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Mathematics of Islamic Art & Geometric Design رياضيات الفن اإلسالمي والتصميم الهندسي Learning Objectives: • To raise awareness of Islamic contribution to Mathematics • To inspire Mathematics through the study of Islamic Geometric Designs • To have fun with Islamic Geometric Designs • To create works of art Formative Assessment to Determine Knowledge Base to Track Progress 1. After which Muslim Mathematician is the term “algorithm” named? A. al-Karaji 2. B. al Jurjani C. ibn Haytham D. al Firnas B. ibn Battuta C. Hasan Selebi D. al Kindi Which Muslim Mathematician, philosopher, musician and physicist has been described as one of the “Twelve great minds of history”? A. ibn Haytham 5. D. al Jazari Which Muslim Polymath is regarded as the first aviator? A. ibn Firnas 4. C. al Biruni Which Muslim Mathematician is regarded as the “Father of Optics”? A. al-Mawsili 3. B. al Khawrizmi B. al Wafa C. al Rammah D. al Kindi Which Italian Mathematician played a major role in promoting the use of Arabic numbers in Europe? A. Galileo B. de Vinci C. Fibonacci D. di Capprio Thabit bin Qurra: Greatest Muslim geometer Kamal al-Din al-Farisi’s work ibn al-Haytham Algebra, Geometry أشهر علماء الرياضيات المسلمين Famous Muslim mathematicians Omar Khayyam: Poet, Mathematician, Astronomer Muhammad Al-Karaji’s work Al-Khwarizmi The “Father of Algebra” Al-Khwarizmi The “Father of Algebra” • The best known of the Islamic Mathematicians • Considered one of the greatest Mathematicians of all times • His books were studied long into the Renaissance • To him we owe the words: Algebra and Algorithm Al-Karaji • Al-Karaji was the first to use mathematical induction to prove the binomial theorem – He proved that if the first statement in an infinite sequence of statements is true, then so is the next one. He proved that: If (13 + 23) = (1 +2)2 Then (13 + 23 + 33) = (1 +2 + 3)2 and so on and so on Omar Al Khayyam • Famous poet and the writer of the “Rubaiyat”, but an important mathematician and astronomer in his own right The Moving Finger writes, and, having written, Moves on: nor all thy Piety nor Wit Shall lure it back to cancel half a Line, Nor all thy Tears wash out a Word of it. Nasir Al-Din Al-Tusi • The first to treat trigonometry as a separate math discipline, distinct from astronomy • Gave the first extensive account of spherical trigonometry • One of his major mathematical contributions was the formulation of the famous law of sine for plane triangles: a⁄ b⁄ c⁄ = = (sin A) (sin B) (sin C) ibn Al-Haytham • Systemized conic sections and number theory on analytic geometry • Worked on the beginnings of the link between algebra and geometry • This in turn had an influence on the development of René Descartes' geometric analysis and Isaac Newton's calculus. Kamal Al-Din al-Farisi • Applied the theory of conic sections to solve optical problems • Pursued work in number theory such as on amicable numbers (e.g., 220 & 284) • Factorization of an integer into powers of prime numbers Thabit bin Qurra • Greatest Muslim geometer • Played an important role in preparing the way for mathematical discoveries: – extension of the concept of number to (positive) real numbers, integral calculus, theorems in spherical trigonometry, analytic and nonEuclidean geometry • Was one of the first to create a new proof for the Pythagorean Theorem Astrolabe • The Astrolabe was highly developed in the Islamic World by 9th Century • It was introduced to Europe from Islamic Spain (Al Andalus) in the early 12th Century • It was the most popular astronomical instrument until about 1650 What is Taught and What Should be Taught? What is Taught: What Should be Taught: Francois Vieta was the first to utilize algebraic symbols. Muslim mathematicians invented algebra. In early 9th century, they In 1591, he wrote an introduced the concept algebra book of using letters for describing equations unknown variables in with letters. equations. What is Taught and What Should be Taught? What is Taught: What Should be Taught: In 1614, John Napier invented logarithms and