Arab Empire (632-end of 13 th century) Main source of knowledge between Greeks and European Renaissance Baghdad established as center of wisdom and learning (9 th century) Many contributions to the study of algebra (800-1450 )
“In the foremost rank of mathematicians of all time stands Al-Khwarizmi. He composed the oldest works on arithmetic and algebra. They were the principal source of mathematical knowledge for centuries to come in the East and the West. The work on arithmetic first introduced the Hindu numbers to Europe, as the very name algorism signifies; and the work on algebra... gave the name to this important branch of mathematics in the European world...” -Mohammad Kahn
Full name: Abu Ja’far Muhammad ibn Musa Al-Khwarizmi Lived 790-850 Of Persian descent May have been born in Baghdad or modern-day Uzbekistan
Wrote Algoritmi de numero Indorum (Al-Khwarizmi on the Hindu Art of Reckoning) Only words (no symbols or numerals) This text was later studied in Europe for centuries Studied quadratic equations and their solutions Invented “completing the square” and developed geometric representations of this process The terms algebra and algorithm come from his name.
Where was the center of wisdom and learning in the 9 th century? To what area of mathematics did Arabic mathematicians make the greatest contributions? Why is Al-Khwarizmi also called the Father of Algebra?
Goal is to manipulate an equation so that it can be factored nicely to solve for x Two methods 1)Al-Khwarizmi’s geometric representation 2)Algebraic representation
Partner on the left complete the square to solve for x: Partner on the right complete the square to solve for x: WHEN I SAY GO: Switch sticky notes with your partner and check their work. If you find a mistake, talk it out with them. When BOTH of you agree on BOTH problems, put your sticky notes on the board. Who can be the first pair to get the correct answer?? x 2 – 8x – 1 = 0 x 2 + 6x – 7 = 0