Tuesday, January  24, 2005
First Class!

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• Discussion of course details:
  
• handout course description
  
• Discussion of the many course features:
  
• In class activities.
• Homework
• Reading
• On-Line Quizzes
  
• Portfolios
• Projects
• The Tool kit
  
• personal info sheet.
  
• Flatland as social commentary/satire.

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• Why focus on Visual Mathematics?
• Mathematics that studies topics related to visual experience. [Geometry, Topology, Motion]
  
• Visualization of mathematics that is not inherently visual. [Visualizing Counting]
• Classification:  Triangles, circles: congruence and  similarity.  What common features are shared by circles and triangles?... They divide the plane into two sectors: "inside and outside". Not in the same class as the symbol.  8.

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• Example of "visual Math" and counting:
• My Name: Martin Flashman
• How to start a letter to me:  Hi ___________
  

Professor	Martin	Flashman
Doctor	Marty	Flash
Mister	Omit	Omit
Omit

• How many different openings are possible?
  
• We can visualize this problem with a "tree"
• This visualization allows us to count the possibilities easily...

seeing there are 9 possibilities for each of 4 title branches
so that the total is 9*4 = 36 possibilities.

• There were several alternative countings suggested for this problem. This may be connected to some ambiguity in the statement of what would be an acceptable opening for the letter. So- if the assumption is made that some entry must be made then the choice of an omission for each selection would be eliminated from the tally, giving 25 possibilities.  A distinction: 
• "vague" meaning "Not clear in meaning or application."  and 
• "ambiguious" meaning "Open to more than one interpretation. Ambiguous indicates the presence of two or more possible meanings."  
• This is an example of a visualization used to understand and solve a problem that initially is not connected to anything visual .