Complete each of the following parts. Part One is merely finishing off the write-ups for the semester. Part Two should be a new web page item. Part Three is the course evaluation.
Review your Write-ups 1 to 12. Revise as you wish to reach the point where you feel that, collectively, the 12 write-ups represent your best work for the course. They are an elctronic portofolio of your work.
Complete a Write-up on your Web Page for the following investigations. This should be individual work.
A. Bouncing Barney. We discussed this investigation in class. Your challenge now is to prepare a write-up on it, exploring the underlying mathematics ideas and conjectures.
Barney is in the triangular room shown here. He walks from a point on BC parallel to AC. When he reaches AB, he turns and walks parallel to BC. When he reaches AC, he turns and walks parallel to AB. Prove that Barney will eventually return to his starting point. How many times will Barney reach a wall before returning to his starting point? Explore and discuss for various starting points on line BC, including points exterior to segment BC. Discuss and prove any mathematical conjectures you find in the situation.
I assume some GSP sketches and explorations will be useful.
B. Multiple Solutions.
1. Find as many solutions as possible for A, B, and C that satisfy both equations:
ABC = 4 3A + 2B - C = 3.
What observations can you make about your results? Again, we discussed some approaches to this one in class. Your task is to prepare a write-up that explores this task. (Not required, but you might want to consider how to explore this one with a spreadsheet as well as with graphing tools.).
2. Create another set of equations that also yield a useful exploration.
C. Consider the Stamp Problem in Assignment 12. Update the data to include the price increases for a first class letter through January 2006 -- when the price will become 39 cents. (Recent increases were 33 cents in 1997, 34 cents in 1999, and 37 cents in 2002.) Prepare a write-up and use your analysis to answer the questions anew:
When will the cost of a first class postage stamp reach $1.00?
When will the cost be 74 cents?
How soon should we expect the next increase?
In 1996, the analysis of stamp data historically seemed to show that the postage doubled every 10 years approximately. The cost in 2006 would seem to argue that pattern is no longer valid. Is there evidence to show a change in the growth pattern? Or, was the 'doubles every ten years' just a bad model?