week 14 lecture china topic 02 mathematical contributions ...franker/week14chinamath02.pdf ·...
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This slide was updated 11/25/2013 1
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
2
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
3
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
4
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.
11/25/2013 5
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
This slide as added 11/25/2013 6
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.
11/25/2013 7
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.
11/25/2013 8
Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Achievements 1. Science historian Joseph Needham has noted that one of the
key features of modern science is “the application of mathematics to nature.”
11/25/2013 9
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…
11/25/2013 10
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
11/25/2013 11
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.
11/25/2013 12
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.
11/25/2013 13
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.
11/25/2013 14
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.
11/25/2013 17
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 )
11/25/2013 18
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
11/25/2013 19
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
11/25/2013 20
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.
11/25/2013 21
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
11/25/2013 22
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
11/25/2013 23
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:
11/25/2013 25
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
11/25/2013 26
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
11/25/2013 28
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
11/25/2013 29
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
11/25/2013 30
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
11/25/2013 31
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
11/25/2013 32
Montclair State University Department of Anthropology
Anth 140: Non Western Contributions to the Western World
Dr. Richard W. Franke
Chinese Mathematical Applications
41. Developed constellations
11/25/2013 33
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 34
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.
11/25/2013 36
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
11/25/2013 37
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
11/25/2013 38
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
11/25/2013 39
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
11/25/2013 40
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
11/25/2013 41
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
11/25/2013 42
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
11/25/2013 43
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
→
11/25/2013 44
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
11/25/2013 45
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
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 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 47
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
11/25/2013 48
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
11/25/2013 49
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
11/25/2013 50
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
11/25/2013 51
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
11/25/2013 52
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:
– saltpeter 15 parts – charcoal 3 parts – sulfur 2 parts
11/25/2013 53
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 54
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 55
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
11/25/2013 56
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.
11/25/2013 57
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.
11/25/2013 58
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 59
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
11/25/2013 60
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.
11/25/2013 61
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 62
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.
11/25/2013 63
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