Math Is Fun Forum

Yes, if L' (length of the bird) is 0, it is an infinite number of times. If not, then it gets a bit more complicated. All I can say for that case is that after t=(L-L')/(2V) time, L' starts monotonically decreasing.

It needs to be a formal rule because there non-associative operations.

The commutative law does not allow omitting parentheses.

That one isn't solvable, I'd say. At least in terms of elementary functions.

What I am doing is just taking

Well, an ellipse isn't exactly a function, but, it can be done, I'd say. It would be very complicated in some cases.

Well, as I said, I don't think it is necessary to fill up the whole table. It is enough to see in how many ways the table below can be filled up with k white and 32-k black pawns.

Actually, I just looked at the info on wikipedia a bit. You are right, you don't need 4 angles. Three is enough.

Hm?

Well, I do not see why it is easy. I just know it was easy for me.

Those coordinates make sense because that's the way the vector can be decomposed in 3D.

I don't think it's around a world axis. It seems to be a rotation of the ship, but neither affect any coordinates, so I'm not sure what that's about.

Yes, I did miss the pun. I quite like it, unlike most people.

Hi Bob

Are you sure it is moving on the surface of the sphere?

I am also stuck with the point of view. The only reference frame that makes sense is the world, but it doesn't seem to be so...

Hm?

I already posted my answer in post #54.