Tuesday, January  24, 2005
First Class!

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

• 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.

• 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 .