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?

Let the angles made by Hour hand, minute hand & seconds hand be theta 1 theta 2 and theta 3

The relative angle between hour hand and minute hand is

= (t /(60*60) - t/(60*60*12))*360

= t*11/120

The relative angle between hour hand and seconds hand is

= ( t/60 - t/(60*60*12))*360

= t*719/120

If the angle between the hands have to be 120 deg

then two possibilities exist Hour hand in between minute and second in forward direction or hour hand in between second hand & minute hand in forward direction

In case 1

t*719/120-360*n*60=120

t*11/120-360*n=-120

t*59/120=120+120*60

14888.14sec

In case 2

t*719/120-360*n*60=120

t*11/120-360*n-360=-120

=14155.93sec

don't know some mistake.

Posted by salil on 2006-02-12 11:13:17