## Find a number in india & location,cell phone number trace in karachi university,student cell phone plans telus - PDF Books

However, now the scenario has changed and even in your region there are several new series, and it is tough to guess the region or the operator on by looking at the starting digits of the phone number. This page at Wikipedia, titled as ‘Mobile telephone numbering in India’ has the full list of the several mobile phone operators, their region based upon the first 4 digits of the mobile phone numbers issued by them. Now, if you want to know about the operator and region of particular mobile phone number, simply use ‘Ctrl+F’ and enter the first 4 digits of the mobile phone number, and hit on search to find out its region and Operator. TP2Location is an online tool, which helps you to find out the location of any mobile phone number across the world, it has a search engine like interface, as shown below. India on a Page has an online tool which tells you about any mobile phone or landline number as well. Indian mobile number lookup is another service which allows you to find the operator and region for any mobile phone number in India, just by entering the first 4 digits of the mobile phone number. All the above ways work pretty fine, go ahead and give them a try, if you know about any other service or way, which can help us to know about a mobile phone number’s service provider (operator) and region, do share with us via comments.

You can also Trace Any Unknown Mobile Number from .You can get all basic information about any Indian mobile Number. Tallying is likely to have predated counting and the use of words to denote specific quantities. In early forms of speech the number five was often expressed by the word for hand, and ten by two hands. Earlier members of the human family, such as Homo erectus, did not leave evidence of an ability to draw or paint. The need to keep track of fields, crops, and herds was a major impetus for the development of ideograms, mnemonic symbols, and tokens in the Neolithic period, around 7000 B.C. Settlements evolved into villages, and some Neolithic villages evolved into largely self-supporting towns with populations of several thousand.

Since planting and harvesting are best carried out in appropriate seasonal conditions, agriculture provided an incentive for the study of seasonal changes in climate and for the accurate reckoning of time. At some point, it occurred to someone to create a token to represent a number of objects, to make it more expedient to record larger quantities. Symbolic representations of words and numbers took various forms and were developed in locations ranging from Egypt to Mesopotamia and the Indus Valley. Egyptian hieroglyphs and Mesopotamian scripts were developed in the Bronze Age, by 3200 B.C.

At some point, the representation of the quantity of an object was separated from the symbol for the object.

Hieratic writing was a simplified version of hieroglyphs used by priests and scribes for common records mostly written on papyrus. The Sumerians were originally peoples from the Caucasus that moved into southern Mesopotamia about 4000 B.C. When representing the number sixty, the place to the right had no value, so that the number sixty was represented the same way as the number one.

Babylonian numbers were written from right to left and used two basic cuneiform numerals: the unit symbol and the ten symbol. When representing a number that was a multiple of sixty, the place to the right had no value, so that the number sixty was represented the same way as the number one, and one hundred and twenty the same way as two.

Small versions of the numerals for ten, one hundred or one thousand were appended to the symbol for five to create numerals for the numbers fifty, five hundred, and five thousand. During Alexander’s Macedonian expansion to the East, the Greeks became aware of the Babylonian use of the positional zero, but few used this concept, since the Greek number system was not positional.

The ancient Romans used a number system in which certain letters of the Latin alphabet are given numeral values.

For large numbers a bar was placed above the base numeral to indicate multiples of one thousand. Numerals from one to five were represented by an increasing number of parallel vertical strokes or rods. The Mayan number system was a vigesimal (base twenty) system, first adopted around 300 B.C. In addition to the dot and bar system, Mayan numbers were expressed for commemorative purposes in terms of face glyphs.

The system used for dates in Mayan calendars was a variation of a pure base twenty system, in that the third position was eighteen rather than twenty, to make it easier to represent the number 360 (twenty times eighteen). In 1524 and 1526 Francisco Pizarro, a Spanish military leader, explored the northern reaches of the Inca Empire, but was unsuccessful in his attempted conquest. In addition to the standard knot, two other knot types were used as special indicators of the end of a number. Different methods appear to have been used to identify the particular numbers recorded in a quipu.

With some modifications, Brahmi numbers were adopted by the Gupta dynasty that ruled in northeast India from 300 A.D.

The Indian number system evolved into a decimal place value system with nine symbols for the numbers one through nine, and an additional numeral for null, or zero. The word algorithm is derived from Al-Khwarizmi’s name, and the word algebra is derived from al-jabr, the Arab word for completion in the title of his book “Compendium on Calculation by Completion and Balancing.” The adopted Indian numerals underwent changes over time and evolved into Arab numerals retaining the functionality of the Indian originals. Roman numbers remained in use throughout Europe after the fall of the Roman Empire in the West in 476 A.D.

Indian-Arabic numbers were introduced in parts of Europe in the eleventh century, but did not see wide use. The new numerals and methods of computation, including the notion of null, or zero, were soon adopted by bookkeepers and merchants in northern Italy. The first printed book, Johann Gutenberg’s 1455 Latin Bible, contained both Indian-Arabic and Roman numerals. The Egyptians used symbols for legs walking right or left to indicate addition and subtraction.

The symbols p and m were used in Europe in the fifteenth and sixteenth centuries to indicate addition and subtraction.

