Term paper On

The mystery of

Submitted by….

Zulfikar Pasha Dipto

B3160B024

Submitted to….

Abul Kalam Azad

Assistant professor

Date of Submission:March 7,2016

ACKNOWLEDGEMENT

The most pleasant part of submitting the report is to get opportunity.I would like to thank those who have contributed to it a lot.Unfortunately,the list of expression of thanks-no matter how extensive is always imcomplete & inadequate.This acknoweledgements are no exception.First,I would thank almighty Allah for bestowing us the patience & courage to finish this huge task within deadline.

In addition,I sincerely acknowledge my debt to Mr. Abul Kalam Azad ,honourable faculty,AIBA for his valuable counseling towards the improvement of the report.Without his encouragement,this would have never been possible.

At last,I would like to convey my gratitude to our honourable senior,Akib Hasan Srabon,BBA-1,for helping us by giving advice.

(i)

ABSTRACTZero was not considered as a number.It was nothing but the idea of empty space.Babylonians around 700 BC used two hooks to denote an empty space in positional notation.Records show that the ancient Greek seemed unsure about the status of zero as a number and not merely a symbol for separation is attributed to India.But by the 9th century AD practical calculations were carried out

using zero which was treated like any other number,even in case of division. It was only around 1600 that zero began to come into widespread use.

And day by day,it became more popular among “Babylonian”, “Roman”, “Mayan” , “Indian”.

Each of them use this number,in different form.Some of them use it as a dot,sometimes it looks like a symbol or mark etc.

(ii)

Table of Contents

Page no.

1. Acknowledgement i2. Abstract ii3. Table of Contents iii4. Introduction 15. Rational of the study 26. Objectives 37. Methodology 48. Numerical Calculation 59. Graphical Representation 610. Result 811. Discussion 912. Conclusion 1113. Reference 15

(iii)

Introduction

“In the history of culture,the discovery of zero will always stand out as one of the greatest single achievements of the greatest single

achievements of the human achievement”

-Tobias Danzig

Existence

Zero was not considered a number.There was the idea of empty space,which may be thought conceptually similar to zero.Babylonians around 700 BC used two hooks to denote an empty space in positional notation.Records show that the ancient Greek seemed unsure about the status of zero as a number and not merely a symbol for separation is attributed to India where by the 9th century AD practical calculations were carried out using zero which was treated like any other number,even in case of division.The concept of zero took some time for acceptance.It was only around 1600 that zero began to come into widespread use after encountering a lot of support and criticism from mathematicians from the world.

(1)

Rational of The Study

Zero is one of the most used term in mathematics.So,we have to know about it’s history& details,so that we can know about how does it come in the number system.

Brief History

The Maya civilization (2000 B.C-900 A.D) in the what is now Mexico used the concept of zero as a PLACEHOLDER:that is,705 is a way bigger number than 75.(like using comma in written language.)The Babylonians used it similarly in the 7th century B.C.

The 7th century Indian mathematician Brahma Gupta treated zero as a “number” and not just as a place-holder.He elaborated the rules mentioned on page 2 of his presentation.

The Hindu-Arabic numbering system that included zero in the way that was used in the west by Leonardo of Pisa- Fibonacci- in his book of counting,published in 1202.

Zero gained a central place in the number system soon afterwards,with it literally separating the positive numbers from the negative ones as in the number line.

In the decimal system,zero serves as a place holder which enables us to use both huge numbers and microscopic figures.

Hence the sheer beauty and usefulness of zero could lend its use to science in its wonderfully succinct scientific notation.

(2)

Objectives

The main objective is to gather knowledge about the invention and theory of the

mystery of ZERO (0). Zero remains as a mystery to us.It is a common matter of

curiosity & thinking about it’s origin.As we can see that it becomes popular since

the pre-historic times.Through the research,we can understand its method, its

usage, calculation procedures, result and conclusion. We will also gain knowledge

about its importance and essence.It will help us to make the proper use in our

practical life.

(3)

Methodology

It is a qualitative research .This research work is done by collecting various data through internet. The link of those useful sites are given below:-

1) http://www.slideshare.net/DivyaRajput6/history-of-zero-mathematics? qid=5c61237a-f10c-4788-868c-62fd4ad7c3a8&v=&b=&from_search=1

2) http://www.slideshare.net/lsccyfairall/history-and-mystery-of-zero? qid=9637ca07-a246-4ee6-b8cb-349765a9ac1a&v=&b=&from_search=1

3) http://www.slideshare.net/Timmy58/zero-34642070?qid=9637ca07-a246-4ee6- b8cb-349765a9ac1a&v=&b=&from_search=5

(4)

Numerical CalculationThere is a close link between numerical notation and writing systems. In fact, the first forms of notation were numerical and it took the form of tallies which is represented by bones. This might explain the fact that in the Semitic languages the words "scribe" and

"count" represents the similar meaning, i.e., SPR. Writing and the notation for abstract numbers emerged in Sumer at precisely the same moment in history.

