The Java applet below shows how an algebraic idea is used in movies and television to make a transition from one scene to another. It shows three pictures. On the left you see an outside view of the Lincoln Memorial. On the right you see the statue of Abraham Lincon inside the memorial. The picture of the memorial is represented inside your computer by the vector a and the picture of the statue is represented inside your computer by the vector b. The picture in the middle is represented by the vector
When the applet first starts t = 0 and the middle picture is the same as the picture on the left. You can change the value of t by clicking on the bar at the bottom of the applet. For example, click at the far right of the bar. It may take a while for the applet to process your change. You have changed t to 1 and after processing this change the middle picture will show the statue. Now click in the middle of the bar. Now the middle picture will show a picture that is halfway between the two pictures. Try different values of t to see the effect on the middle picture.