Instructions (additional general instructions may be given in class):

Last modified Feb 24, 2008 9:24 PM

Does not have to be typed. Draft will be accepted, to be looked over before final version is submitted. Due dates to be announced.
Be sure to return the draft when you turn in your final form of the project.

Refer to the online pdf document,
      Baubles, Bangles, and Beads (pdf).
or to the online Word document,
      Baubles, Bangles, and Beads (Word).

Various sets are defined or described in this document. Your job is to describe these sets in simple geometric terms that could be understood by a competent high school algebra student who is familiar with the coordinate plane. (In some cases, there is only one set defined/described; in other cases, there may be more than one.) Some examples of such descriptions (which may or may not be relevant to the sets given in the project) follow:

• The origin (more precisely, the set containing the origin).
  
  
• The open first quadrant (i.e., the first quadrant not including the coordinate axes).
  
  
• The horizontal axis (sometimes called the x-axis).
  
  
• The set of all lines through the point  (1, 2).
  
  
• The line of slope  m  through the point  (1, 2).  (Here we would need to be given a number  m.)

You are supposed to prove that the set given in the Project is equal to the set you say it is. In some or all cases, this may require you to give a simple, precise set-builder description of the set YOU are talking about. For example, in the list above, the first two sets would be

• The origin:  {(0, 0)}.
  
  
• The open first quadrant:
         {(x, y) : x > 0  and  y > 0 }.

You should be able to construct similar descriptions in the other cases, if needed. 
New Feb 23, 9:30 AM:
     For example, you should be able to define, using set-builder notation, the line of slope  m  through the point  (1, 2),  for a given number  m.

New Feb 24, 9:30 PM:
Then, if you believe (for example) that a bangle is equal to the open first quadrant, you would prove that a bangle as defined in the Project is equal to the open first quadrant as given above.

Last modified Feb 24, 2008 9:24 PM

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