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I was having a blurry thinking of differences about rational and irrational numbers, then I had the idea of ploting them in a specific way:

$$\frac{1}{2}=0.5$$

Getting that value, I've thought about a function for the digit positions, which in the given case would give me

$$\begin{matrix} {f(1)}&=&{0}\\ {f(2)}&=&{5} \end{matrix} $$

And in the case of

$$\frac{1}{3}=0.33333...$$

Would give me

$$\begin{matrix} {f(1)}&=&{0}\\ {f(2)}&=&{3}\\ {f(3)}&=&{3}\\ {f(4)}&=&{3}\\ {f(5)}&=&{3}\\ {f(n>5)}&=&{3}\\ \end{matrix} $$

I've even plotted some examples:

enter image description here

Is there a math field that studies something like that? The nearest thing that comes to my mind are the Ford Circles (although I know they're very different). In the Ford circles, there is a relation between the radius of the circle and the number it represents. I was thinking also if such a relation could be found in this?

I'm not thinking about a relation exactly like Ford circles, I'm thinking about a deeper relation between the line and the given number.

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+1 for being inquisitive! –  Prism Jun 19 '13 at 4:42
    
I may not discover something useful but I guess I'll do mathematics research someday, this is a small pathetic step that I can do with the little I know. –  Vÿska Jun 19 '13 at 4:55
    
@Prism Thanks. :-) –  Vÿska Jun 19 '13 at 5:15

1 Answer 1

Some fields that occur to me are:

  1. Number theory
  2. Normal numbers
  3. Summations for $\pi$ and other constants
  4. Digit-extraction algorithms (for our good friend $\pi$ and other constants
  5. Periods of the reciprocals of primes (and other integers) in different bases
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