Tuesday, January 24, 2005
- Discussion of course details:
- handout course description
- Discussion of the many course features:
- In class activities.
- On-Line Quizzes
- 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,
- Visualization of mathematics that is not inherently visual. [Visualizing
- 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:
- How to start a letter to me: Hi ___________
- 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 .