Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Week 14 Lecture
China Topic 02
Mathematical Contributions from China
Mathematical Applications in Astronomy,
Physics and Military Technology
This lecture was last updated 25 November, 2013
This slide was updated 11/25/2013
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Mathematical Contributions from China
The learning objectives for week 14 are:
– to understand the basic position of China in the history of
mathematics
– to learn the Chinese developed negative numbers, an important part of
modern mathematics
– to appreciate the Chinese observations of the sky that were far in
advance of Europe until quite recently
– to appreciate the Chinese inventions of the compass, seismograph and
gunpowder as well as the crossbow, canon, flamethrower and gun
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Mathematical Contributions from China
Terms you should know for week 14 are:
– decimal system and its origin
– seismograph
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Mathematical Contributions from China:
Additional Sources
Sources:
Joseph, George Gheverghese. 1991. The Crest of the Peacock: Non-European Roots of Mathematics.
London and New York: I. B. Tauris & Co. Ltd.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
These slides correspond to and supplement the reading:
Temple, Robert. 1998. The Genius of China: 3,000 Years
of Science, Discovery and Invention. London: Prion Books
Limited.
Part 2: Astronomy and Cartography, pages 29-39
Part 6: Mathematics, pages 139-147;
Part 7: Magnetism, pages 149-157;
Part 8: The Physical Sciences, pages 159-171;
Part 9: Transport and Exploration, pages 173-197;
Part 11: Warfare, pages 215-248
See the note about page numbers on the next slide
11/25/2013
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Page Numbers Update:
Temple, Robert. 1998. The Genius of China: 3,000 Years of Science,
Discovery and Invention. London: Prion Books
This book has been reprinted several times and some page
numbers might have changed. If your page numbers do not
correspond to those in the previous slide, use the chapter
numbers and topic titles to guide your reading.
This slide as added 11/25/2013
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
First Section is on:
Mathematics: Temple, Chapter 6, pages 139–47
Later sections on astronomy and military technology later in the
lecture.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
1.
Chinese Mathematical Achievements
Science historian Joseph Needham has noted that one of the
key features of modern science is
“the application of mathematics to nature.”
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
2. We saw earlier in the course that the Inca, Maya and
Egyptians excelled at applying mathematics to nature and to
human undertakings such as canals, pyramids, palaces and the
like.
3. The traditional Western view is that mathematics originated in
ancient Greece…
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
4…but the Black Athena research by Martin Bernal and others
has shown that much of Greek mathematics derives from
ancient Egypt and ancient Sumer (Babylonia).
5. Even so, much important mathematical progress was made
during the Greek “Golden Age” from about 600 BC to 300
BC
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
6. Among the most famous of the Greek mathematicians are:
– Pythagoras 569–475 BC
– Euclid 325–265 BC
– Archimedes 287–212 BC
7. They and many ancient Greek colleagues wrote some of the
most famous and important mathematical documents we know
of.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
8. But the application of mathematics to nature and the
development of pure mathematics owes much more to ancient
China than many people realize.
9. Because China’s mathematical developments come later than
those in Egypt, Egyptian influence is possible.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
10. But even if this is the case, Chinese mathematicians clearly
made many discoveries and improvements on their own.
11. The large number of existing Chinese manuscripts means we
have more details from China than from ancient Egypt where
we still depend on a small number of papyri such as the Ahmes
papyrus described earlier in the course.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
12. Among China’s many mathematical contributions…
13. The decimal system, from at least the 14th century BC,
applied in Europe only 2300 years later.