logarithmic tables. Islamic Mathematicians invented logarithms and produced logarithmic tables. These were common in the Islamic world as early as the 13th Century. What is Taught and What Should be Taught? What is Taught: What Should be Taught: The use of decimal fractions in mathematics was first developed by a Dutchman, Simon Stevin, in 1589. Al-Kashi's book, Key to Arithmetic, was the stimulus for the application of decimals to whole numbers and fractions. It was written at the beginning of the 15th century. What is Taught and What Should be Taught? What is Taught: What Should he Taught: The concept that numbers could be less than zero was unknown until 1545 when Cardano introduced the idea. Muslim mathematicians introduced negative numbers for use in arithmetic functions at least 400 years prior to Cardano. Mathematics of Islamic Art & Geometric Design Islamic art explores the geometric systems of the regular division of the circle Islamic Art increases appreciation and understanding of geometry Working only with a ruler and compass, students can discover how to create and study many of the geometric designs Circles, Squares & Octagons The eight-points star, made of two overlapping squares in a circle, is the basis of many Islamic patters Seven overlapping circles Discovering Patterns with Triangle Grid Discovering Patterns with Five Overlapping Circle Grids Discovering Patterns with the Diagonal Grid Activities based on geometric Islamic patterns can support learning about shapes, spaces and measures • • • • • • In Primary, students can learn to draw and recognise circles, triangles, squares, hexagons and octagons Create pictures using 2-D shapes Learn to identify lines of symmetry Recognise reflective and rotational symmetry Upper Primary and Middle school students can study symmetric patterns to produce tessellations. High school students can look at molecular & crystal shapes and calculate spaces occupied Work of AAM Students http://cmcuworkshops.net/?page_id=13 http://www.dynamicgeometry.com/ Review of Math topics using Jigsaws and Islamic Geometric Designs Formulator Tarsia is designed for Teachers of Mathematics to create activities in a form of jigsaws for use in a class. It includes the powerful equation editor for building the math-expressions for the activities. http://www.mmlsoft.com/index.php?option=com_content&task=view&id=9&Itemid=10 3-D Applications (G&T Projects) A few References on Islamic Art & Math • • • • • • • • • • Islamic Art and Geometric Design: Activities for Learning Copyright ©2004 by The Metropolitan Museum of Art, New York: http://www.metmuseum.org/~/media/Files/Learn/For%20Educators/Publications%20for%2 0Educators/Islamic_Art_and_Geometric_Design.pdf Mathematics, Geometry and the Arts Resources (under: Islamic Art and the Sciences) http://cmcuworkshops.net/?page_id=13 ; http://www.dynamicgeometry.com/ Islamic Art & Culture: A resource for Teachers http://ahmadladhani.files.wordpress.com/2009/10/islamic-tp1.pdf The connection between Islamic art and Mathematics http://www.dartmouth.edu/~matc/math5.pattern/lesson5A&M.connection.html Using Technology to investigate mathematics in Islamic Art: http://cmcuworkshops.net/?page_id=13 Formulator Tarsia known earlier as Formulator Jigsaw is an editor designed for Teachers of Mathematics creating the activities in a form of jigsaws or dominos etc for later use in a class. It includes the powerful equation editor for building the math-expressions for the activities. http://www.mmlsoft.com/index.php?option=com_content&task=view&id=9&Ite mid=10 Book of Curiosities of the Sciences and Marvels of the Eyes http://cosmos.bodley.ox.ac.uk/store/Teacher_s-Pack-Inside-pages.pdf Islamic Geometric Patterns by Eric Broug, published by Thames & Hudson Geometric Concepts in Islamic Arts by El-Said Islamic Design: A Genius for Geometry (Wooden Books) by Daud Sutton Learning Objectives: • To raise awareness of Islamic contribution to Mathematics • To inspire Mathematics through the study of Islamic Geometric Designs • To have fun with Islamic Geometric Designs • To create works of art LOLOLO