The work of Fibonacci on practical applications of mathematics, such as unit conversions and profit and loss calculations, had a profound impact on the European business community. In double entry bookkeeping, the daily transactions of a business are recorded in one or more journals. The balance sheet shows how the two sides of the accounting equation (assets = liabilities + capital) balance out. The fall of Constantinople, the last enclave of the Roman Empire in the East, to Islamic invaders in 1453, led to an exodus of scholars to Europe. During the late sixteenth and early seventeenth centuries, Nicolaus Copernicus, Tycho Brahe, Johannes Kepler, and Galileo Galilei developed mathematical models describing planetary motions. Negative numbers were known to the ancient Chinese and Greeks, as results obtained when solving certain equations. Rene Descartes was a French philosopher, physicist and mathematician that lived in the seventeenth century. Descartes thought to extend the real numbers to include negative numbers in a way that made physical sense. In 1637, Descartes published his book Discourse on the Method of Rightly Conducting the Reason in the Search for Truth in the Sciences, in which he provided a philosophical framework for scientific thought. Descartes invented the Cartesian coordinate system (x, y, and z axes perpendicular to each other) and set down the principles of analytical geometry.

A coordinate frame of reference can be used to plot points (numerical solutions) from equations and determine the corresponding shapes. A prime number is a natural number greater than 1 which has exactly two distinct natural number divisors, one and itself. Some early mathematicians felt that the numbers of the form 2n-1 were prime for all primes n, but in 1536 Hudalricus Regius showed that 211-1 = 2047 was not prime (it is 23 x 89). French monk Marin Mersenne asserted in the preface to his Cogitata Physica-Mathematica (1644) that the numbers 2n-1 were prime for n = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257, and were composite for all other positive integers n n-1 is prime it is said to be a Mersenne prime.

By 1947 the range of Mersenne’s assertion, n n-1 for n = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, and 1279.

In 1614, the Scotsman John Napier published Minifici Logarithmorum Canonis Descriptio, a Latin text in which he described a method for simplifying arcane astronomical calculations involving angles.

An arithmetic progression is a sequence an = a1 + (n – 1) d, where d is the common difference and a1 is the initial value. Napier’s method defined logarithms based on a proportional relationship of two distances in a geometric form. Working with English mathematician Henry Briggs, Napier developed a broader application of his logarithms. The work of Napier, Briggs, and Burgi had a significant impact on various disciplines that relied extensively on computations.

The logarithm of x to the base b is written logb (x) or, if the base is implicit, as log (x).

That is, the logarithm of the product of two numbers is the sum of the logarithms of those numbers.

Logarithms are expressed as numbers of the form cc.mm, where cc is the characteristic and mm is the mantissa.

Slide rules are calculation instruments that make use of the arithmetic properties of logarithms. The advent of electronic calculators has not significantly affected the use of logarithms in applications where they provide the ability to conveniently represent very large or small numbers, as well as the ability to carry out multiplication of ratios by simple addition and subtraction. Other fields that make use of logarithms include chemistry, seismology, music, and astronomy. Descartes’ algebraic techniques served as a basis for the development of calculus by Gottfried Leibniz, in Germany, and Isaac Newton, in England, late in the seventeenth century. Some of the concepts in calculus were developed earlier in Greece, India and Persia, but it was Newton and Leibniz that developed a comprehensive approach, including rigorous proofs and notations. Calculus provided the means for solving the negation of motion paradox posed by Zeno twenty one centuries earlier. If Zeno had the tools that Newton and Leibniz provided, he would have realized that taking an infinite number of steps does not necessarily take forever.

Differential calculus involves the analysis of the slope or derivative of a graph or mathematical function. The object arrives at its new position at a new time, the original time, t, plus the amount of time it took to get to the new position, Δt.

We can define the velocity of a moving object precisely at time t (the rate of change of x at time t) by making the increment Δt very small, so small that its value is close to zero. Integral calculus involves two related concepts, the indefinite integral and the definite integral. A smaller value for Δx will give more rectangles and a better approximation of the area. This integral gives the exact value of the area between the axis and the curve for the interval a-b. The fundamental theorem of calculus states that integration and differentiation are inverse operations. The solution of certain polynomial equations yield a quantity equal to the square root of -1. Mathematicians were troubled by the continued appearance of square roots of negative numbers in the solutions of quadratic and cubic equations, until the use of imaginary numbers was formalized with the development of complex numbers.

The numbers that are not imaginary were called real numbers, and a complex number was defined as a particular form of a pair of real numbers. A complex number z was defined as z = x + iy, where x and y are real numbers, and i is the imaginary unit. Geometrically, imaginary numbers lie on the vertical axis of the complex number plane, and are presented orthogonal to the real axis.

Imaginary numbers have fundamental applications in areas such as electrical engineering, electromagnetism, cartography, and control theory.

In 1679, Leibniz discovered a base two method of counting in which only two digits, zero and one, are sufficient for a positional number system.

In 1843, Ada Byron used binary numbers to program an analytical engine devised by Charles Babbage. Base two binary numbers can be simply represented as a series of electrically pulsed on and off states, that is, as strings of ones and zeros. Quaternions, like complex numbers, take the form R + I, where R is a real part and I an imaginary component.