14. We can trace Chinese math through several of the most
famous manuscripts…
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
15. “The Circular Paths of Heaven”
500 BC
Pythagorean theorem, fractions
16. “Book on Arithmetic”
300 BC
Fractions, rectangles
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
17. “9 Chapters on the Mathematical Arts”
300 BC to 200 AD
Root extractions, ratios, simultaneous equations,
areas, volumes, right-angle triangles
18. “Commentary on the 9 Chapters”
130 AD – Square root of 10
Source: Joseph, George Gheverghese. 1991. The Crest of the Peacock: Non-European Roots
of Mathematics. London and New York: I. B. Tauris & Co. Ltd. Page 132
.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
19. “The Mathematical Arts”
200 AD
Theory of large numbers, first mention of the abacus
20. “Commentary on ‘The Circular Paths’”
200 AD
Solution of quadratic equations – (x2 + ax = b2 )
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
21. “Official History of the Sui Dynasty”
450 AD
Value of pi
22. “Continuation of Ancient Mathematics”
AD 625 – 3rd degree (cubic) equations
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
23. “The Sea Mirror”
1248 AD
Higher-degree equations (above cubes); applications of
Pythagorean theorem; minus numbers
24. Negative numbers a Chinese invention early as 2nd
century BC
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
25. “Detailed Analysis of the 9 Chapters”
1261 AD – Arithmetic progressions; decimal fractions;
quadratic equations with negative coefficients of x.
26. “The Precious Mirror”
1303 AD – Pascal’s triangle (350 years before Pascal);
simultaneous equations; matrix methods to solve equations.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
27. “Indeterminate analysis” from 4th century AD
N = 3x + 2
N = 5y + 3
N = 7z + 2
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
28. Calculate the volumes of eg:
–
–
–
–
–
Cylinder
Rectangular pyramid
Tetrahedron
Truncated square pyramid
Truncated triangular right prism
Gheverghese. P. 168
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Montclair State University Department of
Anthropology
Anth 140: Non Western Contributions to the
Western World
Dr. Richard W. Franke
Chinese Mathematical
Achievements
29. Famous “broken
bamboo problem”
30. Find the value of b
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
31. Solution:
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
32. This one of most famous problems in mathematics
– Subject of much analysis and debate in ancient Indian math
– Arab and European interest over many centuries
– Apparently solved in about 6th century by Chinese
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Applications
33. Development of math in China related to other achievements
in
– Astronomy
– Physics
– Military technology
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Applications
34. Astronomy:
Temple, part 2, pages 29 – 39
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Applications
35. Understanding of sunspots – 4th century BC, several
hundred years before Europe
36. Chinese records the oldest continuous set of data known
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Applications
37. Quantitative cartography: relatively accurate maps using
mathematics to generate scale
38. Early as 2nd century AD
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical
Applications
39. Observed and
measured direction of
comet tails early as
6th century AD
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements
40. Equatorial astronomical
instruments to divide sky
into measurable segments –
13th century AD or earlier
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Applications
11/25/2013
41. Developed
constellations
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Achievements in Physics
The next slides correspond to and supplement the reading:
Temple, Robert. 1998. The Genius of China: 3,000 Years of Science,
Discovery and Invention. London: Prion Books Limited.
Chapters 7 – 9 on Magnetism, the Physical Sciences and Transport and
Exploration, Pages 149 – 97
11/25/2013
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Achievements in Physics
42. Compass – 4th century BC –
in use by Han Dynasty
43. Used understanding of
magnetism that derived from Ch’i
44. Pointed south
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Achievements in Physics
45…developed pointers to
make compass more precise
– 3rd century AD.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Achievements in Physics
46. By Sung Dynasty 960 – 1279 AD…knew how to
magnetize iron needles – rub with magnetite then
suspend in water
47. Compass used in navigation first by Chinese
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Achievements in Physics
48. Chinese also understood heating and cooling to change
characteristics of magnets – called thermo-remanence
49. Compass to Europe around 1190 AD
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Achievements in Physics
50. Geobotany: Chinese first to notice relation between plants
and minerals in ground underneath – at least by 3rd century
BC, ie Han Dynasty
51. Newton’s 1st law of motion – body stays at rest or in motion
until changed by outside forces – developed in China 4th
century BC…Newton 18th century AD
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Achievements in Physics
52. Hexagonal shape of snowflakes
in 2nd century BC
53. In Europe 1591
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Achievements in Physics
54. Seismograph: around 130 AD
invented by astronomer Chang
Heng
55. Ball falls into frog’s mouth to
signal earthquake up to 400 km
(250 miles) distant
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Achievements in Physics
56. Chinese first to recognize spontaneous combustion
57. Principle of sedimentation in geology first in China
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Achievements in
Physics
58. The Kite: invented in
China 5th– 4th
century BC – in
Europe known by
1589 AD
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Achievements in Physics
59. Parachute – 2 nd century BC
60. Rudder for guiding ships on
long voyages – Columbus could
not have sailed without one
→
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Achievements in Physics
61. Sails and sail technology
–
–
–
–
–
Chinese influence somewhat disputed
European lateen sails go back 2,000 years
Chinese tacking technology superior
Pivoting masts an advantage
Chinese invented leeboard to hold ship upright while tacking
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Achievements in Physics
62. Paddle wheel boat – 5th century AD
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45
Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare Technology
The next slides correspond to and supplement the reading:
Temple, Robert. 1998. The Genius of China: 3,000 Years of
Science, Discovery and Invention. London: Prion Books
Limited.
