Chasle's Theorem: A study in Euclidean Isometries
- Judah L Schwartz
[You are strongly urged to try the "When is AB equal to BA?" applet before using this applet.] Explore the circumstances under which a single rotation of a shape about a movable point is equivalent to a rotation of the shape followed by a translation of the rotated shape or a translation of the shape followed by a rotation of the translated shape. You can make your own shape by dragging the four small red dots. You can fix the center of rotation by dragging the gold ring. You can fix the angle of rotation by using the white slider. Given a quadrilateral Q, under what circumstances can R[T(Q)] or T[R(Q)] be replaced by a single rotation? What can you say about the center of rotation of the single rotation? What can you say about the angle of rotation of the single rotation?