Do the three hands on an analog clock (hours, minutes, seconds) ever divide the face of the clock into three equal segments, i.e. 120 degrees between each hand?

There are three equations involved, assuming that the second is our unit, for determining the position (in degrees) of the three hands:

s=6t ; m=.1t ;h=(36/4320)t

We are looking for a time "t" that positions the s,m and h 120 degrees away from each other. You could try, for example, to find a "t" that makes "s-m=120" and "m-h=120", but the second hand will surpass the 360 degree mark with these equations after the first minute, so that after ten minutes, it will have reached the 3600 degree mark (equal to 360 or 0 degrees). The solution lies in using the sine and cosine operations, thereby allowing you to add and subtract the equations...

Posted by Henry on 2004-07-23 16:43:09