Are+Number+Systems+Arbitrary?



=__Task 1: Create a Number System__= We'll post some examples of your work here:
 * 1) ===In your group, invent a series of symbols to represent numbers. These symbols should not be the same as any numeral system known to you. The number of different symbols and how they may be combined with one another (if at all) is entirely your choice.===
 * 2) ===You will then need to explain your numeral system to the class and show us how to represent: Three, Forty-five, Twenty, and One hundred and seventeen===
 * 3) ===Devise a series of problems for other students to solve, using your system of symbols.===

Discussion Questions

 * What is the advantage of employing place value?
 * Why does the number system which we generally use have base 10?
 * What is the advantage of having a numeral for zero?
 * Is there a difference between zero and nothing?

=__Task 2: Consider Other Number Systems__=

Now that you have created a number system of your own, exam some other number systems.
Numeral Systems from Different Parts of the World = =

Discussion Questions
=Watch The Story of One= media type="custom" key="18481178" width="202" height="202" align="center"
 * How many symbols are needed in each system?
 * Does the system use a base? If so, what is it?
 * Does it employ place value?
 * Does it use a zero?
 * Where exactly did each of these civilizations exist?
 * What do the dates associated with the development of each number system suggest?

Discussion Questions/points

 * Where does one come from?
 * Is it more a product of nature or the human mind?
 * There is a paradigm shift when Archimedes moves away from making “One” mean something necessarily material like one sheep, or one stone. Mathematics no longer needs to be practical. Mathematics becomes a "creative art" until applications are discovered (some times hundreds of years later). What kind of knowledge do we get from an abstract, creative art?
 * Why are Roman numerals impossible or at least very difficult to use in calculations?
 * Does zero pre-exist humans? Is it possible that zero was discovered rather than invented?
 * In what way is the invention of zero a paradigm shift?