## Number spirals and numeral systems

*Beginning: Number spirals introduction*

Numbers on number spirals can be represented in different number systems. For example, consider the numbers on the main axis of some spirals in different number systems.

*Table 1*shows the numbers on the main axis of the

**2-spiral**in binary, decimal and hexadecimal numeral systems.

Main axis of 2-spiral |

*Table 2*presents the numbers on the main axis of the

**10-spiral**in the same numeral systems.

Main axis of 10-spiral |

Similarly,

*Table 3*presents the numbers on the main axis of the

**16-spiral**.

Main axis of 16-spiral |

As can be seen from the tables above, each

**a-spiral**in the number system with the base

**a**will consist of separate turns with numbers that have the same number of digits in the positional system. Each subsequent turn of the numerical spiral for the number

**a**in the number system with the base

**a**adds one digit in the positional system. Each

**n-turn**consists of numbers written using

**n+1**number of digits.

If we introduce the rule that unit arcs on one turn must be of the same length, then the number spiral will turn into a set of concentric circles. Each circle will contain numbers with the same number of digits. The introduction of such a rule violates the visual continuity of natural numbers.

Thus, each

**a-spiral**is a graphical representation of natural numbers in the numeral system with the base

**a**, which is written in the numeral system we have chosen. By default we use the decimal numeral system.

*Continued: Number spirals and prime numbers.*

## No comments:

## Post a Comment