Quaternions constitute a four-dimensional number system, with peculiar algebraic properties. Rotations in three-dimensional space are not commutative, that is, the order of rotations affect the outcome. When used for rotation computations, quaternions are normalized, that is, they are restricted to have unit magnitude. In 1844, Hermann Gunther Grassmann, a German mathematician and linguist, included a description of vectors in his book Ausdehnungslehre (extension lesson), The Calculus of Extension. The Pythagorean theorem can be used for adding any two vectors which make a right angle to each other. The resultant is obtained graphically by drawing a line from the base of the first to the tip of the second vector. A 3-dimensional (3-D) vector has three components, one along each axis of 3-dimensional space. The magnitude of a 3-D vector, V, can be computed by taking the square root of the squares of the components VX, VY, and VZ. The dot product and the cross product are two ways in which to carry out vector multiplication.

The cross product results in a vector oriented perpendicular to the plane containing the two input vectors. The direction of n is the direction of the thumb using the right hand rule, where the index finger points in the direction of u and the middle finger points in the direction of w. Cross products have applications in mathematics and physics, and in fields such as computer graphics (to define the normal of poligons), inertial guidance (to define orbital planes), and engineering mechanics (in calculations involving torque and angular momentum). Although the properties of binary (bin) numbers make them appropriate for use in digital computers, human beings generally find them unwieldy and awkward to use.

Hexadecimal numbers are represented by the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. To convert a decimal number greater than sixteen to hexadecimal, the number is divided by sixteen, and the remainder (in hexadecimal notation) is the least significant digit. Some numbers have values that are too large or too small to be conveniently written in the usual numerical notation. Scientific notation, a form of exponential notation, follows a set of conventions for writing numbers using a set of significant figures, a base, and an exponent. For decimal numbers, this method takes the form m x 10n, where m is the mantissa, 10 is the base, and n is the exponent. Use of scientific notation became prevalent among computer users around 1960 to emphasize the number of significant digits and avoid the confusion of zeros used only to fix the decimal point.

In encryption through transposition and substitution, a plain text message generally can be revealed only through the use of a secret method and key. In the twentieth century, strong cryptographic methods were developed which relied on applied mathematics and numerical processes. In 1977, Ronald Rivest, Adi Shamir and Leonard Adleman, at the Massachusetts Institute of Technology (MIT), developed the RSA public-key encryption method. It is worth beginning this article with the same quote from Laplace which we give in the article Overview of Indian mathematics.

The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The purpose of this article is to attempt the difficult task of trying to describe how the Indians developed this ingenious system. The second aspect of the Indian number system which we want to investigate here is the place value system which, as Laplace comments in the quote which we gave at the beginning of this article, seems "so simple that its significance and profound importance is no longer appreciated." We should also note the fact, which is important to both aspects, that the Indian number systems are almost exclusively base 10, as opposed to the Babylonian base 60 systems. Beginning with the numerals themselves, we certainly know that today's symbols took on forms close to that which they presently have in Europe in the 15th century.

One of the important sources of information which we have about Indian numerals comes from al-Biruni. Whilst we use letters for calculation according to their numerical value, the Indians do not use letters at all for arithmetic. It is reasonable to ask where the various symbols for numerals which al-Biruni saw originated.

The Brahmi numerals have been found in inscriptions in caves and on coins in regions near Poona, Bombay, and Uttar Pradesh. The Brahmi numerals came from an earlier alphabetic numeral system, possibly due to Panini. Ifrah examines each of the six hypotheses in turn and rejects them, although one would have to say that in some cases it is more due to lack of positive evidence rather than to negative evidence.

It is a nice theory, and indeed could be true, but there seems to be absolutely no positive evidence in its favour. One might hope for evidence such as discovering numerals somewhere on this evolutionary path. If we examine the route which led from the Brahmi numerals to our present symbols (and ignore the many other systems which evolved from the Brahmi numerals) then we next come to the Gupta symbols. The Gupta numerals evolved into the Nagari numerals, sometimes called the Devanagari numerals.

What we [the Arabs] use for numerals is a selection of the best and most regular figures in India.

These "most regular figures" which al-Biruni refers to are the Nagari numerals which had, by his time, been transmitted into the Arab world.

We now turn to the second aspect of the Indian number system which we want to examine in this article, namely the fact that it was a place-value system with the numerals standing for different values depending on their position relative to the other numerals.

The oldest dated Indian document which contains a number written in the place-value form used today is a legal document dated 346 in the Chhedi calendar which translates to a date in our calendar of 594 AD. Many other charters have been found which are dated and use of the place-value system for either the date or some other numbers within the text.

All of these are claimed to be forgeries by some historians but some, or all, may well be genuine. The first inscription which is dated and is not disputed is the inscription at Gwalior dated 933 in the Vikrama calendar which translates to a date in our calendar of 876 AD. There is indirect evidence that the Indians developed a positional number system as early as the first century AD. We are left, of course, with asking the question of why the Indians developed such an ingenious number system when the ancient Greeks, for example, did not. A second hypothesis is that the idea for place-value in Indian number systems came from the Chinese. A third hypothesis is put forward by Joseph in [The crest of the peacock (London, 1991).',2)">2]. To see clearly this early Indian fascination with large numbers, we can take a look at the Lalitavistara which is an account of the life of Gautama Buddha. It is stories such as this, and many similar ones, which convince Joseph that the fascination of the Indians with large numbers must have driven them to invent a system in which such numbers are easily expressed, namely a place-valued notation.

