???? 3500BC ????? 2000BC

1
???? 1.

• ?????
• ???
• ???
• ??
• ??
• ??
• ???

2
?????

• ???? 3500BC ????? 2000BC
• Cuneiform(wedge shaped)
• Numeral (first position system) base 60
  12345
• 24?? 60? 60?
• ??? ??, ??(? ????), ???? 82 1, 4 1 60
  4 64

3
????? ??
4
????? ???

• 1 603 57 602 46 60 40
• 10,12,51,52,30
• 10 602 12 60 5 1/60 52/602 30/603
• ab (a b)2 - a2 - b2/2
• ab (a b)2 - a2 - b2/2
• a/b a (1/b)

5
???

• 2 0 303 0 204 0 155 0 126 0 108
  0 7, 309 0 6, 4010 0 612 0 515 0 4
• 1/13 7/91 7 (1/91) (approx) 7 (1/90)

6
????? ??

• c2 - b2 h2

7
?????

• 3000BC Nile Floods -gt Administration
• numeral hieroglyphs

8
The Rhind Papyrus

• Multiplication and division by
  doubling
• Fraction by unit fractions
• Pi 4(8/9)2 3.1605.

9
The Moscow Papyrus

• 15? ?? V h (a2 ab b2)/3.
• ?? h, ???? a ???? b
  ? trucated piramid

10
?????
11
?????

12
?????569 BC in Samos, Ionia - about 475 BC

• ???, Anaximander
• ????? ??
• ????? ?? ??? ???? ???? ??? ??.
• ????? ?? ??? ???? ??.
• ???? ??? ?? ??? ???? liberal art? ????.
• ???? ???, ????? ??, ???, ????, ?????

13
??? ??? ???

• ????? ???
• ??? 427-347BC ?? ? ???? ?? Let no one
  unversed in geometry enter here.
• ???? ??? ??? ??? ?? ??.

14
???? 325 BC- about 265 BC in Alexandria, Egypt

• ??????
• Elements 13? (??? ??? ???)
• ??? 5?? ???? ???? ???? ????? ??
• Greek mathematics can boast no finer discovery
  than this theory, which put on a sound footing so
  much of geometry as depended on the use of
  proportion.

15
?????? 287 BC in Syracuse, Sicily - 212 BC in
Syracuse, Sicily

• ??, ???? ??
• Spiral, ???(?, ??? ??, ??), ?????? ???
• ??? ??? ???

16
????

• 3000BC ???? Shatapatha Brahmana, Sulbasutra
• Harappan civilization, Indo-Aryan Invasion
• Sulbasutras were composed by Baudhayana (800 BC),
  Manava (750 BC), Apastamba (600 BC), and
  Katyayana (200 BC) pythagoras ??, 2? ???? ???

17
??????

• 0,1,2,3,4,5,6,7,8,9 ???? ??
• The Bakhshali manuscript
  vQ v(A2 b) A b/2A - (b/2A)2/2(A
  b/2A)
• Jaina mathematics (150 BC) the theory of
  numbers, arithmetical operations, geometry,
  operations with fractions, simple equations,
  cubic equations, quartic equations, and
  permutations and combinations. More surprisingly
  a theory of the infinite containing different
  levels of infinity, a primitive understanding of
  indices, and some notion of logarithms to base 2.
  

18
???? ??

• For a long time Western scholars thought that
  Indians had not done any original work till the
  time of Bhaskara II (12??). This is far from the
  truth. Nor has the growth of Indian mathematics
  stopped with Bhaskara II. Quite a few results of
  Indian mathematicians have been rediscovered by
  Europeans. For instance, the development of
  number theory, the theory of indeterminates
  infinite series expressions for sine, cosine and
  tangent, computational mathematics, etc.

19
?? ??

• ??? ??? ?? ??
• al-Khwarizmi (algorithm)
• Successors undertook a systematic application of
  arithmetic to algebra, algebra to arithmetic,
  both to trigonometry, algebra to the Euclidean
  theory of numbers, algebra to geometry, and
  geometry to algebra. This was how the creation of
  polynomial algebra, combinatorial analysis,
  numerical analysis, the numerical solution of
  equations, the new elementary theory of numbers,
  and the geometric construction of equations
  arose.

20
????

• ??, ??, ???
• 1000-500BC Pythagoras ??
• 100BC ????, ???? ???????,???
• Sun Zi (c. 250 C.E.) Chinese remainder problem
• ?????

21
(No Transcript)
22
?? (???)

• 20??
• Astronomy

23
??(??)

• quipu

24
????

• turnbull.mcs.st-and.ac.uk/history/
  Indexes/HistoryTopics.html
• aleph0.clarku.edu/djoyce/mathhist/china.html

25
????

• ?? ??? ??? ?? ? ????
• ?? ?????
• ?? ??? ??? ??? ???? ?????
• ? ????? ?? ??? ??? ??? ?? ????
• ????? ? ????? ??? ?? ??? ??????

26
??

• 190AD ??
• 960-1127 ??