RomeI

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Published on November 1, 2007

Author: Chan

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All Roads Lead to Rome I:  All Roads Lead to Rome I Tong Chong Sze FSC1213 Email: cstong@hkbu.edu.hk http://www.math.hkbu.edu.hk/~cstong/educ4430/educ4430.htm Euclid’s Legacy:  Euclid’s Legacy Before Euclid’s Elements, only results (in the form of theorems or procedure for calculations) were announced Religious reasons (eg Pythagoras) Protect family secrets and enhance status of the scribes Euclid’s Legacy:  Euclid’s Legacy Euclid’s Elements has revolutionized teaching Systematic treatment of a whole branch of knowledge (geometry) based on the axiomatic approach Importance of rigour and proofs Education has shifted from mere transfer of factual knowledge to the enlightenment of the process of reasoning Euclid’s Legacy:  Euclid’s Legacy Euclid’s Elements has effectively implemented Aristotle’s Reductionist Programme His postulates are Aristotle’s Nous All of geometry can be derived from the postulates using logic and certain common notions (which can be consider as part of the Nous or what we now call axioms) Euclid’s Legacy:  Euclid’s Legacy Euclid tried his best to keep the number of postulates to a minimum Proposition Book I:20 (triangle inequality) was ridiculed as being obvious to an ass! Propositions are proved in a logical sequence so that later theorems can be proved efficiently using previous propositions Euclid’s Legacy:  Euclid’s Legacy Euclid’s Elements became the standard for Western mathematics and science Textbook until the 19th century Shaped the development of the whole of Western science in the Reductionist Approach Euclid’s Legacy:  Euclid’s Legacy Geometry became the language of Mathematics and Science Equating areas was one of the main techniques Major unsolved construction problems using compass and straight-edge ruler only: Squaring the circle Duplicating the cube Trisecting the angle Euclid’s Legacy:  Euclid’s Legacy Science became the search for a minimal set of Aristotle’s Nous Engineering can be understood in terms of Archimedes’ Laws and many efficient machines can be built All of Chemistry explained by combinations of three building blocks: electrons, protons and neutrons Physics is the search for Laws of Nature (gravity, electro-magnetic forces, weak force and the strong force) Euclid’s Legacy:  Euclid’s Legacy Science is poised for a great revolution Eratosthenes (276-195 BC; measurement of earth diameter, distance to the moon and sun, heliocentric hypothesis) Appollonius (c. 200 BC; conics) But the ghost of Troy is about to haunt Greece… Greater Greece:  Troy Greater Greece Rome Carthage Syracuse Rise of Rome:  Rise of Rome Rise of Rome:  Rise of Rome Rise of Rome:  Rise of Rome Rise of Rome:  Rise of Rome Governance by US-like senate: Executive, Legislative, and Judicial Rule by tough but fair laws Sworn loyalty to the Emperor Short-lived Military dictators coming to power via coup d’etats Interested in consolidating ties (diplomacy) and governing a large empire (bureaucracy) Not interested in academic studies (availability of slave labour) Rise of Rome:  Rise of Rome Greek culture was assimilated Greek Mathematics and Science condoned but has now lost its flair and impetus Ptolemy (120 AD; astronomy) Diophantus (c. 200 AD; Arithmetica – study of algebraic problems with integer solutions) Pappus, Theon (c. 300-400 AD; commentaries) The Fall of Rome:  The Fall of Rome The Library at Alexandria was destroyed and recreated several times in its history 48 BC at the conquest by Julius Caesar 3rd century AD civil wars 391 AD by fanatical Christian rioters 415 AD The last Head Librarian at Alexandria, Hypatia (Theon’s daughter), was brutally murdered by Christians in a power struggle The Fall of Rome:  The Fall of Rome 642 AD Final destruction by Caliph Omar who allegedly said: "If these writing of the Greeks agree with the book of God [Koran], they are useless and need not be preserved; if they disagree, they are pernicious and ought to be destroyed". Rome split into two halves in 395 AD The Western Roman Empire fell in Sept 4, 476 AD (the last emperor was deposed by Odoacer) The Fall of Rome:  The Fall of Rome With the fall of the Western Roman Empire, Europe went into the Dark Ages The Eastern Roman (Byzantine) Empire finally fell in 29 May 1453 AD by the conquest of the Ottoman Empire Meanwhile, in China:  Meanwhile, in China Warring States Period (600-221 BC) Hundred Schools of Thought Lao Tse Confucius, Mencius (372-289) Huizi (370-310 BC), Zhuangzi Han Fei Zi (d. 233 BC) Meanwhile, in China:  Meanwhile, in China Chou Pei「周髀算經」(c. 100 BC Mainly a book on astronomy Calculated distance to the sun ~60,000 miles << 45 million miles estimate by Aristarchus (310-230 BC) and Hipparchus’ (190-120 BC) Current estimate of solar distance is 92 million miles Meanwhile, in China:  Meanwhile, in China Arithmetic in Nine Sections Liu Hui (c. 200 AD; commentaries on Nine Chapters, estimate of pi, gaussian elimination) Sun Tzi (c. 400 AD; Chinese Remainder Theorem: popularized by Jin Yong) 三人同行七十稀,五树梅花廿一枝, 七子团圆正半月, 余百零五便得知。 Meanwhile, in China:  Meanwhile, in China Zu Chongzhi (428-501 AD; estimate pi by 355/113 using 24576-sided polygon) Proposed new Tam-ing calendar criticized for ”... distorting the truth about heaven and violating the teaching of the classics.” Zu replied “[my calendar is]... not from spirits or from ghosts, but from careful observations and accurate mathematical calculations. ... people must be willing to hear and look at proofs in order to understand truth and facts.” Meanwhile, in China:  Meanwhile, in China Yang Hui (1238-1298 AD) Detailed Analysis of the Nine Chapters Numerical solutions to quadratic equations Magic squares Chu Shih Chieh 朱世杰 Precious Mirror of the Four Elements 《四元玉鑒》 (1303) Pascal Triangle, Systems of equations AP, GP

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