The early use of such large numbers eventually led to the adoption of a series of names for successive powers of ten. A Technology Blog that covers latest Information, How To's, Tutorials, Tips & Tricks about Computer Software, Blogging and useful Websites. Here is the complete guide line which will help you get required details.Why do need the address? Earlier around 2-3 years ago it wasn’t tough to figure out who gave that missed called, because of limited number of mobile phone service providing companies, just by looking at first 3-4 digits of the number you could guess that this number belongs to particular region and hence you could often make a guess that who gave you that missed called. Sometimes when a call from a mobile phone is made to some other mobile phone number in India, the country code doesn’t reflect and the numbers appears to start with 0, in such case, you will have to remove the zero and add +91 or 0091 in order to get the location (region) and operator of the mobile phone number. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. And just as the shape of the letters that they use for writing is different in different regions of their country, so the numerical symbols vary. Historians trace them all back to the Brahmi numerals which came into being around the middle of the third century BC. Dating these numerals tells us that they were in use over quite a long time span up to the 4th century AD. Moving forward leads to many different forms of numerals but we shall choose to examine only the path which has led to our present day symbols.

One is that the numerals came from an alphabet in a similar way to the Greek numerals which were the initial letters of the names of the numbers. However, it would appear that we will never find convincing proof for the origin of the Brahmi numerals. The Gupta period is that during which the Gupta dynasty ruled over the Magadha state in northeastern India, and this was from the early 4th century AD to the late 6th century AD.

This form evolved from the Gupta numerals beginning around the 7th century AD and continued to develop from the 11th century onward. The way in which the Indian numerals were spread to the rest of the world between the 7th to the 16th centuries in examined in detail in [Indian J. Although our place-value system is a direct descendant of the Indian system, we should note straight away that the Indians were not the first to develop such a system.

The evidence is found from inscriptions which, although not in India, have been found in countries which were assimilating Indian culture. In particular the Chinese had pseudo-positional number rods which, it is claimed by some, became the basis of the Indian positional system. His idea is that the place-value in Indian number systems is something which was developed entirely by the Indians. It is hard to date this work since it underwent continuous development over a long period but dating it to around the first or second century AD is reasonable. Getting the address is not quick and easy way in case if you are trying to find mobile number address of an India mobile phone.

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Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. First we will examine the way that the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 evolved into the form which we recognise today. However we must not forget that many countries use symbols today which are quite different from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and unless one learns these symbols they are totally unrecognisable as for example the Greek alphabet is to someone unfamiliar with it. Before he went there al-Biruni already knew of Indian astronomy and mathematics from Arabic translations of some Sanskrit texts. First, however, we look at a number of different theories concerning the origin of the Brahmi numerals. The second type of hypothesis is that they derive from an earlier number system of the same broad type as Roman numerals. To enable the numerals to be written rapidly, in order to save time, these groups of lines evolved in much the same manner as those of old Egyptian Pharonic numerals. The Gupta numerals developed from the Brahmi numerals and were spread over large areas by the Gupta empire as they conquered territory. The name literally means the "writing of the gods" and it was the considered the most beautiful of all the forms which evolved. The Babylonians had a place-value system as early as the 19th century BC but the Babylonian systems were to base 60. The only problem with it is that some historians claim that the date has been added as a later forgery.

Another source is the Bakhshali manuscript which contains numbers written in place-value notation.

Some historians believe that the Babylonian base 60 place-value system was transmitted to the Indians via the Greeks. The word-numeral system, later replaced by an alphabetic notation, was the logical outcome of proceeding by multiples of ten. Of course it is important to realise that there is still no standard way of writing these numerals. In India he made a detailed study of Hindu philosophy and he also studied several branches of Indian science and mathematics. The situation is much more complicated for it was not a place-value system so there were symbols for many more numbers.

There have been quite a number of theories put forward by historians over many years as to the origin of these numerals. Taking into account the kind of material that was written on in India over the centuries (tree bark or palm leaves) and the limitations of the tools used for writing (calamus or brush), the shape of the numerals became more and more complicated with the numerous ligatures, until the numerals no longer bore any resemblance to the original prototypes.

The Indians were the first to develop a base 10 positional system and, considering the date of the Babylonian system, it came very late indeed. Although it was not unusual for such charters to be modified at a later date so that the property to which they referred could be claimed by someone who was not the rightful owner, there seems no conceivable reason to forge the date on this document. The problem here is the dating of this manuscript, a topic which is examined in detail in our article on the Bakhshali manuscript. We have commented in the article on zero about Greek astronomers using the Babylonian base 60 place-value system with a symbol o similar to our zero. You can use this database for SMS marketing and also for election purpose campaign services. The different fonts on this computer can produce many forms of these numerals which, although recognisable, differ markedly from each other.

Also there were no special symbols for 2 and 3, both numbers being constructed from the symbol for 1.