Chapter 11 – Warfare, Pages 215 – 48
11/25/2013
46
Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare
Technology
63. Crossbow – 4 th
century BC
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47
Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare Technology
64. Repeating crossbow allowed
rapid fire of arrows or of multiple
arrows
65. 1st century AD Chinese
invented grid sites (crosshairs)
for more accurate aim of
crossbow
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare Technology
66. Gunpowder: invented accidentally as by-product of medical
research.
67. By 9th century AD
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare Technology
68. Gunpowder a complex set of chemical discoveries
– Saltpeter – potassium nitrate – also called sodium nitrate – detected
by purple flame when it burns
– Chinese knew it possibly from 4th century BC
– Arabs called it “Chinese snow”
– Gunpowder burns by taking oxygen not from the air but from the
saltpeter
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare Technology
69. Sulfur the second key ingredient
–
–
–
Lowers point of ignition of saltpeter
Increases speed of the combustion (explosion)
When saltpeter is up to 75% sulfur causes explosion speed burning
of the saltpeter
70. Charcoal provides carbon – third necessary element
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare Technology
71. General ratio for gunpowder:
–
–
–
11/25/2013
saltpeter 15 parts
charcoal 3 parts
sulfur 2 parts
52
Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare
Technology
72 By 850 AD
gunpowder in use
73. Despite Western
myths to the
contrary…
11/25/2013
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare Technology
74. The Chinese did not limit their use of gunpowder to fireworks
for entertainment
75. To the contrary, they invented…
11/25/2013
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare Technology
76. The flamethrower – 10th
century AD
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare Technology
77. Bombs, grenades and
rockets of several types.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare Technology
78. Siege engines
and other early
forms of artillery.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare
Technology
79. The
canon…by at
least 1341
…and…
11/25/2013
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare Technology
80. The gun by at least 1288 AD,
but possibly as early as the 11th
century
81. Mid 10th century called a “fire
lance”
82. Guns reached Europe by 1327
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare Technology
83. Canons and guns altered the power relations between knights
and peasants on the battlefield and played a role in ending the
Medieval period of European history. Can you see how?
84. In 1866 Alfred Nobel in Sweden invented dynamite, the
first safely manageable explosive since gunpowder.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare Technology
85. Dynamite uses nitroglycerin.
86. In recent years dynamite has been replaced by “water gel
explosives.”
11/25/2013
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Warfare Technology
87. Modern firearms use a smokeless propellant [the explosive
that pushes the bullet out of the barrel] usually based on
cordite, a mixture of nitroglycerine and nitrocellulose.
88. …and gunpowder is used primarily in fireworks and for
shooting blanks or flares where the visible smoke is an asset.
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Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
End of Week 14 Lecture on
Mathematical Contributions from China
Mathematical Applications in Astronomy,
Physics and Military Technology
Week 14 – China Topic 02
11/25/2013
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