CENTRAL ASIA: THE PLACE WHERE ALGEBRA WAS BORN

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CENTRAL ASIATHE PLACE WHERE ALGEBRA WAS BORN?
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CENTRAL ASIATHE PLACE WHERE ALGEBRA WAS BORN?

• Sponsored by the following
• UNC Office for Diversity and Multicultural
  Affairs
• UNC Graduate School
• UNC Center for Slavic, Eurasian, and East
  European Studies
• Carolina Center for the Study of the Middle East
  and Muslim Civilizations
• UNC Cell and Developmental Biology Department
• Central Asian Focus Group

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CENTRAL ASIATHE PLACE WHERE ALGEBRA WAS BORN?
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CENTRAL ASIATHE PLACE WHERE ALGEBRA WAS BORN?
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CENTRAL ASIATHE PLACE WHERE ALGEBRA WAS BORN?
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CENTRAL ASIATHE PLACE WHERE THE WEST AND EAST
MET
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CENTRAL ASIATHE PLACE WHERE THE WEST AND EAST MET
The Battle of Issus (333 BC)
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CENTRAL ASIATHE PLACE WHERE THE WEST AND EAST MET
Hellenistic States, Greek influence till 2nd
century AD
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CENTRAL ASIATHE PLACE WHERE THE WEST AND EAST
MET
ZIAN QUANG,138-126 BC
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THE SILK ROUTE
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KHORAZM
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CALIPHATE

• Prophet Muhammad, Arabia
• Abu Bakr - khalifa (gtcaliph) (prophets)
  successor (632-634), Syria and Iraq, campaign
  against Sassanid Iran and Byzantium
• Omar (634-644), Iran and Palestine
• Uthman (644-656) immediate contact with Central
  Asia
• Ali (656-661)
• Umayyad caliphs (661-750), further expansion into
  Central Asia

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Expansion into Central Asia

• Qutaiba ibn Muslim - 705-715
• Romitan - 707
• Varakhsha and Bukhara - 709
• Shumon, Nasaf and Kesh - 710
• Khorezm and Samarkand - 712
• Shosh, Farghona and Koshghar - 715

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CALIPHATE
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Practical Necessity to Develop Science

• Finance, communication, calendar
• Trade relations, transportation, navigation
• Civil engineering, measurement of distances on
  the globe, direction to Mecca
• Levy tax, division of heritage
• justification of decisions

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Preservation and Development

• Library devoted to translation and preservation
  Persian works, first from Pahlavi (Middle
  Persian), then from Syriac, Sanscrit, and Greek,
  under Caliph al-Mansour (754-775).
• Bait al-Hikma House of Wisdom - was established
  under caliph al-Mamun (786-833)- shift to
  research in mathematics, astronomy, philosophy...

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Algebra Why?

• Equations of various degrees and necessity to
  find solutions
• Babylon about 4000 years ago, by means of tables
• Egypt Ahmes papyrus, about 2000-1700 BC
• Greece geometric methods
• Diophantus 3rd century CE, by means of tables
• India
• Maya, Aztec, Inca

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Breakthrough - Al-Khwarizmi

• Born around 780, died around 850
• AbuAbd Allah (Abu Jafar) Muhammad ibn Musa
  al-Khwarizmi al-Majousi al-Katarbali.

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Al-Khwarizmi - Breakthrough

• Kitab al-mukhtasar fi hisab al-jabr wa'l-muqabala
  (820) (The Compendious Book on Calculation by
  Completion and Balancing) - algebra
• Kitab al-jam wa-l-tafriq bi-?isab al-hind
  (825)("The Book of Addition and Subtraction
  According to the Hindu Calculation") - arithmetic

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Al-Khwarizmi - Books

• Kitab surat al-ard ("Book on the appearance of
  the Earth" or "The image of the Earth" (833),
  translated as Geography)
• Zij al-sindhind ("astronomical tables") (820)
• Risala fi istikhraj tarikh al-yahud ("Extraction
  of the Jewish Era")
• Marifat saat al-mashriq fi kull balad (on the
  morning width)
• Marifat al-samt min qibal al-irtifa (the
  determination of the azimuth from a height)

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Al-Khwarizmi - Books

• Kitab ar-Ru?ama(t) (the book on sundials)
• Kitab al-Tarikh (the book of history) (the two
  have been lost)

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Al-Khwarizmi - Books

• Several Arabic manuscripts in Berlin, Istanbul,
  Tashkent, Cairo and Paris contain further
  material that surely or with some probability
  comes from al-Khwarizmi

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Al-Khwarizmi - Algebra

• al-Kitab al-mukhtasar fi hisab al-jabr
  wa'l-muqabala (The Compendious Book on
  Calculation by Completion and Balancing) (820)

al-jabr - algebra
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Geometric Method
x2 bx c
A2
B2
S2/4
A1
B1
A
B
x2 S1
S2/4
bx S2
S1
S2/4
x
x
D
C
D1
C1
S2/4
C2
D2
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Geometric Method
or
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(No Transcript)
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Al-Khwarizmi - Algebra

