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In . . .

ISLAMIC & INDIAN

MATH

ISLAMIC & INDIAN

MATH

INTRODUCTION INTRODUCTION

Indian scientists and mathematicians were leaders , especially in mathematics and engineering.

Needs of everyday life (such as trade, civil engineering, etc.) in India incite on development of mathematic.

Old Indian mathematic was mostly arithmetic oriented

Mathematic in India was just a part of astronomical and astrological works.

BEGINNINGSBEGINNINGS The introduction of special characters for The introduction of special characters for the the numbers from zero to nine, brings numbers from zero to nine, brings progress in progress in ancient indian mathematics. ancient indian mathematics.

These signs of the numbers are very similar to our .

Old Indian used positional system only for writing numbers, but not for fractional.

Indian discovery of zero is newer than the date of Babylon

The oldest records that are preserved, and include early forms of Indian numerals are on the stone pillars that were in every significant city. Monarch of Maury empire gave build those stone pillars.

Indian discovery of zero was closely connected with the Indian philosophy and religion.

A sign for zero facilitated skilled computing

Ashoka’s pillar

HOW THEY WERE HOW THEY WERE CALCULATING?CALCULATING? Old Indian were calculating on their

blackboards.

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They were putting mathematical tasks in poetic attire.

The method of solving problems was inversion.

Oh beautiful maiden with beaming eyes, tell me, since you understand the method of inversion, what number multiplied by 3, then increased by three-quarters of the product, then divided by 7, then diminished by one-third of the result, then multiplied by itself, then diminished by 52, whose square root is then extracted before 8 is added and then divided by 10, gives the final result of 2?

THE BIGGEST THE BIGGEST ACCOMPLISHMENTSACCOMPLISHMENTS The old Indians have also had very good

approximations of number.

They had a good approximation for number accurate on five decimal places

In the 6th century B.C. they have known about Pythagora’s triples and proof of Pythagora’s theorem.

THE OLD INTHE OLD INDIANDIAN MATHEMATICIANS MATHEMATICIANS

The most important Old Indian mathematicians were:            - Aryabhatta (V century)            - Brahmagupta (VI century)            - Mahavira (IX century)            - Bhaskara (XII century)

the father of the Decimal number system which has become universal today .

he used letters of the alphabet to denote numbers

worked on the approximation for Pi and may have realized that Pi is irrational

Today his algorithm, is the standard method for solving first order Diophantine equations, and it is often referred to as the Aryabhata algorithm

ARYABHATAARYABHATA

made use of an important concept in mathematics, the number zero

solved many different types of equations using general methods

developed rules for four fundamental operations using Indian numerals

BRAHMAGUPBRAHMAGUPTATA

asserted that the square root of a negative number did not exist

is highly respected among Indian Mathematicians, because of his establishment of terminology for concepts such as equilateral, and isosceles triangle

MAHAVIRAMAHAVIRA

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His book on arithmetic is the source of interesting legends that assert that it was written for his daughter, Lilavati

A proof of the Pythagorean theorem by calculating the same area in two different ways and then canceling out terms to get a² + b² = c².

BHASKARABHASKARA

Contribution of Arabic in mathematic is much higher then just translating informations.

Many ideas which are credited to Europeans in the late middle ages and a renaissance was Arabic.

The first person who encouraged the translation of Greek texts (for example Euclid’s elements) to Arabic language was caliph al-Hajjaj.

INTRODUCTIONINTRODUCTION

ARABIC NUMBERSARABIC NUMBERS

3 different types of number system:

calculating with the fingers

sexsagesimal (base-60 number) system

Indian decimal system

ARABIC ARABIC MATHEMATICIANSMATHEMATICIANS

AL-KHWARIZMIAL-KHWARIZMI full name: Abu' Abdallah Muhammad ibn Musa al-Magusi al-Khwarizmi al-Choresmi

wrote about algebra, geometry and astronomy.

used zero in positional base notation

in his main work Hisab al-jabr w'al-muqabala has given us the word algebra

OMAR KHAYYAMOMAR KHAYYAM He was a poet and a mathematician.

He discovered a geometrical method of solving cubic equations by intersecting a parabola with a circle

He is thought to have been born into a family of tent makers (literally, al-khayyami means "tent maker")

                                            

  باش خوش مستى باده ز اگر خيامباش خوش نشستى اگر رخى ماه بااست نيستى جهان كار عاقبت چونباش خوش هستى چو نيستى، كه انگار

A literal translation could read:If with wine you are drunk be happy,If seated with a moon-faced (beautiful), be happy,Since the end purpose of the universe is nothing-ness;Hence picture your nothing-ness, then while you are, be happy!

NASIR AL-DIN NASIR AL-DIN AL-TUSIAL-TUSI

he formulated the famous law of sines for plane triangles, which was one of his main mathematical contributions

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• wikipedia wikipedia

• googlegoogle

• Tarkan- Dudu (remix)Tarkan- Dudu (remix)

• Fatboy slim – Material girl remixFatboy slim – Material girl remix

•http://ahyco.ffri.hr/seminari2007/http://ahyco.ffri.hr/seminari2007/povijestmatematike/6-4.htmpovijestmatematike/6-4.htm

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