What is the significance of the repeating pattern in a circle of numbers?

In summary, the conversation discusses the concept of cyclic numbers, specifically focusing on the number 142857. This number, when multiplied by 2, 3, 4, or 5, produces a result that is readable within the original number in a circular pattern. This is known as a cyclic number, and it occurs when the reciprocial of a prime has a repeating block of p-1 digits. The conversation also mentions that this phenomenon occurs with numbers such as 17, 19, and 23.
  • #1
soeren
19
0
hi,

i've got a question (don't know, if this is the right forum for this.. but i think, it isn't really a brain-teaser)

My biology teacher told me this and said, that he doesn't know anything about the reason for them.
It isn't a homework or something like that, but I and my friends are very interested in solving the "problem".. or even being able to explain it to oneself.

I've got the Numbers written in this circle:

[tex]\begin{matrix}& 7 & 1 & \\ 5 & & & 4 \\ & 8 & 2 & \end{matrix}
[/tex]


When i read it to the right, I get for example the number 285714

When i multiplicate this with 2, i get ..
The amazing thing of them is, that 285714 is readable in that circle, too.

That works with the factor 3; 4; 5, 6; too.

142857 * 2 = 285714
142857 * 3 = 428571
142857 * 4 = 571428
142857 * 5 = 714285
...

I tried to explain this to myself, but i didn't really understand it.

Can one of you please tell me why this works with that numbers?
Is contingency or _must_ it be like that?

thnx for help!

greets

Soeren

ps: sorry for my bad english, but this is not my mother-language...
 
Last edited:
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  • #2
soeren said:
hi,

142857 * 2 = 285714
142857 * 3 = 428571
142857 * 4 = 571428
142857 * 5 = 714285
QUOTE]

what you seem to be talking about are cyclic numbers. In the case above 1/7 repeats in blocks of six digits, which same digits are also found in 2/7, 3/7...6/7.

This will occur when the reciprocial of a prime has a repeating block of p-1 digits. The next cases are: 17, 19, 23.

There is an article on this: http://mathworld.wolfram.com/CyclicNumber.html
 
  • #3
very thanks! That explains it very good. :-)

greets

soeren
 

1. What is a circle with 6 numbers?

A circle with 6 numbers is a graphical representation of a group of 6 data points, typically used in statistics and data analysis. The numbers are plotted around the circumference of the circle, with lines connecting them to create a visual representation of the relationship between the data points.

2. How is a circle with 6 numbers used in science?

A circle with 6 numbers is often used in science to display and analyze data, particularly in fields such as statistics, economics, and social sciences. It can help researchers identify patterns and relationships between data points.

3. What do the numbers on a circle with 6 numbers represent?

The numbers on a circle with 6 numbers represent different data points, such as numerical values or categories. They can also represent different variables or factors being studied in a scientific experiment or analysis.

4. How is a circle with 6 numbers different from a scatter plot?

A circle with 6 numbers and a scatter plot both represent data points, but they are visually different. A circle with 6 numbers plots the data points around a circle, while a scatter plot plots the data points on a Cartesian coordinate system. Additionally, a circle with 6 numbers is often used to display categorical data, while a scatter plot is used for numerical data.

5. Can a circle with 6 numbers be used for any type of data?

While a circle with 6 numbers is commonly used for categorical data, it can also be used for numerical data. However, it may not be the most appropriate or effective way to display numerical data compared to other types of graphs or charts. It is important to choose the most appropriate visualization method for the type of data being analyzed.

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