• 5x2 40x
• 25/5x2100
• 5x 10
• x2 10x 39
• x2 21 10x
• 12x 288 x2

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Al-Khwarizmi - Algebra

• squares equal roots
• squares equal number
• roots equal number
• squares and roots equal number
• squares and number equal roots
• roots and number equal squares

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Al-Khwarizmi - Algebra

• ax2 bx
• ax2c
• bx c
• ax2 bx c
• ax2 c bx
• bx c ax2

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Al-Khwarizmi - Algebra

• 5x2 40x
• 25/5x2100
• 5x 10
• x2 10x 39
• x2 21 10x
• 12x 288 x2
• squares equal roots ax2 bx
• squares equal number ax2c
• roots equal number bx c
• squares and roots equal number ax2 bx c
• squares and number equal roots ax2 c bx
• squares and number equal roots bx c ax2

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Al-Khwarizmi - Algebra

• 2x2 50 20x 29 x2 10x
• x2 - 10x 21 0
• ax2 bx c 0

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Al-Khwarizmi - Algebra

• 2x2 50 20x 29 x2 10x
• Aljabr - completion
• 2x2 50 10x 29 x2 20x
• Almuqabala - balancing
• x2 21 10x

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Al-Khwarizmi
We
Divide the number of roots by two
Multiply it by itself
Subtract number of it
Extract square root of it
Subtract it from half number of roots
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or add it to half number of roots
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Al-Khwarizmi - Ariphmetic
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Al-Khwarizmi - Ariphmetic
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Al-Khwarizmi - Ariphmetic
I, II, III, IV, V, VI, VII, VIII, IX, X, L, C, D,
M CDLXXXVII - 487
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
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ABACI
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Al-Khwarizmi - Ariphmetic
487 x 15
487 x 15 2435 487 7305
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Al-KhwarizmiImpact on European Mathematics

• Al Kitab al muhtasar fi hisab aljabr va al
  muqabala
• Robert of Chester, 1145
• Gerard of Cremona, 12th century
• Leonardo of Pisa commented on 6 types of
  quadratic equations

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Al-KhwarizmiImpact on European Mathematics

• Kitab al jam va tafriq bi hisab al hind -
  Algorizms book on arithmetical practice -
  Johannes of Toledo, 12th century.
• 1135 to 1153, The book spread in Europe.
• 13th c., Socrobosco, Algorismus Vulgaris (The
  Simple Algorism). Danish scholar Ingversen,
  comments in 1290.
• 13th c., Demonstratto de algorismo (The
  explanation of algorism) by Iordan Nomoraria.
  Besides, Algorithmus demonstatus (The explained
  algorism) is known. Nurnberg, 1534, and Paris,
  1570.
• In Italian Tractatus algorismi (Treatise on
  Algorism), by Giacobo of Florence, 1307. Italian
  Prosdocimo de Beldomodos Algorismi tractatus
  peritulis et necessarus (The very useful and
  necessary treatise on algorism) Padua, 1483,
  Venice, 1540.
• 13th., poetic book Carmende algorismo (The song
  on algorism), French Alexander, in French,
  English, and Iceland.
• 14th century the French mathematician Nicol
  Orems Algorismus proportionus (The algorism of
  proportions). 15th century Peierbachs book
  Algorithmus - the main aid book in the Austrian
  universities.

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Al-KhwarizmiImpact on European Mathematics

• Kitab al jam va tafriq bi hisab al hind -
  Algorizms book on arithmetical practice -
  Johannes of Toledo, 12th century.
• 1135 to 1153, The book spread in Europe.
• 13th c., Socrobosco, Algorismus Vulgaris (The
  Simple Algorism). Danish scholar Ingversen,
  comments in 1290.
• 13th c., Demonstratto de algorismo (The
  explanation of algorism) by Iordan Nemoraria.
  Besides, Algorithmus demonstatus (The explained
  algorism) is known. Nurnberg, 1534, and Paris,
  1570.
• In Italian Tractatus algorismi (Treatise on
  Algorism), by Giacobo of Florence, 1307. Italian
  Prosdocimo de Beldomodos Algorismi tractatus
  peritulis et necessarus (The very useful and
  necessary treatise on algorism) Padua, 1483,
  Venice, 1540.
• 13th., poetic book Carmende algorismo (The song
  on algorism), French Alexander, in French,
  English, and Iceland.
• 14th century the French mathematician Nicolas
  Orems Algorismus proportionus (The algorism of
  proportions). 15th century Peierbachs book
  Algorithmus - the main aid book in the Austrian
  universities.

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Algebra after Al-Khwarizmi

• In the East
• Ghiyas od-Din Abul-Fatah Omar ibn Ibrahim Khayyam
  Nishaburi or Omar Khayyam (1048 1131)
• Ulugbek (1394-1449)
• Ghiyath al-Din Jamshid ibn Masud al-Kashi (c.
  1380 1429)

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Algebra after Al-Khwarizmi

• In the West
• Niccolò Fontana Tartaglia (1499/1500 1557)
  cubic equations
• Gerolamo Cardano (1501 - 1576)
• Scipione del Ferro cubic equations
• Lodovico Ferrari (1522 1565)
• François Viète (or Vieta), (1540 - 1603),

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CENTRAL ASIATHE PLACE WHERE ALGEBRA WAS BORN

• Questions?

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• Thank you