Question 603010
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The angular difference between the 12 where the minute hand was at exactly 12 and the 4 which is where the minute hand is at exactly 12:20 is exactly one-third of a circle.  But while the minute hand was moving through this one-third of the whole circle, the hour hand was moving one-third of the way from the 12 (where it was at 12 o'clock exactly) to the 1 (where it will be when the minute hand gets all the way back around to the 12).  The angular difference between the 12 and the 1 is one-twelfth of a circle.  So the minute hand has moved a full one-third of the circle but the hour hand has moved one-third of one-twelfth of the circle. Then recall that there are 360 degrees in a circle.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left[\frac{1}{3}\ -\ \left(\frac{1}{12}\,\cdot\,\frac{1}{3}\right)\right]\,\cdot\,360]


You Win!  You get to do your own arithmetic.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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