Homework 1, due Thursday 8/26.
1. Make sure that you know how to do the GSP constructions from
class: orthocenter, centroid, circumcenter, "April's center".
(Don't hand anything in for problem 1.)
2. Write a short (two page) report on ONE of the four centers of triangles we discussed in class. Explain how you find the center, and explain any special properties it has. Is it always inside the triangle? If not, for which triangles is it inside and for which triangles is it outside? Do you see any theorems related to the center? No proofs are required, but your statements should be clearly written.
More advanced optional questions (mainly for grad students): Can you find any other interesting centers of triangles? Prove that the centroid really is the center of gravity. For which triangles are the circumcenter and "April's center" the same? (Prove it.) What about centers of quadrilaterals or polygons with more than 4 sides?
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