2-spiral |

On a

**2-spiral**the main axis is formed by successive powers of the number

**2**. All odd numbers are located at the beginning of the numerical

**N-rays**, all even numbers are located on the

**N-rays**of the spiral.

On the

**2.0-turn**there is one single arc of size

**360°**, at the beginning of this turn there is the number

**1**. This is the only number spiral that has no other numbers other than one on the zero turn. The number of numbers and unit arcs is determined by formula (2).

The

**2.1-turn**is divided into two single arcs of size

**180°**and there are two numbers on it -

**2**and

**3**. Here and on the remaining turns, the number of numbers and unit arcs is determined by formula (1).

Calculations for 2-spiral |

The

**2.2-turn**form four single arcs measuring

**90°**, on which the numbers

**4, 5, 6, 7**are located. The number

**6**is located on the continuation of the

**3-ray**.

The

**2.3-turn**form

**8**single arcs measuring

**45°**. This turn contains numbers from

**8**to

**15**inclusive. The numbers

**10, 12**and

**14**are located on the continuation of the

**5-ray, 3-ray**and

**7-ray**respectively.

The further arrangement of natural numbers on the

**2-spiral**can be traced in the figure above.

## 3-spiral

3-spiral |

The main axis of the

**3-spiral**is formed by successive powers of the number

**3**. On the

**3.0-turn**there are two single arcs of size

**180°**and there are two numbers on it - these are

**1**and

**2**. The number of unit arcs and numbers is determined by formula (2).

The

**3.1-turn**is divided into six single arcs measuring

**60°**, on which the numbers

**3, 4, 5, 6, 7**and

**8**are located. The number of unit arcs and numbers is determined by formula (1). The number

**6**is located on the continuation of the

**2-ray**and is the result of multiplying the number

**2**by the number

**3**.

Calculations for 3-spiral |

The

**3.2-turn**is formed by eighteen single arcs of size

**20°**, on which the numbers

**9**to

**26**are located.

## 4-spiral

4-spiral |

The main axis of the

**4-spiral**is formed by successive powers of the number

**4**. On the

**4.0-turn**there are three single arcs of size

**120°**and on it there are three numbers -

**1, 2**and

**3**.

The

**4.1-turn**is divided into twelve single arcs measuring

**30°**.

Calculations for 4-spiral |

The

**4.2-turn**is divided into forty-eight unit arcs measuring

**7.5°**.

Each turn of the

**4-helix**contains two compressed turns of the

**2-helix**. Compression occurs unevenly and is determined by the structure of the zero turn of the

**4-helix**. Zero and even turns of the

**2-helix**are compressed to

**1/3**turns of the

**4-helix**, the first and odd turns - to

**2/3**. This uneven compression ensures that the single angular segments of all turns in the

**4-helix**structure are equal.

Similar uneven compression occurs on the remaining spirals, built on numbers equal to the power of the number

**a**, greater than the first power. Thus, for an

**8-helix (a=2**, each turn of which contains three turns of a

^{3})**2-helix**, the proportions are equal:

**1/7, 2/7, 4/7**.

## 5-spiral

5-spiral |

The main axis of the

**5-helix**is formed by successive powers of the number

**5**. On the

**5.0-turn**there are four single arcs of size

**90°**and on it there are four numbers -

**1, 2, 3**and

**4**.

The

**5.1-turn**is divided into twenty single arcs measuring

**18°**.

Calculations for 5-spiral |

The

**5.2-turn**is divided into one hundred unit arcs of size

**3.6°**.

In a similar way, you can build a number spiral for any natural number.

*Continued: Analysis of number spirals.*

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