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3: Historical Counting Systems

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    In the following chapter, we will try to focus on two main ideas. The first will be an examination of basic number and counting systems and the symbols that we use for numbers. We will look at our own modern (Western) number system as well those of a couple of selected civilizations to see the differences and diversity that is possible when humans start counting. The second idea we will look at will be base systems. By comparing our own base-ten (decimal) system with other bases, we will quickly become aware that the system that we are so used to, when slightly changed, will challenge our notions about numbers and what symbols for those numbers actually mean.

    • 3.1: The Evolution of Numeration Systems
    • 3.2: The Number and Counting System of the Inca Civilization
    • 3.3: The Hindu-Arabic Number System
      Our own number system, composed of the ten symbols {0,1,2,3,4,5,6,7,8,9} is called the Hindu-Arabic system. This is a base-ten (decimal) system since place values increase by powers of ten. Furthermore, this system is positional, which means that the position of a symbol has bearing on the value of that symbol within the number. The development of these ten symbols and their use in a positional system comes to us primarily from India.
    • 3.4: The Development and Use of Different Number Bases
      In this section, we will explore exactly what a base system is and what it means if a system is “positional.” We will do so by first looking at our own familiar, base-ten system and then deepen our exploration by looking at other possible base systems. In the next part of this section, we will journey back to Mayan civilization and look at their unique base system, which is based on the number 20 rather than the number 10.
    • 3.5: The Mayan Numeral System
      In this chapter, we discussed the the Mayan civilization (1500 B.C.E to 1700 C.E.) that actually used a base system other than 10.
    • 3.6: Exercise

    Thumbnail: Roman Numerals. (Public Domain; Monaneko via Wikipedia)

    This page titled 3: Historical Counting Systems is shared under a CC BY-SA 3.0 license and was authored, remixed, and/or curated by David Lippman (The OpenTextBookStore) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.