![]() ![]() Also, the Chinese had a base-10 system, probably derived from the use of a counting board. However, there is not much evidence that the Babylonian system had much impact on later numeral systems, except with the Greeks. The Babylonians (as we will see in Chapter 3) used a positional system with 60 as their base. The Indians were not the first to use a positional system. However, some evidence suggests that they may have actually developed a positional system as far back as the first century C.E. Although it is in slight dispute, the earliest known document in which the Indian system displays a positional system dates back to 346 C.E. More important than the form of the number symbols is the development of the place value system. Other examples of variations up to the eleventh century include:įinally, one more graphic shows various forms of these numerals as they developed and eventually converged to the 15 th century in Europe. ![]() It is believed that the Arabs were instrumental in spreading them to other parts of the world, including Spain (see below). These numerals were adopted by the Arabs, most likely in the eighth century during Islamic incursions into the northern part of India. Note that by this time, the symbol for 0 has appeared! The Mayans in the Americas had a symbol for zero long before this, however, as we shall see later in the chapter. The Gupta numerals eventually evolved into another form of numerals called the Nagari numerals, and these continued to evolve until the 11 th century, at which time they looked like this: If we compare these to the Gupta numerals above, we can try to see how that evolutionary process might have taken place, but our imagination would be just about all we would have to depend upon since we do not know exactly how the process unfolded. One possibility is this: īecause these symbols would have taken a lot of time to write, they eventually evolved into cursive symbols that could be written more quickly. His theory is that there were originally nine numerals, each represented by a corresponding number of vertical lines. However, there are other hypotheses that are offered, one of which is by the researcher Ifrah. The second type of hypothesis states that they were derived from some earlier number system. ![]() This is not uncommon…the Greek numerals developed in this manner. The first type of hypothesis states that the numerals came from the initial letters of the names of the numbers. Many possible hypotheses have been offered, most of which boil down to two basic types. How the numbers got to their Gupta form is open to considerable debate. The Gupta numerals were prominent during a time ruled by the Gupta dynasty and were spread throughout that empire as they conquered lands during the 4 th through 6 th centuries. One of those paths led to our current numeral system, and went through what are called the Gupta numerals. ![]() For example, in the first century C.E., one particular set of Brahmi numerals took on the following form:įrom the 4 th century on, you can actually trace several different paths that the Brahmi numerals took to get to different points and incarnations. These numerals were used all the way up to the 4 th century C.E., with variations through time and geographic location. The Brahmi symbols for 1, 2, and 3 are shown below. They had separate symbols for the numbers 1 through 9, as well as distinct symbols for 10, 100, 1000,…, also for 20, 30, 40,…, and others for 200, 300, 400, …, 900. The Brahmi numerals were more complicated than those used in our own modern system. It is then that the Brahmi numerals were being used. When we look at the origins of the numbers that al-Biruni encountered, we have to go back to the third century B.C.E. Al-Biruni, who was born in modern day Uzbekistan, had visited India on several occasions and made comments on the Indian number system. One important source of information on this topic is the writer al-Biruni, whose picture is shown here. However, the history of these numbers and their development goes back hundreds of years. It was not until the 15 th century that the symbols that we are familiar with today first took form in Europe. The development of these ten symbols and their use in a positional system comes to us primarily from India. We’ll explore base systems more thoroughly later. For example, the position of the symbol 3 in the number 435,681 gives it a value much greater than the value of the symbol 8 in that same number. Furthermore, this system is positional, which means that the position of a symbol has bearing on the value of that symbol within the number. This is a base-ten (decimal) system since place values increase by powers of ten. ![]()
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