonbe inscribed on his tombstone. Thestonemasondeclined, stating thatthe difficult construction would essentially look like a circle.[8]The year 1796 was most productive for both Gauss and number theory. He discovered a construction

of the heptadecagon on 30 March.[9]

He further advancedmodular arithmetic, greatly simplifying

manipulations in number theory.[citation needed]

On 8 April he became the first to prove thequadraticreciprocitylaw. This remarkably general law allows mathematicians to determine the solvability of

any quadratic equation in modular arithmetic. The prime number theorem, conjectured on

31 May, gives a good understanding of how theprime numbersare distributed among the integers.Gauss also discovered that every positive integer is representable as a sum of at most three
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triangular numberson 10 July and then jotted down inhis diarythe famous note: "!num = + + ". On October1 he published a result on the number of solutions of polynomials

with coefficients infinite fields, which 150 years later led to theWeil conjectures.Middle years (17991830)

This section needs additional citations for verification. Please help improvethis articleby adding citations to reliable sources. Unsourced material may be

challenged and removed.(July 2012)In his 1799 doctorate in absentia, A new proof of the theorem that every integral rational algebraic

function of one variable can be resolved into real factors of the first or second degree, Gauss proved

the fundamental theorem of algebra which states that every non-constant single-variablepolynomialwith complex coefficients has at least one complex root. Mathematicians includingJean le Rond d'Alemberthad produced false proofs before him, and Gauss's dissertation containsa critique of d'Alembert's work. Ironically, by today's standard, Gauss's own attempt is not

acceptable, owing to implicit use of the Jordan curve theorem. However, he subsequentlyproduced three other proofs, the last one in 1849 being generally rigorous. His attempts clarified the

concept of complex numbers considerably along the way.

Gauss also made important contributions to number theorywith his 1801 bookDisquisitionesArithmeticae(Latin, Arithmetical Investigations), which, among things, introduced the symbol

for congruence and used it in a clean presentation ofmodular arithmetic, contained the first two

proofs of the law of quadratic reciprocity, developed the theories of binary and ternaryquadratic forms, stated the class number problem for them, and showed that a regularheptadecagon(17-sided polygon) can beconstructed with straightedge and compass.

Title page of Gauss'sDisquisitiones Arithmeticae

In that same year, Italian astronomer Giuseppe Piazzi discovered the dwarf planet Ceres.Piazzi could only track Ceres for a few months, following it for three degrees across the night sky.Then it disappeared temporarily behind the glare of the Sun. Several months later, when Ceres

should have reappeared, Piazzi could not locate it: the mathematical tools of the time were not ableto extrapolate a position from such a scant amount of datathree degrees represent less than 1% ofthe total orbit.

Gauss, who was 23 at the time, heard about the problem and tackled it. After three months of intensework, he predicted a position for Ceres in December 1801just about a year after its first sighting

and this turned out to be accurate within a half-degree when it was rediscovered by Franz Xavervon Zachon 31 December atGotha, and one day later byHeinrich OlbersinBremen.

Gauss's method involved determining aconic sectionin space, given one focus (the Sun) and the

conic's intersection with three given lines (lines of sight from the Earth, which is itself moving on anellipse, to the planet) and given the time it takes the planet to traverse the arcs determined by theselines (from which the lengths of the arcs can be calculated by Kepler's Second Law). This problem

leads to an equation of the eighth degree, of which one solution, the Earth's orbit, is known. The

solution sought is then separated from the remaining six based on physical conditions. In this work

Gauss used comprehensive approximation methods which he created for that purpose.[10]

One such method was thefast Fourier transform. While this method is traditionally attributed toa 1965 paper by J. W. Cooley and J. W. Tukey, Gauss developed it as a trigonometric

