Originally posted by XanthosNZThat was my result also except I have (-1/6 h) not (+ 1/6h).
In radians we'd have:
Angle = abs ((pi/6 * h + pi/360 * m) - (pi/30 * m))
Originally posted by crazyblueYou're right about the simplification I should have done that. And the different ways of calculating difference don't matter in the end (as abs(a-b)=abs(b-a)).
That was my result also except I have (-1/6 h) not (+ 1/6h).
I did one more thing after that. No biggie though:
Angle = abs (11/360 m - 1/6 h) * pi
Strange thing is, I checked it was some examples and got correct but also wrong results. I'm too tired now to figure out what went wrong there.
Originally posted by howardbradleyThe following Matlab program returns no solutions:
A question along similar lines (and one to which I don't know the answer) - I hope it hasn't appeared here before.
Is it possible for the hands of a clock/watch to exactly divide the face into thirds? ie all the hands are at 120 degrees to each other. Again it it the sort of clock where the hands move continuously and don't "jump" from exact minut ...[text shortened]... t minute etc.
As an example: 20 seconds past 8 O'clock comes close - but is not exact.
Originally posted by sonhouseThat's not a proof.
Its easy to see why a clock cannot have a time like that, the two hands being mechanically in sync so the only way it would work is if it started out 20 minutes fast or slow. A clock can obviously be at 12:00
starting out that way, by the time the minute hand gets to 20 the hour hand would have moved one third of an hour also so its impossible, unless it starts out 20 minutes off.
Originally posted by XanthosNZOf course not a maths proof but a physical proof. If there was a case where one could get out of sync then in an infinite series, letting the clock go forever, you might run into a time setting like the problem wants but it repeats exactly each day so you are limited to the time within that span so you clearly cannot have the hands 120 degrees apart. You don't need maths for that.
That's not a proof.