A brief history of numerical systems - Alessandra King
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The three major areas of exploration with regard to number systems are: 1) their variety and diversity; 2) the bases they use and that can be used; and 3) the symbols used to represents digits.
Variety of Number Systems: if we think we may have taken for granted the (Hindu-Arabic) number system we are so familiar with, studying how other systems work allows us to understand and appreciate ours better while at the same time having fun with the many ways a numerical system can be built and numbers can be written. To this end, we can look at the influence of Ancient Egypt, read how the Babylonians managed without a zero, learn about the Roman or the Mayan systems, and even play online Maya math games.
Number Bases: In any numerical system, the basis or radix is the number of unique symbols used to represent numbers. For example the decimal system, the most commonly used system today, uses base 10, or 10 unique symbols (from 0 to 9). However, 10 is not the only possible base, as other systems used base 20 (Aztec and Mayan), base 60 (Babylonians) and so on. Using other bases can deepen our understanding of our own system and it is also a lot of fun: try it out here. In fact, base 2, 8 and 16 are used in all our electronic devices, as this is the way we communicate with computers and they communicate with each other. To better understand how these bases work, you can look at how to translate a number from hexadecimal to binary here or play the binary game. The National Council of Teachers’ of Mathematics has even published a set of problems based on a cartoon strip to engage middle school students in studying different numerical bases. Finally, some people would argue that 12 would be preferable to 10 as base for a number system and explain their reasoning here.
Glyphs: Various symbol sets can be used to express numerical quantities. Each culture (from the Egyptian to the Ancient Chinese) had their own set of symbols that also evolved with time. So it is for the glyphs that we are now using in the decimal system – the history of their origin and their transmission is not a simple one… but that’s a story for another time.
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