Therefore, despite the doubts, we can be fairly sure that this document provides evidence that a place-value system was in use in India by the end of the 6th century. The theory here is that these ideas were transmitted to the Indians who then combined this with their own base 10 number systems which had existed in India for a very long time. Freudenthal is another historian of mathematics who supports the theory that the idea came entirely from within India. The decimal place-value system developed when a decimal scale came to be associated with the value of the places of the numbers arranged left to right or right to left. In particular his account of Indian astronomy and mathematics is a valuable contribution to the study of the history of Indian science.

Taking this as a first level he then carries on to a second level and gets eventually to 10421.

You can also Trace Any Unknown Mobile Number from .You can get all basic information about any Indian mobile Number. Tallying is likely to have predated counting and the use of words to denote specific quantities. In early forms of speech the number five was often expressed by the word for hand, and ten by two hands. Earlier members of the human family, such as Homo erectus, did not leave evidence of an ability to draw or paint. The need to keep track of fields, crops, and herds was a major impetus for the development of ideograms, mnemonic symbols, and tokens in the Neolithic period, around 7000 B.C. Settlements evolved into villages, and some Neolithic villages evolved into largely self-supporting towns with populations of several thousand.

Since planting and harvesting are best carried out in appropriate seasonal conditions, agriculture provided an incentive for the study of seasonal changes in climate and for the accurate reckoning of time. At some point, it occurred to someone to create a token to represent a number of objects, to make it more expedient to record larger quantities. Symbolic representations of words and numbers took various forms and were developed in locations ranging from Egypt to Mesopotamia and the Indus Valley. Egyptian hieroglyphs and Mesopotamian scripts were developed in the Bronze Age, by 3200 B.C.

At some point, the representation of the quantity of an object was separated from the symbol for the object.

Hieratic writing was a simplified version of hieroglyphs used by priests and scribes for common records mostly written on papyrus. The Sumerians were originally peoples from the Caucasus that moved into southern Mesopotamia about 4000 B.C. When representing the number sixty, the place to the right had no value, so that the number sixty was represented the same way as the number one.

Babylonian numbers were written from right to left and used two basic cuneiform numerals: the unit symbol and the ten symbol. When representing a number that was a multiple of sixty, the place to the right had no value, so that the number sixty was represented the same way as the number one, and one hundred and twenty the same way as two.

Small versions of the numerals for ten, one hundred or one thousand were appended to the symbol for five to create numerals for the numbers fifty, five hundred, and five thousand. During Alexander’s Macedonian expansion to the East, the Greeks became aware of the Babylonian use of the positional zero, but few used this concept, since the Greek number system was not positional.

The ancient Romans used a number system in which certain letters of the Latin alphabet are given numeral values.

For large numbers a bar was placed above the base numeral to indicate multiples of one thousand. Numerals from one to five were represented by an increasing number of parallel vertical strokes or rods. The Mayan number system was a vigesimal (base twenty) system, first adopted around 300 B.C. In addition to the dot and bar system, Mayan numbers were expressed for commemorative purposes in terms of face glyphs.

The system used for dates in Mayan calendars was a variation of a pure base twenty system, in that the third position was eighteen rather than twenty, to make it easier to represent the number 360 (twenty times eighteen). In 1524 and 1526 Francisco Pizarro, a Spanish military leader, explored the northern reaches of the Inca Empire, but was unsuccessful in his attempted conquest. In addition to the standard knot, two other knot types were used as special indicators of the end of a number. Different methods appear to have been used to identify the particular numbers recorded in a quipu.

With some modifications, Brahmi numbers were adopted by the Gupta dynasty that ruled in northeast India from 300 A.D.

The Indian number system evolved into a decimal place value system with nine symbols for the numbers one through nine, and an additional numeral for null, or zero. The word algorithm is derived from Al-Khwarizmi’s name, and the word algebra is derived from al-jabr, the Arab word for completion in the title of his book “Compendium on Calculation by Completion and Balancing.” The adopted Indian numerals underwent changes over time and evolved into Arab numerals retaining the functionality of the Indian originals. Roman numbers remained in use throughout Europe after the fall of the Roman Empire in the West in 476 A.D.

Indian-Arabic numbers were introduced in parts of Europe in the eleventh century, but did not see wide use. The new numerals and methods of computation, including the notion of null, or zero, were soon adopted by bookkeepers and merchants in northern Italy. The first printed book, Johann Gutenberg’s 1455 Latin Bible, contained both Indian-Arabic and Roman numerals. The Egyptians used symbols for legs walking right or left to indicate addition and subtraction.

The symbols p and m were used in Europe in the fifteenth and sixteenth centuries to indicate addition and subtraction.

The work of Fibonacci on practical applications of mathematics, such as unit conversions and profit and loss calculations, had a profound impact on the European business community. In double entry bookkeeping, the daily transactions of a business are recorded in one or more journals. The balance sheet shows how the two sides of the accounting equation (assets = liabilities + capital) balance out. The fall of Constantinople, the last enclave of the Roman Empire in the East, to Islamic invaders in 1453, led to an exodus of scholars to Europe. During the late sixteenth and early seventeenth centuries, Nicolaus Copernicus, Tycho Brahe, Johannes Kepler, and Galileo Galilei developed mathematical models describing planetary motions. Negative numbers were known to the ancient Chinese and Greeks, as results obtained when solving certain equations. Rene Descartes was a French philosopher, physicist and mathematician that lived in the seventeenth century. Descartes thought to extend the real numbers to include negative numbers in a way that made physical sense. In 1637, Descartes published his book Discourse on the Method of Rightly Conducting the Reason in the Search for Truth in the Sciences, in which he provided a philosophical framework for scientific thought. Descartes invented the Cartesian coordinate system (x, y, and z axes perpendicular to each other) and set down the principles of analytical geometry.

