Thursday, January 22

---

• Note : There is a smaller section of Math 103 (25-35 students) - with a more conventional organization and seats available:
  

  24606    MATH103     Contemporary Math   MWF   0800 0850    ART 027    Triana, Lourdes

• More Introduction to course organization.
• Web Materials
• Another example of "visual Math":
• My Name: Martin Flashman
• How to start a letter to me:  Hello ___________
  

Professor	Martin
Doctor	Marty	Flashman
Mister	Flash	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 8 possibilities for each of 4 title branches
so that the total is 8*4 = 32 possibilities.
• This is an example of a visualization used to understand and solve a problem that initially is not connected to anything visual .
• Miscellaneous: Some topics we will study.
• The film lists as a guide to the course topics.
• The color problem.
• The Sphere  and the Torus.

Who first showed the earth was a sphere?
Galileo
Egyptian Shadows?
Magellan: Circumnavigated
Copernicus: Belief
Pictures from "outer space"
Perry.Polar expeditions. Air navigational history
Curvature
• Flatland as social commentary/satire.

---

• Measurement and the Pythagorean Theorem (PT) [1.1]

a² + b² = c²




• Measuring angles, lengths and areas.
• Squares, rectangles, parallelograms and triangles.
• Dissections, cut and paste methods of measurement.
• Cutting and reassembling polygons.
• The Square Me Puzzle.
• Do Pythagorean Activity Sheet
• Virtual Manipulative for PT.
• Discuss Pythagorean Theorem and proofs.
• Over 30 proofs of the Pythagorean theorem!
• Many Java Applets that visualize proofs of the Pythagorean Theorem

---

• Show video on PT
• Puzzles and Polygons [1.2]
• Flatland and the plane
• The triangle, quadrilateral, pentagon, and hexagon.
• More on measurements of angles and areas of polyons.
• Activity: 1.2 Ex. 4, 5, 6