### Problem of Equal Steps

The following problem was invented by Dan Shapiro from Ohio State University. I obtained it through the good services and enthusiasm of Professor William McWorter.

AO and BO are the two given lines forming angle f, as shown. The first step is made from B to A and the second from A to C. Denote angle ABO as a, and let's compute several other angles. Our goal is to determine the angle BAC', where C' is the reflection of C in line AO.

This same problem is discussed elsewhere. The difference is in the implementation of applets. On the other page, the angle f between the lines is defined as 180°·m/n, where m and n are determined via two spin controls. Here, the angle is defined directly from 0° to 179° in increments of 1°.

(The angle between the lines can be adjusted with the scroll bar. The small circles on the lines define the starting step (from one of the points to the other.) To clear the applet area before starting another set of iterations, click on the applet. In addition, the applet allows you to display steps and distances to the origin relative to a fixed point.)

### This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

 What if applet does not run?

Solution