interpolation method. His paper, Theoria Interpolationis Methodo Nova Tractata, was only
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%C3%A4us_Olbershttp://en.wikipedia.org/wiki/Gotha_Observatoryhttp://en.wikipedia.org/wiki/Franz_Xaver_von_Zachhttp://en.wikipedia.org/wiki/Franz_Xaver_von_Zachhttp://en.wikipedia.org/wiki/Ceres_%28dwarf_planet%29http://en.wikipedia.org/wiki/Dwarf_planethttp://en.wikipedia.org/wiki/Giuseppe_Piazzihttp://en.wikipedia.org/wiki/Italyhttp://en.wikipedia.org/wiki/Disquisitiones_Arithmeticaehttp://en.wikipedia.org/wiki/Compass_and_straightedge_constructionshttp://en.wikipedia.org/wiki/Heptadecagonhttp://en.wikipedia.org/wiki/Class_number_problemhttp://en.wikipedia.org/wiki/Quadratic_formhttp://en.wikipedia.org/wiki/Quadratic_reciprocityhttp://en.wikipedia.org/wiki/Modular_arithmetichttp://en.wikipedia.org/wiki/Latinhttp://en.wikipedia.org/wiki/Disquisitiones_Arithmeticaehttp://en.wikipedia.org/wiki/Disquisitiones_Arithmeticaehttp://en.wikipedia.org/wiki/Number_theoryhttp://en.wikipedia.org/wiki/Jordan_curve_theoremhttp://en.wikipedia.org/wiki/Jean_le_Rond_d%27Alemberthttp://en.wikipedia.org/wiki/Root_of_a_functionhttp://en.wikipedia.org/wiki/Polynomialhttp://en.wikipedia.org/wiki/Fundamental_theorem_of_algebrahttp://en.wikipedia.org/wiki/Wikipedia:Verifiability#Burden_of_evidencehttp://en.wikipedia.org/wiki/Template:Citation_neededhttp://en.wikipedia.org/wiki/Help:Introduction_to_referencing/1http://en.wikipedia.org/w/index.php?title=Carl_Friedrich_Gauss&action=edithttp://en.wikipedia.org/w/index.php?title=Carl_Friedrich_Gauss&action=edithttp://en.wikipedia.org/wiki/Weil_conjectureshttp://en.wikipedia.org/wiki/Finite_fieldhttp://en.wikipedia.org/wiki/Eureka_%28word%29http://en.wikipedia.org/wiki/Gauss%27s_diaryhttp://en.wikipedia.org/wiki/Triangular_number


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published posthumously in Volume 3 of his collected works. This paper predates the first

presentation byJoseph Fourieron the subject in 1807.[11]

Zach noted that "without the intelligent work and calculations of Doctor Gauss we might not have

found Ceres again". Though Gauss had up to that point been financially supported by his stipend

from the Duke, he doubted the security of this arrangement, and also did not believe puremathematics to be important enough to deserve support. Thus he sought a position in astronomy, and

in 1807 was appointed Professor of Astronomy and Director of the astronomicalobservatory inGttingen, a post he held for the remainder of his life.The discovery of Ceres led Gauss to his work on a theory of the motion of planetoids disturbed by

large planets, eventually published in 1809 as Theoria motus corporum coelestium in sectionibusconicis solem ambientum (Theory of motion of the celestial bodies moving in conic sections around

the Sun). In the process, he so streamlined the cumbersome mathematics of 18th century orbital

prediction that his work remains a cornerstone of astronomical computation.[citation needed]

It

introduced the Gaussian gravitational constant, and contained an influential treatment of the

method of least squares, a procedure used in all sciences to this day to minimize the impact ofmeasurement error. Gauss proved the method under the assumption ofnormally distributederrors (seeGaussMarkov theorem; see alsoGaussian). The method had been described earlierby Adrien-Marie Legendre in 1805, but Gauss claimed that he had been using it since1795.

[citation needed]

Thales

Thales of Miletus

Thales

Born c. 624 BC
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Died c. 547546 BC

School Ionian, Milesian school, Naturalism

Main interestsEthics, Metaphysics, Mathematics,

Astronomy

Notable ideasWater is the arche, Thales' theorem,

intercept theorem

Influenced by[show]

Influenced[show]

Thales of Miletus(/eliz/; Greek: (), Thals; c. 624 BCc. 546 BC) was a pre-Socratic Greek philosopher from Miletus in Asia Minor, and one of the Seven Sages of Greece.

Many, most notably Aristotle, regard him as the first philosopher in the Greek tradition.[1]

According

to Bertrand Russell, "Western philosophy begins with Thales."[2]

Thales attempted to explain natural

phenomena without reference to mythology and was tremendously influential in this respect. Almostall of the other Pre-Socratic philosophers follow him in attempting to provide an explanation of

ultimate substance, change, and the existence of the worldwithout reference to mythology. Thosephilosophers were also influential, and eventually Thales' rejection of mythological explanations

became an essential idea for the scientific revolution. He was also the first to define generalprinciples and set forth hypotheses, and as a result has been dubbed the "Father of Science", though

it is argued that Democritus is actually more deserving of this title.[3][4]

In mathematics, Thales used geometry to solve problems such as calculating the height of pyramidsand the distance of ships from the shore. He is credited with the first use of deductive reasoning

applied to geometry, by deriving four corollaries to Thales' Theorem. As a result, he has been hailed

as the first true mathematician and is the first known individual to whom a mathematical discoveryhas been attributed.