In the ancient alphabetic scripts, Semitic and Greek, for example, the letters of the alphabet were also used to represent numbers. The first ten letters represented one through ten respectively. The next nine letters represented 20, 30, and up to 100.

The Romans also developed a number system using the letters of the alphabet, but in a more abstract manner. A much smaller number of letters was needed, namely, I, V, X, L, C, D, and M. The system was also more abstract because the numerical values depended to some extent on the placement of the signs. For example IV = 4 whereas VI = 6. There is no zero element in this system and numerical calculations are extremely clumsy.

(5)

Graphical representation1) Zero in Mayans :

Six hundred years later and 12,000 miles from Babylon, the Mayans developed zero as a placeholder around A.D. 350 and used it to denote a placeholder in their elaborate calendar systems. Despite being highly skilled mathematicians, the Mayans never used zero in equations . The symbol for 0 in the Mayans looks like a bowl or an eye. Their numeral system was 20.They used 0 to represent 20. 

2) Zero in Babylon :The Babylonians got their number system from the Sumerians.They are the first people in the world to develop a counting system. They created 0 in the third century B.C. The Babylonians were the first culture to invent the place value system. The Babylonian placeholder was not a true zero because it was not used alone. Even it wasn’t used at the end of a number. They had a sexigesimal number system, in which, they counted in 60s, as we count in tens. They never developed the idea of zero as a number. This is their numeral system.

(6)

3) Zero in India :The number 0 appear in the late 10th century in India. The concept of zero as a number and not merely a symbol for separation is attributed to India, where, by the 9th century CE, practical calculations were carried out using zero, which was treated like any other number, even in case of division .The word for zero in Hindu-India is “shunya” meaning void or empty. India is recognized with great

respect for its invention of Zero by importance with Technological world .These are the numbers that the Hindus and the Arabic use.

(7)

Result

The calculations consisting long division or fractions become more complicated with Roman numerals. The advantages with Hindu-Arabic numbers are obvious.

Arabic numerals are obviously the most abstract numerical notation. On the other hand,the alphabet is the most abstract form of writing. It is ironic that the alphabet achieves its abstraction through phonetization whereas the Arabic numerals are logograms or ideograms that represent ten numerical values including zero. The letters of the alphabet and the Arabic numerals, however, share four important features that enable them to act abstractly:

Each number system contains some elements; twenty-six letters (for the English alphabet) and ten numerals. Both systems form a complete set. The total set of possible spoken words can be represented alphabetically and any number, no matter how large it will be, can be represented in terms of some combination of the ten numerals 0 through 9.The individual elements of the two systems, the letters and the numerals, are atomic. That is, they are identical and repeatable.And finally, the sound or numerical values of the aggregate elements (the words or numbers) of the system depend not only on the letters and numerals of which they are made up but also on their order. In other words, both the letters and their order determine a word and both the numerals and their order determine a number. For example TOP is not the same as POT. Similarly,24 & 42 aren’t the same thing.

(8)

Discussion

So, as we can see,the development of the place number system depended on the invention of the concept of zero, an idea that seems extremely simple and yet is quite sophisticated. For this reason, the discovery of the concept of zero is often taken for granted. Many assume that the Greeks, the originators of formal geometry and logic, made use of it. We are taught about zero in elementary school, geometry in high school, and logic in college. Therefore, many people believe logic and geometry are mathematically more sophisticated than the concept of zero. This is not true and is an example of the distortion of the history of science effected by textbooks and school curricula, as pointed out by Kuhn (1972). The Greeks never developed the operational notion of zero, yet their achievements in geometry and logic were unparalleled. But as a result of not having a concept of zero, their arithmetic calculations were laborious and their development of algebra was stunted.Hindu mathematicians invented zero more than 2,000 years ago. Their discovery led them to positional numbers, simpler arithmetic calculations, negative numbers, algebra with a symbolic notation, as well as the notions of infinitesimals, infinity, fractions, and irrational numbers.The historians of mathematics have always been wondered that the germinal idea of zero was a discovery of the Hindus and not the Greeks. Laplace, A great mathematician of the 18th century, wrote:"It is India that gave us the fabulous method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value, a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to all computations put

(9)

our arithmetic into the first rank of useful inventions, and we shall remember that it escaped the genius of Archimedes and Apollonius, two of the great men produced by antiquity" (Dantzig 1954, pp. 19-20). More recent historians of mathematics have been equally surprised. Particularly puzzling to Tobias Dantzig was the fact "that the great mathematicians of Classical Greece did not stumble on it" (ibid., p. 30). For

Constance Reid, the great mystery of zero is that "it escaped even the Greeks" (Reid 1964, p. 4).Why did the ideas of zero and algebra develop in India and not ancient Greece? It’s a common question that will be rise in our mind & it is true. The answer of this query does not lie in an examination of Greek mathematics but rather in a comparison of Greek and Hindu philosophy. Paradoxically, it was the logical thought patterns of the Greeks that hindered the development of algebra and the invention of zero.

