42510011 0010 1010 1101 0001 0100 1011

Muslim Mathematicians and Astronomers,

and Why We Need to Thank Them

Fozia S. QaziSaint Mary’s College

February 9, 2009

Can you add?

CCLI + DXXXVIII =DCCLXXXIX

(CXII )× (MMCXXXVII)=????

251 538

(CXII ) (MMCXXXVII)=????

789

This system was used in Europe for centuries. So how was it replaced and why?

Map of the Islamic World9th Century

Islamic Scholarship

• Knowledge is a collective pursuit to which all cultures have contributed.

• Islamic contribution began with the House of Wisdom – a library and research center built in Baghdad in the 8th century.

• Translation of books from many cultures including Greek, Chinese, Indian, Persian etc

• Paper mill founded in Baghdad. Transmission of knowledge became easy

• The time period 700-1200 C.E. is regarded as the Golden Age of Islamic civilization and Baghdad was its intellectual center.

• Many important contributions made after 1200 C.E. as well

• Muslims made significant contributions in many fields

• This knowledge was later transmitted to Europe and Arabic books were translated into Latin

• Sharing is a good thing!

Number Systems

• What does 323 mean?– 3 hundreds, 2 tens and 3 units

(3×100 + 2×10 + 3×1)

• In Roman numerals – CCCXXIII (C=100, X=10, I=1)

• In Arabic – ٣٢٣

Let us add again!

٢١٥٤٤٢٣٢٥٧

٧

2154 4232577

Decimal System

• Only10 symbols used

• We can use any set of 10 symbols to represent 0,1,2,3,4,5,6,7,8,9 e.g. , , , , , £, , , , = 2707

• Position or place of the number is important

• These are the reasons why calculations easier with this system

Thank you Khwarizmi!

• Al-Khwarizmi was the first to write a book about the decimal number system in about 825 C.E.

• Decimal system was developed by Muslim mathematicians from an older and incomplete Indian system

• Muslim mathematicians extended the system to fractions.

• Other major contributors were Al-Samawal, Al-Karaji, Al- Uqlidisi and Al-Kashi

• Transmitted to Europe mainly in the 13th century by Fibonacci. It took over 200 years for Europeans to adapt this system fully.

Uqlidisi’s Use of Decimal Fractions

The first recorded of the use of decimal fractions appears in Abul Hassan Al-Uqlidisi’s book written in 952 C.E. Short vertical mark points out the units place.

162.85

Al-Khwarizmi- The Father of Algebra

• Muhammad Ibn Musa al-Khwarizmi

• Born in 780 C.E. in Kwarizm (now Khiva, Uzbekistan). He was a scholar at the House of Wisdom in Baghdad.

• He invented Algebra and wrote a book about it called ‘Kitab al-jabr wal-muqabala’ كتاب الجبرولمقابله (Book of Restoring and Balancing)

• He was also an astronomer and a geographer and constructed a map of the known world

Algebra

• Finding the unknown quantity

• Using equations to describe real world problems and solving these equations to find the unknown quantity

• Symbols are used to represent unknown quantities and we treat them just like numberse.g. I have a bag of oranges and I give you 5 oranges from it. If

I now have 3 oranges left, how many were in the bag?

Sol: x - 5 = 3

x - 5 + 5 = 3 + 5

x = 8

• More complex equations can also be solved using techniques of algebra

A Page from Al-Khwarizmi’s Algebra

• First ever algebra book

• The word algebra is a derived from al-jabr from the title of this book and the word algorithm is derived from Al-Khwarizmi

• Other major contributors to Algebra were Khayyam, Ibn-Qurra, Al-Samawal and Al-Karaji among others

Astronomy and Copernicus• Study of planets, stars etc and their motion. It is

one of the oldest sciences• Math is an important tool for astronomers and

many old mathematicians were also astronomers• For a long time people believed that the Earth was

the center of our universe• 16th century olish astronomer Nicolaus Copernicus

is considered to be the first astronomer who showed that the Sun was the center of our universe

• In his most important book he uses several math theorems and planetary models of Muslim astronomers to prove his theory (Tusi, Ibn-Shatir, Urdi)

• He makes no reference to these astronomers

Nasir-u-Din Tusi (1201-1274)

• Born in Tus, present day Iran. Worked in Maragha, Iran

• An astronomer and mathematician of high caliber.

• Major contribution in trigonometry

• Developed Tusi Couple – a method for transforming circular motion into linear motion.

• Established a famous observatory at Maragha and started the ‘Maragha Revolution’. Urdi and Ibn-Shatir a product of this revolution

Tusi Couple

Copernicus’ Use

Computational Math – Al-Kashi (about 1380-1429 C.E.).

• Jamshid Mas’ud al-Kashi. Born in Kashan, Iran. Worked in Samarkand

• Calculated to 16 decimal places!• Designed and wrote a book on an

analog computer called equatorium for finding the position of planets

• Wrote a famous book The Calculator’s Key that became a standard math textbook for the next 300 years

• Gave a systematic exposition of arithmetic

• Could calculate the 5th root of a number larger than a trillion!

There are many other Muslim mathematicians, astronomers and scientists who made great contributions. Too many of them to list here!

There was also one female astrolabist Al-Ijliya. Astrolabe is an astronomical instrument used for predicting the position of planets and stars and has many other uses. One needs considerable mathematical skill to be able to build a good astrolabe.

Multiplication with the Decimal System

74×2=148

Multiplication Technique Developed by Muslim Mathematicians

752439×1680=1264097520