[5]

Thales political life had mainly to do with the involvement of theIonians in the defense ofAnatoliaagainst the growing power of the Persians, who were then new to the region. A king had come to

power in neighboring Lydia, Croesus, who was somewhat too aggressive for the size of his army. He

had conquered most of the states of coastal Anatolia, including the cities of the Ionians. The story istold in Herodotus.

[10]

The Lydians were at war with the Medes, a remnantof the first wave of Iranians in the region, over the

issue of refuge the Lydians had given to some

Scythian soldiers of fortune inimical to the Medes.

The war endured for five years, but in the sixth aneclipse of the Sun (mentioned above) spontaneously

halted a battle in progress (the Battle of Halys).

Total eclipse of the Sun

It seems that Thales had predicted this solar eclipse.The Seven Sages were most likely already in

existence, as Croesus was also heavily influenced bySolon of Athens, another sage. Whether Thales was

present at the battle is not known, nor are the exact

terms of the prediction, but based on it the Lydiansand Medes made peace immediately, swearing a

blood oath.

The Medes were dependencies of the Persians under Cyrus. Croesus now sided with the Medesagainst the Persians and marched in the direction of Iran (with far fewer men than he needed). He
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was stopped by the river Halys, then unbridged. This time he had Thales with him, perhaps byinvitation. Whatever his status, the king gave the problem to him, and he got the army across by

digging a diversion upstream so as to reduce the flow, making it possible to ford the river. Thechannels ran around both sides of the camp.

The two armies engaged at Pteria in Cappadocia. As the battle was indecisive but paralyzing to both

sides, Croesus marched home, dismissed his mercenaries and sent emissaries to his dependents andallies to ask them to dispatch fresh troops to Sardis. The issue became more pressing when the

Persian army showed up at Sardis. Diogenes Laertius[11] tells us that Thales gained fame as acounselor when he advised the Milesians not to engage in a symmachia, a "fighting together", withthe Lydians. This has sometimes been interpreted as an alliance, but a ruler does not ally with his

subjects.

Croesus was defeated before the city of Sardis by Cyrus, who subsequently spared Miletus because ithad taken no action. Cyrus was so impressed by Croesus wisdom and his connection with the sagesthat he spared him and took his advice on various matters.

The Ionians were now free. Herodotus says that Thales advised them to form an Ionian state; that is,

a bouleuterion (deliberative body) to be located atTeos in the center of Ionia. The Ionian citiesshould be demoi, or districts. Miletus, however, received favorable terms from Cyrus. The othersremained in an Ionian League of 12 cities (excluding Miletus now), and were subjugated by the

Persians.While Herodotus reported that most of his fellow Greeks believe that Thales did divert the riverHalys to assist King Croesus' military endeavors, he himself finds it doubtful.

[12]

The Ionic Stoa on the Sacred Way in MiletusDiogenes Laertius

[13] tells us that the Seven Sages were created in the archonship of Damasius at

Athens about 582 BC and that Thales was the first sage. The same story, however, asserts that

Thales emigrated to Miletus. There is also a report that he did not become a student of nature untilafter his political career. Much as we would like to have a date on the seven sages, we must reject

these stories and the tempting date if we are to believe that Thales was a native of Miletus, predicted

the eclipse, and was with Croesus in the campaign against Cyrus.

Thales had instruction from Egyptianpriest. It was fairly certain that he came from a wealthy andestablished family, and the wealthy customarily educated their children. Moreover, the ordinary

citizen, unless he was a seafaring man or a merchant, could not afford the grand tour in Egypt, and in

any case did not consort with noble lawmakers such as Solon.He did participate in some games, most likely Panhellenic, at which he won a bowl twice. He

dedicated it to Apollo at Delphi. As he was not known to have been athletic, his event was probably

declamation, and it may have been victory in some specific phase of this event that led to his being

designated sage.Theories

The Greeks often invoked idiosyncratic explanations of natural phenomena by reference to the will

ofanthropomorphic gods and heroes. Thales, however, aimed to explain natural phenomena via a

rational explanation that referenced natural processes themselves. For example, Thales attempted toexplain earthquakes by hypothesizing that the Earth floats on water, and that earthquakes occur

when the Earth is rocked by waves, rather than assuming that earthquakes were the result of

supernatural processes. Thales was a Hylozoist (those who think matter is alive).[14]

It is unclearwhether the interpretation that he treated matter as being alive might have been mistaken for his

thinking the properties of nature arise directly from material processes, more consistent with modern

ideas of how properties arise as emergent characteristics of complex systems involved in theprocesses ofevolution and developmental change.

