Directed by: MELITA ČALIŠ Written by: IVA JURASOVIĆ Executive producers: Iviccaa & Meli Starring: KRISTINA LASTAVICA MATEA PAP IVONA LUČIĆ MELITA ČALIŠ IVA JURASOVIĆ In... ISLAMIC & INDIAN MATH ISLAMIC & INDIAN MATH

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 developmentof mathematic.  Old Indian mathematic was mostly arithmetic oriented  Mathematic in India was just a part of astronomicaland astrological works.

BEGINNINGS T TT The introduction of special characters for the numbers from zero to nine, brings progress in ancient indian mathematics.  These signs of the numbers are very similar to our.  Old Indian used positional system only for writingnumbers, but not for fractional.  Indian discovery of zero is newer than the date ofBabylon

 The oldest records that are preserved, and include early forms of Indian numerals areon the stone pillars that were in every significant city. Monarch of Maury empire gave build those stone pillars.  Indian discovery of zero was closely connectedwith the Indian philosophy and religion.  A sign for zero facilitated skilled computing Ashoka’s pillar

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

 T 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 ACCOMPLISHMENTS  T The old Indians have also had very good approximationsof number.  T They had a good approximation for number accurateon five decimal places  I In the 6th century B.C. they have known about Pythagora’s triples and proof of Pythagora’s theorem.

THE OLD INDIAN MATHEMATICIANS  T 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 ARYABHATA

 made use of an important conceptin mathematics, the number zero  solved many different types of equations using general methods  developed rules for four fundamentaloperations using Indian numerals BRAHMAGUPTA

 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 MAHAVIRA No image……

 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. BHASKARA

 Contribution of Arabic in mathematic is much higher then just translating informations.  M Many ideas which are credited to Europeans in the late middle ages and a renaissance was Arabic.  T The first person who encouraged the translation of Greek texts (for example Euclid’s elements) to Arabic language was caliph al-Hajjaj. INTRODUCTION

ARABIC NUMBERS 3 different types of number system:  c calculating with the fingers  sexsagesimal (base-60 number) system  I Indian decimal system

ARABIC MATHEMATICIANS AL-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 KHAYYAM  He was a poet and a mathematician. e discovered a geometrical method of solving cubic equations by intersecting a parabola with a circle e is thought to have been born into a family of tent makers (literally, al-khayyami means "tent maker")

خيام اگر ز باده مستى خوش باش با ماه رخى اگر نشستى خوش باش چون عاقبت كار جهان نيستى است انگار كه نيستى، چو هستى خوش باش 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 AL-TUSI  he formulated the famous law of sines for plane triangles, which was one of his main mathematical contributions

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