At exactly 12:00, the hour, minute, and second hands are all pointing straight up.

Are there any other times that all three hands are superimposed?
If so, when?

The hour and the minute hand are together once every 12/11 hour. The number of hours past noon is the first column on the below table; then the time in h:mm:ss.sss format and the position in degrees clockwise from the 12-o'clock position of the hour-, minute- and second-hands:

 1.091  1:05:27.27  32.72727273  32.72727273 163.63636364


 2.182  2:10:54.55  65.45454545  65.45454545 327.27272727


 3.273  3:16:21.82  98.18181818  98.18181818 130.90909091


 4.364  4:21:49.09 130.90909091 130.90909091 294.54545455


 5.455  5:27:16.36 163.63636364 163.63636364  98.18181818


 6.545  6:32:43.64 196.36363636 196.36363636 261.81818182


 7.636  7:38:10.91 229.09090909 229.09090909  65.45454545


 8.727  8:43:38.18 261.81818182 261.81818182 229.09090909


 9.818  9:49: 5.45 294.54545455 294.54545455  32.72727273


10.909 10:54:32.73 327.27272727 327.27272727 196.36363636


12.000 12: 0: 0.00   0.00000000   0.00000000   0.00000000

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In none of these instances does the angle of the second hand match the angle of the other two hands except at 12. Of course you could say that midnight is different from noon, but both are 12 o'clock.

Posted by Charlie on 2004-01-30 09:39:00