search of various historical aspects of the number
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In a narrow, yet highly unspecific, sense, a number system is a way in which humans represent numbers.
We have limited our discussion already, for it is merely humans among all known species who have the
ability to count and form numbers which we later can perform calculations upon. Many—often very
different—number systems have been employed by many—again, very different—cultures and
civilizations throughout the ages, and there still exists a wide variety of them even today, in our
comparatively global society.
In a much more broad sense, a number system is a set of the many ways humans reason about
numbers and this is the definition we will use for our discussion in this paper. But what do we mean by
this above definition? Well, let us discuss the ways in which we, as humans, reason about numbers. We
reason about numbers by talking about them, so we need a way to represent numbers in speech. We
reason about numbers by writing about them, so we need a way to represent numbers in writing/text; this
representation is known as a notation. Furthermore, when reasoning about numbers, we need some sort
of number base, or radix, which is the fundamental number in which all other numbers stand in relation
to. In recent times—we're talking perhaps a couple of centuries back in time—we also reason a lot about
different sets of numbers that we have been able to create; therefore, the term number system has also
been made to mean one of these sets. We will now give a gentle introduction to these four parts and put
them in relation to the rest of this paper.
1.1. Numbers and Speech — Number Words
Number words are a way for us to discuss numbers in speech. Any language generally has number words
for a finite set of numbers, e.g., the numbers smaller than the number base of the number system and
perhaps certain multiples of the number base, and rules to form larger ones from these. This second
property of a language is not always true. Some—albeit historical and now dead—languages actually can
not form numbers larger than some certain limit; most often due to lack of necessity.
This paper will describe the number words of a number system only if they are of some larger
importance or of curious interest, and even then in a very abstract manner, not indulging ourselves to
make a linguistic survey.
1.2. Numbers and Writing — Number Notation
Number notation is the way in which we form numbers in text. The notation is often tightly linked with
the language being employed as there is often a connection between the way words are formed in speech
and in the way they are formed in writing. This is, however, not always the case. And even if it is, there
may exist many notations for use depending on context and application. The notation may also change
greatly over time, even if the number system as a whole changes little—often depending on other
achievements in society, such as writing material.
Notation is of central importance in this paper. Most of our discussion will revolve around the
notation used by different societies through history. There are three reasons for this. First, and somewhat
trivial, it is the cornerstone in our understanding of number systems from past times, as it is more or less
the only record we have of them. Second, notation tells a lot more about the mathematical advancement
of the civilization in which it was used than do number words—if their use has been preserved. Third,
notation is such a beautiful thing. Your author truly loves the written word. Not so much the content,
rather the actual building blocks that forms it.
1.3. Numbers in Relation — Number Base
A number base is a number in which other numbers stand in relation to. Numbers are expressed in a
certain number base and calculations are performed using the values of a number given its base.
Throughout the ages there have been an exceedingly large number of radices—a somewhat more
scientific term with the same meaning as number base—by which mathematicians have performed their
calculations. Perhaps surprisingly, and we are jumping the conclusions somewhat, our decimal—base 10
—number base, where all numbers are expressed as multiples of ten, is not the oldest, nor the one most
often used.
The number base is of grave importance to the possibility of further advancement of a number
system and the mathematics utilizing it. As we will see, a number base can stagnate a whole civilizations
mathematical progression, and we will therefore give it an important role in our discussion.
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Answer: Here is your answer,
In the long history of the number π, there have been many twists and turns, many inconsistencies that reflect the condition of the human race as a whole. Through each major period of world history and in each regional area, the state of intellectual thought, the state of mathematics, and hence the state of π, has been dictated by the same socio-economic and geographic forces as every other aspect of civilization. The following is a brief history, organized by period and region, of the development of our understanding of the number π.
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