ETHNOMATHEMATICS ACROSS MULTICULTURE AND ITS HISTORY

When ancient Greece fell into decline, mathematical progress stagnated as Europe fell under the shadow of the Dark Ages. But in the East, mathematics would reach new heights.

Prof. Marcus du Sautoy visits China and explores how mathematics helped build imperial China and was at the heart of such amazing feats of engineering as the Great Wall. He discovers the first use of a decimal place number system; the ancient Chinese fascination with patterns in numbers and the development of an early version of Sudoku; and their belief in the mystical powers of numbers, which still exists today.

Marcus also learns how mathematics played a role in managing how the Emperor slept his way through the imperial harem to ensure the most favorable succession - and how internet cryptography encodes numbers using a branch of mathematics that has its origins in ancient Chinese work on equations.

Traditional decimal notation in China that symbolize for each of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 100, 1000, and 10000, example 2034 would be written with symbols for 2,1000,3,10,4, meaning 2 times 1000 plus 3 times 10 plus 4. The Chinese numerical writing is

Pascal's triangle was first illustrated in China by Yang Hui in his book Xiangjie Jiuzhang Suanfa, although it was described earlier around 1100 by Jia Xian.Although the Introduction to Computational Studies written by Zhu Shijie in 1299 contained nothing new in Chinese algebra, it had a great impact on the development of Japanese mathematics.

 The Pascal’s triangle in China can be written bellow:

In India Prof. Marcus du Sautoy discovers how the symbol for the number zero was invented - one of the great landmarks in the development of mathematics. He also examines Indian mathematicians’ understanding of the new concepts of infinity and negative numbers, and their invention of trigonometry.

The decimal number in India can be written as bellow:

In 650AD the use of zero as a number came into Indian mathematics. The Indians also used a place-value system and zero was used to denote an empty place. In around 500AD Aryabhata devised a number system which has no zero yet was a positional system. He used the word "kha" for position and it would be used later as the name for zero.

We now come to considering the first appearance of zero as a number. Let us first note that it is not in any sense a natural candidate for a number. From early times numbers are words which refer to collections of objects. Certainly the idea of number became more and more abstract and this abstraction then makes possible the consideration of zero and negative numbers which do not arise as properties of collections of objects. Of course the problem which arises when one tries to consider zero and negatives as numbers is how they interact in regard to the operations of arithmetic, addition, subtraction, multiplication and division. In three important books the Indian mathematicians Brahmagupta, Mahavira and Bhaskara tried to answer these questions.

Brahmagupta attempted to give the rules for arithmetic involving zero and negative numbers in the seventh century. He explained that given a number then if you subtract it from itself you obtain zero. He gave the following rules for addition which involve zero. The sum of zero and a negative number is negative, the sum of a positive number and zero is positive; the sum of zero and zero is zero.

India was not only developing numerical system but also develop algebraic system. Since in the development of India, there was development of Islam also, so the development of Indian mathematics was affected on Islam development. Al-Khwarizmi lived in Baghdad, and incidentally gave his name to 'algorithm', while the words al jabr in the title of one of his books gave us the word 'algebra'. Al khwarizmi is one of mathematical scientist that affected Indian mathematics.

Next, Prof. Marcus du Sautoy examines mathematical developments in the Middle East, looking at the invention of the new language of algebra, and the evolution of a solution to cubic equations. This leg of his journey ends in Italy, where he examines the spread of Eastern knowledge to the West through mathematicians such as Leonardo Fibonacci, creator of the Fibonacci sequence.

Leonardo Fibonacci developed Fibonacci sequence based on rabbit’s problem. If we have a pair of rabbit, one moth later the total of the rabbit is still one pair. But in three moths is two pairs. The next moth is three pairs, five pairs, eight pairs, etc. From this problem we can write 1,1,2,3,5,8,…. And this sequence usually called as Fibonacci sequence.