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What is the significance of Nasir al-Din al-Tusi's work in trigonometry?
What is the significance of Nasir al-Din al-Tusi's work in trigonometry?
What is the name of the book written by Nasir al-Din al-Tusi that contains astronomical tables of planetary movements?
What is the name of the book written by Nasir al-Din al-Tusi that contains astronomical tables of planetary movements?
What is the name of the mathematician who was a student of Sharaf al-Din al-Tusi and is considered one of the greatest minds of the Islamic Golden Age?
What is the name of the mathematician who was a student of Sharaf al-Din al-Tusi and is considered one of the greatest minds of the Islamic Golden Age?
What is the term used to describe the method used by Nasir al-Din al-Tusi to analyze cubic equations?
What is the term used to describe the method used by Nasir al-Din al-Tusi to analyze cubic equations?
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How many years later was the derivative properly defined after Nasir al-Din al-Tusi's time?
How many years later was the derivative properly defined after Nasir al-Din al-Tusi's time?
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What is the name of the era in which Nasir al-Din al-Tusi lived and worked?
What is the name of the era in which Nasir al-Din al-Tusi lived and worked?
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What is the title of the book that contains information about Nasir al-Din al-Tusi's work?
What is the title of the book that contains information about Nasir al-Din al-Tusi's work?
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What is the name of the author of the book that contains information about Nasir al-Din al-Tusi's work?
What is the name of the author of the book that contains information about Nasir al-Din al-Tusi's work?
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What is the significance of Nasir al-Din al-Tusi's use of the derivative in his work?
What is the significance of Nasir al-Din al-Tusi's use of the derivative in his work?
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What is the significance of Nasir al-Din al-Tusi's work in the history of mathematics?
What is the significance of Nasir al-Din al-Tusi's work in the history of mathematics?
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Study Notes
The Golden Age of Islamic World
- The Golden Age of Islamic World lasts from 750 AD to 1250 AD.
- During this period, the Abbasid Caliphs established the House of Wisdom, a large library that fostered scientific progress through translation of Greek, Indian, Persian, and other language books into Arabic.
Development of Mathematics
- Mathematics in this era was a synthesis of Greek, Indian, and Mesopotamian influences.
- Number systems, arithmetic, trigonometry, and algebra were influenced by Mesopotamian and Indian mathematics.
- Geometry was influenced by Greek mathematics.
- There were nearly 50 mathematicians who lived during this era and whose work survived until today.
Muhammad ibn Musa al-Khwarizmi
- Al-Khwarizmi was a Persian mathematician who wrote influential works in mathematics, astronomy, and geography.
- He became a librarian in the House of Wisdom after 810 AD.
- Al-Khwarizmi wrote four books: on geography, astronomy, arithmetic, and algebra.
- His most famous book, "The Compendious Book on Calculation by Completion and Balancing", was translated into Latin in 1440 and used as a textbook until the 1600s.
Contributions of Al-Khwarizmi
- Al-Khwarizmi presented the first systematic solution of linear and quadratic equations.
- He classified a second-degree equation ax^2 + bx + c = 0 into six classes and showed an algorithmic approach for solution in each case.
- The word "algorithm" comes from the Latinized name "Al-Khwarizmi".
- Algebra became an area in mathematics after his book, and the name "algebra" originated from it.
The Book on Arithmetic: Algorithmo de Numero Indorum
- Al-Khwarizmi's second most influential work was on arithmetic, which survived in Latin translations but lost in the original Arabic.
- He codified the various Indian numerals and introduced the decimal positional number system to the Western world.
- Al-Khwarizmi explained how to use modern number representation (0, 1, 2, ...) in arithmetic, where 0 is not a number but a symbol to fill blanks.
Omar Khayyam
- Omar Khayyam was a mathematician, astronomer, philosopher, and poet.
- He was born in Neyshabur, northeastern Persia, and entered the service of Malik-Shah in 1074.
- Khayyam designed the Jalali calendar, a solar calendar with a very precise 33-year cycle.
Contributions of Omar Khayyam
- Khayyam computed the length of a year as 365.24219858156 years based on observation and measurement.
- He classified 3rd degree polynomials (ax^3 + bx^2 + cx + e = 0) and found their roots using a geometric approach by means of conic sections.
- Khayyam observed that a cubic (3rd degree polynomial) may have more than one root.
Sharaf al-Din al-Tusi
- Al-Tusi was a Persian mathematician and astronomer.
- He worked on finding roots of cubic polynomials.
- Al-Tusi divided equations of degree at most three into 25 different types.
Contributions of Sharaf al-Din al-Tusi
- Al-Tusi remarkably used a method which we call discriminant, D, of polynomial today.
- He analyzed cases where D > 0, D = 0, and D < 0.
- Al-Tusi stated that for a cubic equation of the form x^3 − cx = e to have a solution in a certain interval, the value e must be between the maximum and minimum of x^3 − cx.
- He finds max and min by finding the derivative!
Nasir al-Din al-Tusi
- Nasir al-Din al-Tusi was a very famous Persian mathematician, architect, philosopher, physician, scientist, and theologian.
- He is a student of a student of Sharaf al-Din al-Tusi.
- Nasir al-Din al-Tusi was the first to write a work on trigonometry independently of astronomy.
- He prepared Zij-i Ilkhani, a Zij book with astronomical tables of planetary movements.
- Nasir al-Din al-Tusi became the most cited scientist of the Islamic Age by the Western world.
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Explore the significant contributions of the Islamic World to mathematics and science during the Golden Age. Learn about the House of Wisdom and the translation movement of ancient texts into Arabic.
