(This is NOT homework) just my personal interpretation,(adsbygoogle = window.adsbygoogle || []).push({});

because these are the formulas as you already know:

r = √(x^2 + y^2 + z^2)

φ = arctan(y/x)

θ = arccos(z/r)

using (x,y,z) = (∞,∞,∞)

I come across a bit of a sinister problem:

r = √(∞^+∞^+∞^) = √(3∞^2)

which is right because if we just said that ∞ was x, then it would be:

x^2 + x^2 + x^2 = 3x^2 right? (just the small proof)

that means that (using surd rules)

√(3∞^2) = √3 x √∞^2 = ∞x√3 =∞√3

r =∞√3

φ = arctan(∞/∞) = arctan(1) = 45° or ∏/4 radians.

θ = arccos(∞/∞√3) <---- (z / r) ||| arccos(∞/∞√3) = arccos(1/√3) - because can I please say that we shouldn't forget that the ∞'s cancel out(???) so:

θ = 54.73561032° <--- This is what I don't understand, why is it that if you use x,y,z as infinity, why is the angle of θ NOT 60°? (I assume it's because r is in equidistance from x,y,z as they are all infinity, and φ is 45°, it shows r is equidistant from x and y) -

^ That is my thesis, I don't know why θ doesn't equal φ if all the lengths are equal, (again because r is equidistant from the line x, line y and line z) they SHOULD be the same no? (again, I assume it's because of the 1/√3 - but there is 3 infinities (to find out r) so it should be √3∞^2 no?)

Thank's for reading, I was just reading through the spherical co-ordinate theories and formulas, it's not homework, it's actually something I thought other people would want to see.

Thanks for reading.

Eggman100

Oh, -.-, I think I forgot that Phi is the angle with respect to r in the x and y axis, I think when I said about the equidistance, then I think I forgot that, "respect to r in the x and y axis" - I think I used it so that its the angle from the x axis and r which of course would have to implement a 'z' which ofcouse phi is only the x/y plane angle, sorry.

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# Cartesian to Spherical co-ordinates (x,y,z) = (∞,∞,∞) | φ,θ are different.

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