Congratulations on all your hard work, seminarians.  It has been a pleasure and an honor working with each of you.

Email me your seminar reflection ASAP – by Friday morning at the latest.

Here are the prompts I put on the board:

Qualities of a good problem solver:

• curious
• persevering
• organized
• good communicator
• inventive
• seeks proof
• extends/generalizes
• takes risks
• follows through
• enjoys mathematics

For everything you say in your reflection, be specific.  You can refer to specific moments in class or specific pieces of work.

You may also want to consider: 

• What will you remember/take away with you from your experience in this class?
• What are some goals you have for your future work in math?

Since Tuesday is a Friday schedule, we’ll do these problems in class.  Please print them out and pring them with you – but you don’t need to solve them.

Use the rules you found in class to solve these circle geometry problems.

There is one piece of given information missing in the first problem – arc AC is supposed to be labeled 110 degrees.

Enjoy!

Answer these questions (typed).  Be thorough and clear.  Use illustrations as needed.  If you’d like an extra challenge (or a 4) try the bonus.

1. Is the incenter the best strategy for game 1 (racing to the sides)?  Why or why not?  Explain what you think is the best strategy.
2. Is the circumcenter the best strategy for game 2 (racing to the vertices)? Why or why not?  Explain what you think is the best strategy.
3. Is there ever a time when the orthocenter is the best place to stand for game 2?  When?

Bonus:  Is there ever a situation when the best place to stand for games 1 and 2 are the same? Explain.

Homework Holiday – see you next week.

Triangular Pastimes from Another Universe

Show diagrams (several for each game) and a few sentences of explanation for each.  Also, if you can, relate your strategy to some of the centers we talked about in class:  angle bisectors, perpendicular bisectors, altitudes, midpoints, etc.

Game 1:

The referees define a triangular field having three goal lines (sides).  The field could be equilateral, scalene, right, obtuse – any kind of triangle.  A caller calls which side is the goal for that round, and you try to race to be the first one to reach that side.  Your current theory is that the best way to win is to find the place that is an equal distance from each side.  Where is this point?  How can you identify it on different shaped fields?

Game 2:

Again, the referees define a triangular field, this time by placing three cones.  Your goal is to reach the cone that is called on any given round and you’d like to be in a good position for a play at any cone.  You want to be the same distance from each cone.  Where do you stand?  How do you find this spot?  How is it different in different shaped fields?