A coordinate frame of reference can be used to plot points (numerical solutions) from equations and determine the corresponding shapes. A prime number is a natural number greater than 1 which has exactly two distinct natural number divisors, one and itself. Some early mathematicians felt that the numbers of the form 2n-1 were prime for all primes n, but in 1536 Hudalricus Regius showed that 211-1 = 2047 was not prime (it is 23 x 89). French monk Marin Mersenne asserted in the preface to his Cogitata Physica-Mathematica (1644) that the numbers 2n-1 were prime for n = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127 and 257, and were composite for all other positive integers n n-1 is prime it is said to be a Mersenne prime.

By 1947 the range of Mersenne’s assertion, n n-1 for n = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, and 1279.

In 1614, the Scotsman John Napier published Minifici Logarithmorum Canonis Descriptio, a Latin text in which he described a method for simplifying arcane astronomical calculations involving angles.

An arithmetic progression is a sequence an = a1 + (n – 1) d, where d is the common difference and a1 is the initial value. Napier’s method defined logarithms based on a proportional relationship of two distances in a geometric form. Working with English mathematician Henry Briggs, Napier developed a broader application of his logarithms. The work of Napier, Briggs, and Burgi had a significant impact on various disciplines that relied extensively on computations.

The logarithm of x to the base b is written logb (x) or, if the base is implicit, as log (x).

That is, the logarithm of the product of two numbers is the sum of the logarithms of those numbers.

Logarithms are expressed as numbers of the form cc.mm, where cc is the characteristic and mm is the mantissa.

Slide rules are calculation instruments that make use of the arithmetic properties of logarithms. The advent of electronic calculators has not significantly affected the use of logarithms in applications where they provide the ability to conveniently represent very large or small numbers, as well as the ability to carry out multiplication of ratios by simple addition and subtraction. Other fields that make use of logarithms include chemistry, seismology, music, and astronomy. Descartes’ algebraic techniques served as a basis for the development of calculus by Gottfried Leibniz, in Germany, and Isaac Newton, in England, late in the seventeenth century. Some of the concepts in calculus were developed earlier in Greece, India and Persia, but it was Newton and Leibniz that developed a comprehensive approach, including rigorous proofs and notations. Calculus provided the means for solving the negation of motion paradox posed by Zeno twenty one centuries earlier. If Zeno had the tools that Newton and Leibniz provided, he would have realized that taking an infinite number of steps does not necessarily take forever.

Differential calculus involves the analysis of the slope or derivative of a graph or mathematical function. The object arrives at its new position at a new time, the original time, t, plus the amount of time it took to get to the new position, Δt.

We can define the velocity of a moving object precisely at time t (the rate of change of x at time t) by making the increment Δt very small, so small that its value is close to zero. Integral calculus involves two related concepts, the indefinite integral and the definite integral. A smaller value for Δx will give more rectangles and a better approximation of the area. This integral gives the exact value of the area between the axis and the curve for the interval a-b. The fundamental theorem of calculus states that integration and differentiation are inverse operations. The solution of certain polynomial equations yield a quantity equal to the square root of -1. Mathematicians were troubled by the continued appearance of square roots of negative numbers in the solutions of quadratic and cubic equations, until the use of imaginary numbers was formalized with the development of complex numbers.

The numbers that are not imaginary were called real numbers, and a complex number was defined as a particular form of a pair of real numbers. A complex number z was defined as z = x + iy, where x and y are real numbers, and i is the imaginary unit. Geometrically, imaginary numbers lie on the vertical axis of the complex number plane, and are presented orthogonal to the real axis.

Imaginary numbers have fundamental applications in areas such as electrical engineering, electromagnetism, cartography, and control theory.

In 1679, Leibniz discovered a base two method of counting in which only two digits, zero and one, are sufficient for a positional number system.

In 1843, Ada Byron used binary numbers to program an analytical engine devised by Charles Babbage. Base two binary numbers can be simply represented as a series of electrically pulsed on and off states, that is, as strings of ones and zeros. Quaternions, like complex numbers, take the form R + I, where R is a real part and I an imaginary component.

Quaternions constitute a four-dimensional number system, with peculiar algebraic properties. Rotations in three-dimensional space are not commutative, that is, the order of rotations affect the outcome. When used for rotation computations, quaternions are normalized, that is, they are restricted to have unit magnitude. In 1844, Hermann Gunther Grassmann, a German mathematician and linguist, included a description of vectors in his book Ausdehnungslehre (extension lesson), The Calculus of Extension. The Pythagorean theorem can be used for adding any two vectors which make a right angle to each other. The resultant is obtained graphically by drawing a line from the base of the first to the tip of the second vector. A 3-dimensional (3-D) vector has three components, one along each axis of 3-dimensional space. The magnitude of a 3-D vector, V, can be computed by taking the square root of the squares of the components VX, VY, and VZ. The dot product and the cross product are two ways in which to carry out vector multiplication.

