Genady

This is not true.

OK, then [math]\frac{xy}{2}=\frac{1}{\sin 2\beta}[/math].

According to the drawing, the radius of the circle is 1. You should've asked me, what is [math]\alpha[/math]. It is an angle between the green line and the axis.

The Riemann curvature tensor in one dimension does not vanish but rather is undefined. It has no components in 1D.

[math]\frac{xy}{2}=\frac{1}{\sin 2 \alpha}[/math]

You are correct. It includes only a finite number of radicals.

On one hand, (notice the very last statement) ... On the other hand, [math]x=\sqrt[5]{2+5\sqrt[5]{2+5\sqrt[5]{2+...}}}[/math] solves that polynomial. What's wrong?

And that's why the OP question is misleading. IOW, a waste of time. P.S. I should've guessed so as it is in The Lounge and not in The Puzzles.

, for our convenience. Another not Fibonacci: 328, 176, 105, 83, ... What are the next terms?

You're right. They are equivalent. This is not a meaningful sequence; the order is arbitrary.

It can be, e.g., [math]F_n=2F_{n-2}+F_{n-3}[/math].

This is a different question, not the one in the OP. I'm sorry you say this.

Yes, but we're not given the next two numbers, so we don't know that it is not fibonacci.

You're asking, why it is not a Fibonacci sequence, but it looks like a Fibonacci sequence to me.

It was for a different sequence, before the OP edit, so I deleted it.

It was referred to as "Red Army" in reference to events which occurred before the end of WWII. It was referred to as "Soviet Army" in reference to the later events.

Perhaps, in the West, but not in the Soviet Union. There, it was referred to only in historical terms.

There was no "Red Army" in Afghanistan in 1980-1985.

There is an important, albeit not often mentioned, requirement for a coordinate system, without which one real parameter would've sufficed to specify any point in any dimensional manifold.

My Dutch friends here also have cancelled their plans to visit the US, because of him.

Guidelines - Science Forums: "members should be able to participate in the discussion without clicking any links"

Most people know nothing about how gravity works or doesn't work and thus they don't have any way to know that this conspiracy theory is not true.

The sequence [math]r_n=\sum_{i=1}^n 2^{-f(i)}[/math] is increasing and bounded, thus it converges.

This is a proof of a statement in Stillwell's "Reverse Mathematics", p.77: My question is, how do we know that the sequence [math]r_1, r_2, ...[/math] converges?

A new direction of thinking has appeared recently in a discussion of this question. During the discussion, it has been noticed that Black coral - Wikipedia says, "The corals derive their name from their black skeletons, which are composed of protein and chitin," which has brought up this response: "which are composed of protein and chitin Your answer is in there somewhere. The laying down of the components has to have some electrical or chemical offset that produces the coiling. Probably not from the helicity at the nano scale of assembly. Cellulose does the same twisting for plants - is vines. Here is some discussion of chitin on the nano to macro scale, regarding colour, iridescence of insects and the like, and colours from cellulose in plants. As well as twisting - macro needs more research to explain it all. https://hal.science/hal-04202351v1/file/Adv Funct Mat 2023_M Mitov.pdf" The previous hypothesis has focused on development of the coral polyps. This new direction rather focuses on development of the coral skeleton.