Mathematics in the Near and Far East

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Mathematics in the Near and Far East
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Background

• Islam was born in 610 and it became the driving
  force behind the expansion of the Arabs.
• By 732 the Arabian empire was larger than the
  Roman empire ever was.
• They built the new capital in Baghdad. It was
  there that the House of Wisdom was developed.
• The House of Wisdom was comparable to the Museum
  at Alexandria.

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Major Near (Middle) Eastern Contributors

• Mohammed ibn Musa al-Khowarizmi
• (Al-Khowarizmi)
• 2. Abu Kamil
• 3. Thabit ibn Korra (Thabit)
• 4. Umar al-khayyami (Omar Khayyam)

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Al-Khowarizmi
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Abu-Kamils thoughts about Al-Khowarizmi

• ... the one who was first to succeed in a book of
  algebra and who pioneered and invented all the
  principles in it.
• I have established, in my second book, proof of
  the authority and precedent in algebra of
  Muhammad ibn Musa al-Khowarizmi,
• http//www-history.mcs.st-andrews.ac.uk/history/Ma
  thematicians/Abu_Kamil.html

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Al-Khowarizmi (780-850)

• Most well-known of the Arab mathematicians
• Known by many as the father of algebra
• Western Europeans were first introduced to
  algebra through his work.
• The term algebra comes from the title of his
  work Hisab al-jabr wal muqabalah.
• The title of this piece is translated the
  science of reunion and reduction refer to page
  228.

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Abu-Kamil (850-930)

• The second great Arabic algebra writer
• Also known as The Reckoner from Egypt and The
  calculator from Egypt
• Introduced irrational solutions for some
  quadratics
• His methods were considered common property
• Fibonacci even used a great deal of Abu-Kamils
  work

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Thabit
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Thabit (836-901)

• Distinguished physician, skilled translator, and
  prolific writer
• Translated much of the Greek mathematical work
  including Euclids elements
• His Book on the Determination of Amicable Numbers
  is supposedly the first totally original Arabic
  work. This work was based on the construction of
  pairs of (amicable) numbers each of which is
  equal to the sum of the proper divisors of the
  other.

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Omar Khayyam
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Omar Khayyam (1048-1123)

• Renowned poet and author of the Rubaiyat, also
  was a very accomplished scientist
• Claimed to be the first mathematician to solve
  every kind of cubic equation having a positive
  root.
• His work with the geometrical theory of the
  general cubic is considered one of the greatest
  accomplishments of any Arabic mathematician.

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Major Far Eastern Contributors

• Liu Hui
• Chin Chu-shao
• Li Ye
• Chu Shih-chieh

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Liu Hui
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Liu Hui (200s AD)

• The Nine Chapters on the Mathematical Art is the
  oldest mathematics textbook in existence.
• Liu Huis commentary on this compilation is
  actually what stands today.
• It has been used for over a thousand years.
• This book was written more practically than
  theoretically.
• Liu Hui also wrote the Sea Island Mathematical
  Manual which dealt with measuring distances to
  inaccessible points.

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Chin Chu-shao (1202-1261)

• He did most of his work when the Mongols began to
  take control of China.
• Chin started the custom of printing negative
  numbers in black type and positive ones in red.
• Chin wrote the Mathematical Treatise in Nine
  Sections.
• This piece was the oldest existing Chinese work
  to contain a round symbol for zero and the first
  to deal with equations higher than 3rd degree.

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Li Ye (1192-1279)

• He did work with constructing quadratic equations
  derived from imaginative configurations of
  circles, squares, rectangles, and trapezoids.
• refer to page 240
• He was credited with indicating negative numbers
  by drawing a diagonal line through the last digit
  of the number being used.
• refer to page 241

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Chu Shih-chieh (1270-1330?)

• Wrote two important texts Introduction to
  Mathematical Studies and Precious Mirror of the
  Four Elements.
• Introduction to Mathematical Studies was
  basically a textbook for beginners and greatly
  influenced the development of Japanese
  mathematics.
• Precious Mirror of the Four Elements dealt with
• Numerical equations up to the 14th degree and
• Binomial expansions (x1)n which came to be known
  as a triangular arrangement called Pascals
  triangle.

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The end of an era

• Chu Shih-chiehs Precious Mirror represented the
  peak of Chinese Mathematics.
• Chinese mathematics dramatically declined from
  this point.
• Sadly, many of the accomplishments of this era
  were lost or forgotten.

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Arabic Mathematical Examples

• 5.51 a. and b.
• 5.53 a.

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The Nine Chapters on the Mathematical Art

• http//www.math.sfu.ca/histmath/China/1stCenturyAD
  /NineChapters.htm
• Examples
• 5.515 a.
• 5.516 a.