Megan Barnett

EMAT 4680

Aug. 23, 2000

1. Four Centers of Triangles-I found that when I rotated the triangle into a right angle, the orthocenter fell directly on the 90-degree angle (point A) and that the circumcenter lied on the hypotenuse. When I turned the triangle into an equilateral triangle, all four points clustered together in the center of the triangle. Furthermore, I noted that when the triangle was formed into many different shapes, the orthocenter and the circumcenter left the inside of the triangle at the same times while the incenter and centroid remained inside the triangle. Lastly, it appeared that the incenter disappeared when I formed an obtuse triangle.

2. Overlapping Squares-When I moved point P past point D, the overlap shaded one-fourth of the square. When I moved point P 360-degrees around the other square, the overlap disappeared at points A and B. It also appeared that the yellow square is overlapped by an overall 75 percent (3/4) of the continuously moving square (3/4 is shaded green).