## Number spirals

*Beginning: Number spirals introduction*

If you use angle units of measurement and an arbitrary spiral to visually display natural numbers, then all numbers can be ordered according to the following rules:

1. On the main axis of the

**a-spiral**there are numbers of the form

**a**in ascending order, where

^{n}**а>1, n≥0**.

2. The main axis coincides with the zero ray of angle units of measurement and has the following form:

The main axis of the number spiral |

3. The main axis divides the spiral into separate turns measuring

**360°**, which are appropriately numbered according to the exponent of the number

**a**located at the beginning of each turn. For example,

**a.0-turn, a.1-turn, a.n-turn**. The distance between the turns of the spiral is arbitrary.

4. Each turn of the

**a-spiral**is divided by rays into an equal number of single angular sectors, which divide the turn into single arcs. Each unit arc has an arbitrary length and corresponds to one numerical unit. Unit arcs separate two adjacent natural numbers, which are located at the intersections of rays and turns of the spiral.

5. The number of unit sectors and the number of natural numbers

**m**for each

_{n}**a.n-turn**is determined by formula (1).

6. For zero turns of all

**a-spirals**the number of unit sectors and natural numbers is determined by formula (2).

Number spirals formulas |

7. Each unit arc from a turn

**m**is divided into

_{n}**a**unit arcs on the next turn

**m**with new rays.

_{n+1}8. At the beginning of each ray

**(N-ray)**, at the intersection with the turn, there is a natural number

**N**of the form

**P**, prime with respect to the number

_{a}**a**.

9. On the continuation of the

**N-rays**, at the points of intersection with subsequent turns, there are natural numbers that are multiples of the number

**a**, forming the main axis of the

**a-spiral**.

*Continued: Description of number spirals.*

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