Thales, according to Aristotle, asked what was the nature (GreekArche) of the object so that it

would behave in its characteristic way. Physis () comes from phyein (), "to grow", related
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to our word "be".[15]

(G)natura is the way a thing is "born",[16]

again with the stamp of what it is initself.

Aristotle[17]

characterizes most of the philosophers "at first" () as thinking that the "principlesin the form of matter were the only principles of all things", where "principle" is arche, "matter" is

hyle ("wood" or "matter", "material") and "form" is eidos.

Arche is translated as "principle", but the two words do not have precisely the same meaning. Aprinciple of something is merely prior (related to pro-) to it either chronologically or logically. An

arche (from , "to rule") dominates an object in some way. If the arche is taken to be an origin,then specific causality is implied; that is, B is supposed to be characteristically B just because itcomes from A, which dominates it.

The archai that Aristotle had in mind in his well-known passage on the first Greek scientists are not

necessarily chronologically prior to their objects, but are constituents of it. For example, in pluralismobjects are composed of earth, air, fire and water, but those elements do not disappear with the

production of the object. They remain as archai within it, as do the atoms of the atomists.

What Aristotle is really saying is that the first philosophers were trying to define the substance(s) of

which all material objects are composed. As a matter of fact, that is exactly what modern scientistsare attempting to accomplish in nuclear physics, which is a second reason why Thales is described as

the first western scientist.

Water as a first principleThales most famous philosophical position was his cosmological thesis, which comes down to usethrough a passage from Aristotle's Metaphysics.

[18] In the work Aristotle unequivocally reported

Thales hypothesis about the nature of matter that the originating principle of nature was a singlematerial substance: water. Aristotle then proceeded to proffer a number of conjectures based on hisown observations to lend some credence to why Thales may have advanced this idea (though

Aristotle didnt hold it himself).Aristotle considered Thales position to be roughly the equivalent tothe later ideas ofAnaximenes, who held that everything was composed ofair.Aristotle laid out his own thinking about matter and form which may shed some light on the ideas of

Thales, inMetaphysics983 b6 8-11, 17-21 (The passage contains words that were later adopted by

science with quite different meanings.)

"That from which is everything that exists and from which it first becomes and into which it isrendered at last, its substance remaining under it, but transforming in qualities, that they say is the

element and principle of things that are. For it is necessary that there be some nature (),either one or more than one, from which become the other things of the object being saved... Thalesthe founder of this type of philosophy says that it is water."

In this quote we see Aristotle's depiction of the problem of change and the definition ofsubstance .

He ask if an object changes, is it the same or different? In either case how can there be a change

from one to the other? The answer is that the substance "is saved", but acquires or loses differentqualities (, the things you "experience").Aristotle conjectured that Thales reached his conclusion by contemplating that the "nourishment of

all things is moist and that even the hot is created from the wet and lives by it."

While Aristotles conjecture on why Thales held water was the originating principle of water is hisown thinking, his statement that Thales held it was water is generally accepted as genuinelyoriginating with Thales and he is seen as an incipient matter-and-formist.

Heraclitus Homericus[19]

states that Thales drew his conclusion from seeing moist substance turninto air, slime and earth. It seems likely that Thales viewed the Earth as solidifying from the water

on which it floated and which surrounded Ocean.

Writing centuries later Diogenes Laertius also states that Thales taught "Water constituted(, 'stood under') the principle of all things."[20]Practice and Theory
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Thales was known for his innovative use of geometry. His understanding was theoretical as well aspractical. For example, he said:Megiston topos: hapanta gar chorei ( )Space is the greatest thing, as it contains all thingsTopos is in Newtonian-style space, since the verb, chorei, has the connotation of yielding before

things, or spreading out to make room for them, which is extension. Within this extension, thingshave a position. Points, lines,planes and solids related by distances and angles follow from this

presumption.Thales understood similar triangles and right triangles, and what is more, used that knowledge inpractical ways. The story is told in DL (loc. cit.) that he measured the height of the pyramidsby their

shadows at the moment when his own shadow was equal to his height. A right triangle with two

equal legs is a 45-degree right triangle, all of which are similar. The length of the pyramids shadowmeasured from the center of the pyramid at that moment must have been equal to its height.

This story indicates that he was familiar with the Egyptian seked, or seqed - the ratio of the run to

the rise of a slope (cotangent). The seked is at the base of problems 56, 57, 58, 59 and 60 of the

Rhind papyrus - an ancient Egyptian mathematics document.In present day trigonometry, cotangents require the same units for run and rise (base and

perpendicular), but

muḥammad ibn mūsā al.docx

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