[kveldulf980]

Well yes and no, I take it no one here is/was a math major. The circles form a 60deg angle, however they also spin another 60deg going to the next gap, making 120. 8 gaps so 8 * 120 = 960 => 2 and 2/3 spins. It's in the above post.

[Jonathan183]

Originally Posted by minthaka

It would turn 480 degrees, because it needs 60 degrees to turn from 1 gap to another.

This is correct but there are only 8 balls + ball x in the original post. a and b are the start and end position of ball x. So the answer is 6*60 deg for rotation between each valley + 2*120 for rotation from a to first valley and last valley to b. Total rotation 600 deg or 1 2/3 rotations.

[minthaka]

The question is, whether the ball X in its initial position lays over ball a and at the end over b. In that case I can still keep the result 480 degrees. But if it starts at the place of ball a and finishes its route at the place of ball b, then you're right, the result is 600 degrees or 1 and 2/3 spins. The task-givers picture suggests that the ball X should go from valley 1. to valley 9. Let him says what did he mean.

[usamamuneeb]

Sorry, but I found the images were not accessile without credentials of my account. But now they are visible. So give it another try.

To kveldulf980: You were not right at ths point. See the second image which proves that when circle rools over other identical circles in a straight line, only 60*/360* = 1/6 of the circumference of the lied circles are in contact with the moving one.

To minthaka: They are 10 sectors all right if you consider the extra two the ends which take the circle up and then down.

[fingal]

Originally Posted by usamamuneeb

To minthaka: They are 10 sectors all right if you consider the extra two the ends which take the circle up and then down.

Didn't you say that a & b were 'not to be considered as balls'? If that's the case, why count them in this way?

[usamamuneeb]

For sure, a and b are not to be considered as balls. They are start and end positions of ball X. But the balls lifts up from the beginning and goes down at the end, which takes an extra 60* + 60*. Right?

The only difference between the mathematical arguments of Greeks and this are that the equipment of a better forum, than a Greek market.

[kveldulf980]

Ok, so I just did this using identical cans and I was right. What you are ignoring is that the point from which the ball starts rolling is 120deg from the last such point, 60 for the triangle and 60 for the actual roll. Try it for yourself or just think about it and you will see.

[minthaka]

In that case I agree with Johathan183, the final result is 600 degrees or 1 and 2/3 spins. 60+60=120 for up and down, 8X60=480 for the rolling over 8 balls, all together 600 degrees.

[usamamuneeb]

120 degrees from beginning to the first valley + ...
60 degree to the second valley +...
60 degree to the third valley +...
60 degree to the fourth valley +...
60 degree to the fifth valley +...
60 degree to the sixth valley +...
60 degree to the seventh valley +...
120 degree from the seventh valley to downwards
= 600 degrees.

600/360 = 1 whole 2/3 revolutions.

I explained with the help of diagram plus supposed circumfrence (360 cm) and it worked.

[usamamuneeb]

Is it now safe to call it a "Law of Circular Rotation?" I bet nothing as such existed!