(10)

Conclusion

The Sumerians were the first to develop a counting system to keep an account of their stock of goods & domestic Animals. The Sumerian system was positional; that is, the placement of an individual symbol related to others denoted its value. The Sumerian system was handed down to the Acadians around 2500 BC. And then in 2000 BC. It was the Babylonians who first conceived of a mark to signify that a number was absent from a column; just as 0 in 1025 signifies that there are no hundreds in that number. Although zero's Babylonian ancestor was a good start, it would still be centuries before the symbol as we know it appeared.The popular mathematicians among the Ancient Greeks, who learned the fundamentals of their math from the Egyptians, did not have a name for zero, nor did their system feature a placeholder as did the Babylonian. But actually, there is no exact evidence to say the symbol even existed in their language. At last, the Indians started to understand zero both as a symbol and as an idea of number.Brahmagupta was the first who formalize arithmetic operations using zero. He used dots to indicate a zero. These dots were alternately referred to as 'sunya', which means empty. Brahmagupta experimented by writing standard rules for reaching zero through addition , subtraction, multiplication as well as the results of operations with zero. The only error in his rules was division by zero.But only a few centuries before zero reached Europe. First, the great Arabian voyagers would bring the texts of Brahmagupta and his colleagues back from India along with spices and other exotic.

(11)

items. by 773 AD Zero reached Baghdad and would be developed in the Middle East by Arabian mathematicians who would base their numbers on the Indian system. In the ninth century, Mohammed ibn-Musa al-Khowarizmi was the first who experimented on equations that equaled zero, or algebra as it has come to be known. He also advanced quick methods for multiplying

and dividing numbers known as algorithms (a corruption of his name). Al-Khowarizmi called zero 'sifr', from which our cipher is derived. By 879 AD, zero was written almost as we now know it, an oval - but in this case smaller than the other numbers. And salute to the conquest of Spain by the Moors, zero finally reached Europe; by the middle of the twelfth century, translations of Al-Khwarizmi’s work had spread throughout England.

Then the Italian mathematician, Fibonacci, built on Al-Khwarizmi’s work with algorithms in his book Liber Abaci, or "Abacus book," in 1202. Until that time, the abacus had been the most prevalent tool to perform arithmetic operations. Fibonacci's developments quickly gained notice by Italian merchants and German bankers, especially the use of zero. Accountants knew their books were balanced when the positive and negative amounts of their assets and liabilities equaled zero. But governments were still suspicious of Arabic numerals because of the ease in which it was possible to change one symbol into another. Though outlawed, merchants continued to use zero in encrypted messages, thus the derivation of the word cipher, meaning code, from the Arabic sifr.The next great mathematician to use zero was Rene Descartes, the founder of the Cartesian coordinate system.

(12)

Although zero was now becoming more common, the fathers of calculus, Newton and Leibniz, would make the final step in understanding zero.Adding, subtracting, and multiplying by zero are relatively simple operations. But division by zero created confusion even great minds. How many times does zero go into ten? Or, how many non-existent apples go into two apples? The answer is indeterminate, but working with this concept is the key to calculus. For example, when one drives to the store, the speed of the car is never constant due to stoplights, traffic jams, and different speed limits all cause the car to speed up or slow down.Even accident or technical problem of a car can push the car to stop, But how would one find the exact speed of the car at one particular instant? This is where zero and calculus enter the picture.

If you wanted to know your speed at a particular instant, you would have to measure the change in speed that occurs over a set period of time. By making that set period smaller and smaller, you could reasonably estimate the speed at that instant.Even you have to know the time intervals during accident. In effect, as you make the change in time approach zero, the ratio of the change in speed to the change in time becomes similar to some number over zero - the same problem that stumped Brahmagupta.In the 1600's, Newton and Leibniz solved this problem independently and opened the world to tremendous possibilities. By working with numbers as they approach zero, calculus was born without which we wouldn't have physics, engineering, and many aspects of economics and finance.In the twenty-first century zero is so familiar that to talk about it seems like much ado about nothing. But it is precisely understanding and working with this nothing that has allowed civilization to progress. The development of zero across continents, centuries, and minds has made it one of the greatest accomplishments of human society. Because math is a global language, and calculus its crowning

(13)

achievement, zero exists and is used everywhere.

(14)

References

1)Nils-Bertil Wallin. Yale Global, 19 November 2002.

2)Seife, Charles (2000). Zero: The Biography

3)Kaplan, Robert (2000). The Nothing that Is: A Natural History of Zero. New York:Oxford

University Press.

4)Robert K. Logan. Academia, University of Toronto.

(15)