It’s not a spiral, it’s a helix, and helixes have symmetry.

Never mind, I see you are trolling.

No it isn’t. The image is part of the question and is there to make clear exactly what the geometrical situation is.

Not sure if joking. This isn’t some kind of troll exam. The picture illustrates the situation in the question.

A helix does have symmetry. Symmetry isn’t restricted to reflections and rotations. Symmetry means you can non-trivially map an object into itself. You can do this with a helix because no part of the helix is different to any other. So what it’s really saying is that it has constant slope.

I know... and the reason for that is that the challenging part of the puzzle is in working out the correct approach, not in number crunching.

How do you know they hadn’t seen helixes before?

I lol’d.

Yeah, given that the thickness of the twine isn’t specified. The intended model is implicit.

By symmetry it means no point of the helix is different from any other.

Messy numbers don’t make a puzzle better. It’s not supposed to be a test of your ability to use a calculator or use basic formulae. What a silly comment.

That’s incorrect, sorry. Emphasis is on the “tha”.

If the rod were a kilometre long instead of 12cm would you still think it’s 16cm?

Use the cylinder as a rolling pin. Stick the left end of the string into some pastry, and then roll the cylinder forwards so that the string gets progressively stuck into the pastry as you roll. The resulting diagonal string goes along by 12cm and forwards by 4*4cm = 16cm, so by Pythagoras, the string is of length…

Your explanation was so inadequate that I suspect you don’t understand the basic details of the puzzle.

Not trying to burst any bubbles here, but that’s not why Euler’s equation is remarkable. sqrt2 is irrational. If you multiply sqrt2 by sqrt2 you get a rational. That’s not particularly surprising.

I'm not sure what cosmic time is, but yes, light travels at a fixed speed, regardless of your velocity, which is a bizarre fact and central to special relativity. Note that this doesn't have anything to do with the expansion of the universe; special relativity would work equally well in a static universe. It means…

Yes, time being revealed by the pattern is a more accurate way of putting it; like I say, we never actually perceive concepts directly. In that sense it's no different from mass, energy, space, or any other physical concept. Again, we can ask all of the same questions of these things; "is it the measurement or is it…

Why is that odd? That's what geoblocked means.

An essential means to understand the universe because it's an observed pattern in the universe. The point is that this is not an atypical criterion for reality; it's the only criterion we ever use. Mass, space, force, anything; we never "directly" perceive them. All we do is abstract these concepts from our basic…