The cross product results in a vector oriented perpendicular to the plane containing the two input vectors. The direction of n is the direction of the thumb using the right hand rule, where the index finger points in the direction of u and the middle finger points in the direction of w. Cross products have applications in mathematics and physics, and in fields such as computer graphics (to define the normal of poligons), inertial guidance (to define orbital planes), and engineering mechanics (in calculations involving torque and angular momentum). Although the properties of binary (bin) numbers make them appropriate for use in digital computers, human beings generally find them unwieldy and awkward to use.

Hexadecimal numbers are represented by the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, and F. To convert a decimal number greater than sixteen to hexadecimal, the number is divided by sixteen, and the remainder (in hexadecimal notation) is the least significant digit. Some numbers have values that are too large or too small to be conveniently written in the usual numerical notation. Scientific notation, a form of exponential notation, follows a set of conventions for writing numbers using a set of significant figures, a base, and an exponent. For decimal numbers, this method takes the form m x 10n, where m is the mantissa, 10 is the base, and n is the exponent. Use of scientific notation became prevalent among computer users around 1960 to emphasize the number of significant digits and avoid the confusion of zeros used only to fix the decimal point.

In encryption through transposition and substitution, a plain text message generally can be revealed only through the use of a secret method and key. In the twentieth century, strong cryptographic methods were developed which relied on applied mathematics and numerical processes. In 1977, Ronald Rivest, Adi Shamir and Leonard Adleman, at the Massachusetts Institute of Technology (MIT), developed the RSA public-key encryption method. It is worth beginning this article with the same quote from Laplace which we give in the article Overview of Indian mathematics.

The ingenious method of expressing every possible number using a set of ten symbols (each symbol having a place value and an absolute value) emerged in India. The purpose of this article is to attempt the difficult task of trying to describe how the Indians developed this ingenious system. The second aspect of the Indian number system which we want to investigate here is the place value system which, as Laplace comments in the quote which we gave at the beginning of this article, seems "so simple that its significance and profound importance is no longer appreciated." We should also note the fact, which is important to both aspects, that the Indian number systems are almost exclusively base 10, as opposed to the Babylonian base 60 systems. Beginning with the numerals themselves, we certainly know that today's symbols took on forms close to that which they presently have in Europe in the 15th century.

One of the important sources of information which we have about Indian numerals comes from al-Biruni. Whilst we use letters for calculation according to their numerical value, the Indians do not use letters at all for arithmetic. It is reasonable to ask where the various symbols for numerals which al-Biruni saw originated.

The Brahmi numerals have been found in inscriptions in caves and on coins in regions near Poona, Bombay, and Uttar Pradesh. The Brahmi numerals came from an earlier alphabetic numeral system, possibly due to Panini. Ifrah examines each of the six hypotheses in turn and rejects them, although one would have to say that in some cases it is more due to lack of positive evidence rather than to negative evidence.

It is a nice theory, and indeed could be true, but there seems to be absolutely no positive evidence in its favour. One might hope for evidence such as discovering numerals somewhere on this evolutionary path. If we examine the route which led from the Brahmi numerals to our present symbols (and ignore the many other systems which evolved from the Brahmi numerals) then we next come to the Gupta symbols. The Gupta numerals evolved into the Nagari numerals, sometimes called the Devanagari numerals.

What we [the Arabs] use for numerals is a selection of the best and most regular figures in India.

These "most regular figures" which al-Biruni refers to are the Nagari numerals which had, by his time, been transmitted into the Arab world.

We now turn to the second aspect of the Indian number system which we want to examine in this article, namely the fact that it was a place-value system with the numerals standing for different values depending on their position relative to the other numerals.

The oldest dated Indian document which contains a number written in the place-value form used today is a legal document dated 346 in the Chhedi calendar which translates to a date in our calendar of 594 AD. Many other charters have been found which are dated and use of the place-value system for either the date or some other numbers within the text.

All of these are claimed to be forgeries by some historians but some, or all, may well be genuine. The first inscription which is dated and is not disputed is the inscription at Gwalior dated 933 in the Vikrama calendar which translates to a date in our calendar of 876 AD. There is indirect evidence that the Indians developed a positional number system as early as the first century AD. We are left, of course, with asking the question of why the Indians developed such an ingenious number system when the ancient Greeks, for example, did not. A second hypothesis is that the idea for place-value in Indian number systems came from the Chinese. A third hypothesis is put forward by Joseph in [The crest of the peacock (London, 1991).',2)">2]. To see clearly this early Indian fascination with large numbers, we can take a look at the Lalitavistara which is an account of the life of Gautama Buddha. It is stories such as this, and many similar ones, which convince Joseph that the fascination of the Indians with large numbers must have driven them to invent a system in which such numbers are easily expressed, namely a place-valued notation.

