Math 412 Geometry II

Planned schedule:

Monday Wednesday Friday

1/24 The golden ratio
A resource page.

More about the golden ratio. (The golden ratio assignment is due next Monday) Flow charts intro (assn due Monday)
Proof blocks to print
an article about flow chart proofs
1/31 Compass and straightedge constructions (assn due Friday) Patty-paper constructions (Serra 3.1-3.5)
______________

Incenter and Circumcenter (Serra 3.7)
_______________ (assn due Mon?)

2/7 Excenter and Orthocenter

Centroid (Serra 3.8)
_____________ (prep assn due Friday. Part 1 of assn)

 Review with emphasis on flow chart proofs.

2/14 Inscribed angles (Serra 6.3)
_____________

 Problems likely to be on the exam
Triangle centers treasure hunt.		 Exam
Similarity theorems intro (Serra 11.2)
___________

2/21 How do you prove similarity?
Power of a point

 
Pythagorean theorem proofs take 1
____________
(____________) 		2/28 Circles and the Pythagorean theorem (Serra 9.6)
_______________		  
  Review
Look again at the best angles in circles problems
If you want to practice more on area with scaled up figures, go here		 Exam
3/14 spring break  
  Patterns in Fractals (Serra p. 135-137)
____________		 Self similarity and fractal dimension
3/28 Chaos game Mandelbrot set
Practice
Web site

 
4/4 Continue investigating compositions of transformations. more compositions, and a little group theory more compositions and frieze patterns
Homework: create a frieze pattern for each of the 7 frieze pattern groups.
4/11 more frieze patterns and wallpaper patterns

more wallpaper patterns or Euler's theorem.
Practice for test (note that these first ones were written on the Math 126 level, and I expect you to be able to solve more complicated problems than I expect of them):

  • Lengths of fractal iterations
  • Self similarity dimension
  • Iterations that define Julia sets and the Mandelbrot set.
  • Plot the result of doing two composed isometries to a figure, and then expressing the result as a single isometry
  • Find and describe a full set of isometries in a frieze or wallpaper pattern
  • Make up a frieze pattern given its isometries.
  • Explain how to derive the formula for the area of a circle
 exam
4/18 isometric drawings tessellations tessellations
4/25 tessellations--Escher and transformations topology--1-D and Euler part 1 topology Euler part 2
5/2 topology finish topology and Euler

review
concurrency theorems and proofs

Grading breakdown:

30% homework, projects, etc, 70% tests.