Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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:


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


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.

share|cite|improve this question
+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. – Voyska Jun 19 '13 at 4:55
@Prism Thanks. :-) – Voyska Jun 19 '13 at 5:15

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
share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.