The early use of such large numbers eventually led to the adoption of a series of names for successive powers of ten. A Technology Blog that covers latest Information, How To's, Tutorials, Tips & Tricks about Computer Software, Blogging and useful Websites. Here is the complete guide line which will help you get required details.Why do need the address? Earlier around 2-3 years ago it wasn’t tough to figure out who gave that missed called, because of limited number of mobile phone service providing companies, just by looking at first 3-4 digits of the number you could guess that this number belongs to particular region and hence you could often make a guess that who gave you that missed called. Sometimes when a call from a mobile phone is made to some other mobile phone number in India, the country code doesn’t reflect and the numbers appears to start with 0, in such case, you will have to remove the zero and add +91 or 0091 in order to get the location (region) and operator of the mobile phone number. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. And just as the shape of the letters that they use for writing is different in different regions of their country, so the numerical symbols vary. Historians trace them all back to the Brahmi numerals which came into being around the middle of the third century BC. Dating these numerals tells us that they were in use over quite a long time span up to the 4th century AD. Moving forward leads to many different forms of numerals but we shall choose to examine only the path which has led to our present day symbols.

One is that the numerals came from an alphabet in a similar way to the Greek numerals which were the initial letters of the names of the numbers. However, it would appear that we will never find convincing proof for the origin of the Brahmi numerals. The Gupta period is that during which the Gupta dynasty ruled over the Magadha state in northeastern India, and this was from the early 4th century AD to the late 6th century AD.

This form evolved from the Gupta numerals beginning around the 7th century AD and continued to develop from the 11th century onward. The way in which the Indian numerals were spread to the rest of the world between the 7th to the 16th centuries in examined in detail in [Indian J. Although our place-value system is a direct descendant of the Indian system, we should note straight away that the Indians were not the first to develop such a system.

The evidence is found from inscriptions which, although not in India, have been found in countries which were assimilating Indian culture. In particular the Chinese had pseudo-positional number rods which, it is claimed by some, became the basis of the Indian positional system. His idea is that the place-value in Indian number systems is something which was developed entirely by the Indians. It is hard to date this work since it underwent continuous development over a long period but dating it to around the first or second century AD is reasonable. Getting the address is not quick and easy way in case if you are trying to find mobile number address of an India mobile phone.

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Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. First we will examine the way that the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 evolved into the form which we recognise today. However we must not forget that many countries use symbols today which are quite different from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and unless one learns these symbols they are totally unrecognisable as for example the Greek alphabet is to someone unfamiliar with it. Before he went there al-Biruni already knew of Indian astronomy and mathematics from Arabic translations of some Sanskrit texts. First, however, we look at a number of different theories concerning the origin of the Brahmi numerals. The second type of hypothesis is that they derive from an earlier number system of the same broad type as Roman numerals. To enable the numerals to be written rapidly, in order to save time, these groups of lines evolved in much the same manner as those of old Egyptian Pharonic numerals. The Gupta numerals developed from the Brahmi numerals and were spread over large areas by the Gupta empire as they conquered territory. The name literally means the "writing of the gods" and it was the considered the most beautiful of all the forms which evolved. The Babylonians had a place-value system as early as the 19th century BC but the Babylonian systems were to base 60. The only problem with it is that some historians claim that the date has been added as a later forgery.

Another source is the Bakhshali manuscript which contains numbers written in place-value notation.

Some historians believe that the Babylonian base 60 place-value system was transmitted to the Indians via the Greeks. The word-numeral system, later replaced by an alphabetic notation, was the logical outcome of proceeding by multiples of ten. Of course it is important to realise that there is still no standard way of writing these numerals. In India he made a detailed study of Hindu philosophy and he also studied several branches of Indian science and mathematics. The situation is much more complicated for it was not a place-value system so there were symbols for many more numbers.

There have been quite a number of theories put forward by historians over many years as to the origin of these numerals. Taking into account the kind of material that was written on in India over the centuries (tree bark or palm leaves) and the limitations of the tools used for writing (calamus or brush), the shape of the numerals became more and more complicated with the numerous ligatures, until the numerals no longer bore any resemblance to the original prototypes.

The Indians were the first to develop a base 10 positional system and, considering the date of the Babylonian system, it came very late indeed. Although it was not unusual for such charters to be modified at a later date so that the property to which they referred could be claimed by someone who was not the rightful owner, there seems no conceivable reason to forge the date on this document. The problem here is the dating of this manuscript, a topic which is examined in detail in our article on the Bakhshali manuscript. We have commented in the article on zero about Greek astronomers using the Babylonian base 60 place-value system with a symbol o similar to our zero. You can use this database for SMS marketing and also for election purpose campaign services. The different fonts on this computer can produce many forms of these numerals which, although recognisable, differ markedly from each other.

Also there were no special symbols for 2 and 3, both numbers being constructed from the symbol for 1.

Therefore, despite the doubts, we can be fairly sure that this document provides evidence that a place-value system was in use in India by the end of the 6th century. The theory here is that these ideas were transmitted to the Indians who then combined this with their own base 10 number systems which had existed in India for a very long time. Freudenthal is another historian of mathematics who supports the theory that the idea came entirely from within India. The decimal place-value system developed when a decimal scale came to be associated with the value of the places of the numbers arranged left to right or right to left. In particular his account of Indian astronomy and mathematics is a valuable contribution to the study of the history of Indian science.

Taking this as a first level he then carries on to a second level and gets eventually to 10421.

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