Tusi, Mathematician, Mathematics Educator and Teacher, and the Saviour of the Mathematics by Ali Tootian B.Sc., Shahid Bahonar University, 1992 Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science in the Mathematics Education Program Faculty of Education Ali Tootian 2012 SIMON FRASER UNIVERSITY Fall 2012 All rights reserved. However, in accordance with the Copyright Act of Canada, this work may be reproduced, without authorization, under the conditions for “Fair Dealing.” Therefore, limited reproduction of this work for the purposes of private study, research, criticism, review and news reporting is likely to be in accordance with the law, particularly if cited appropriately. Partial Copyright Licence iii Abstract Searching for mathematicians who had contributed to the improvement of mathematics education during Islamic Era in Persia became an interest of the author of this thesis during the Master’s Program at Simon Fraser University. It was found that Nasir-al-Din Tusi has been an icon in the mathematics education of the Islamic Era. The purpose of this study was to investigate Tusi’s contributions to the improvement of mathematics education. This goal required a summary of the political and educational situation of Persia from the start of Arab control to the Mongol rule and then a focus on Tusi’s particular contributions. The method for collecting the information was to initially research books written by historians and mathematicians in North America. Then the search was continued to obtain the opinions of Iranian historians and mathematicians. The sources include Iran’s National Library, the library of universities, peer reviewed books available in Iran’s mathematics education books market, and the proceedings of conferences about Tusi held in Iran. It was found that Tusi compiled series of mathematics books and treatises, wrote redactions to many of them, and kept them in a library at the location of an observatory and school he established in Maragheh, the capital of the Mongol Empire. The results of the study revealed that Tusi trained mathematics teachers, taught mathematics. He collected data from twelve years of observation with his team of mathematicians and astronomers in Maragheh. He compiled a calendar from the data. Tusi also recast the entire collection of astronomy books from Euclid’s “Elements” to Ptolemy’s “Almagest.” The principal conclusion is that Tusi had both influenced and preserved the scholarly life of mathematicians and astronomers. Another conclusion is that he planned and defined a reformed mathematics education by combining written books and translated books into a quality terminology which helped educators teach mathematics with greater ease. He also made academic courses separated from religious studies, and offered them to the candidate from public instead of only from affluent families. Keywords: Tusi; mathematics education; mathematics books; iv Dedication To my mother, Farrah, who had dreamed of my graduate education since I was a little boy. To my wife, Laya, for her patience, understanding, and encouragement. To my son, Ario, for his enthusiasm, and understanding that I was involved with a research and a full time teaching responsibility. To my daughter, Auva, for her patience with me who often was found with his laptop. v Acknowledgements I herewith acknowledge, with deep appreciation, and sincere thanks: My dear wife who supported me in all aspects of this journey. My senior supervisor, Dr. Peter Liljedhal, who believed in my ability to perform this research, and provided outstanding support and encouragement as I learned how to become a researcher. My thesis committee member, Dr. Rina Zazkis, for her careful reading and thoughtful feedback to my work. My external member of the defense session, Dr. Stephen Campbell, for his input for the corrections and editing. My dear uncle, Abdullah, for collecting the data was not simply possible without his help. A copy of “Mutiwassitat” was sent to me, miraculously, by him in early days of my research. Markaz-e-Dayeratol Maarefe Eslami (The Islamic Encyclopedia Centre), for providing me with important information about how to locate and collect data in Iran. The staff and counsellors of the National Library of Iran, for their welcoming approach on the thirty days I spent there for collecting data. The staff and graduate students of Tarbiat Modarres University, for their time guiding me toward resources. The staff of the Library of Azad University, for helping me with finding articles. The counsellors of Sazmane Mirase Maktoob, for their advice and direction. Dr. Shiva Gol Tabaghi and Mrs. Darien Allan for proofreading my thesis and suggestions for increasing its quality. vi Table of Contents Approval .......................................................................................................................... ii Partial Copyright Licence ............................................................................................... iii Abstract .......................................................................................................................... iv Dedication ....................................................................................................................... v Acknowledgements ........................................................................................................ vi List of Tables ................................................................................................................... x List of Figures................................................................................................................. xi Chapter 1. Mathematics Education during Islamic Era .......................................... 1 Motivation ........................................................................................................................ 1 Vision .............................................................................................................................. 2 Planning .......................................................................................................................... 3 Execution ........................................................................................................................ 4 Chapter 2. A General History of Persia from Arab’s Conquest to the Fall of the Mongols........................................................................................ 7 Umayyad Dynasty (AD 661 – 750) .................................................................................. 9 Independence Movements ............................................................................................ 10 Abbasid Dynasty (AD 750 - 1258) ................................................................................. 12 Persians in Abbasid Empire .................................................................................. 13 Resistance Movements against Abbasid .............................................................. 15 Mongol’s Conquest of Persia ......................................................................................... 17 Mongol and Ismaili................................................................................................ 18 Fall of Baghdad ............................................................................................................. 21 Chapter 3. A Summary of the History of the Life of Tusi ..................................... 23 Tusi’s Background ......................................................................................................... 23 Tusi’s Migration to Alamut ............................................................................................. 25 The Fall of Alamut ......................................................................................................... 28 Tusi and Fall of Baghdad .............................................................................................. 29 The Years of Peace and Results ................................................................................... 30 Chapter 4. Tusi Developed a Series of Updated Mathematics Books ................. 33 A New Beginning for the Mathematics Community ........................................................ 34 Overcoming Lack of Proper Connection Between Existing Books ................................. 34 Gaps Between the Topics ............................................................................................. 35 Similar Original Books and Similar Treatises ........................................................ 35 Similar Translations of One Book ......................................................................... 36 Challenging Topics ........................................................................................................ 37 Out of Norm Topics ....................................................................................................... 38 vii New Topics and Applications ........................................................................................ 39 Omitting Unnecessary Topics ........................................................................................ 40 What is Tahrir? .............................................................................................................. 40 The Quality of Books ..................................................................................................... 41 Chapter 5. Tusi Connected Euclid’s