Tag Archives: Graph

Numbers of the World

Recently Matt Parker uploaded a video to his YouTube channel where he discussed numbers and the words used to represent them in different languages, more precisely the length of these words:

The basic idea is the following:

  1. one has 3 letters,
  2. two has 3 letters,
  3. three has 5 letters,
  4. four has 4 letters,
  5. five has 4 letters,
  6. six has 3 letters,
  7. seven has 5 letters,
  8. eight has 5 letters,
  9. nine has 4 letters,
  10. ten has 3 letters,

and so on... This can be seen as a function

f(n) = \text{number of letters of $n$ spelled out}.

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Visualising the Riemann Hypothesis

One stubborn source of frustration when working with complex numbers is the fact that visualisation becomes tedious, if not impossible. Complex numbers have 2 "real" dimensions in themselves, which give rise to the complex plane. That's all good and fair. But if you talk about a function with complex domain and codomain, you already deal with a 4-dimensional graph. Unfortunately, my mind can only handle 3 dimensions (on a good day). One can resort to taking the absolute value of the function instead, or map real and imaginary part individually, resulting in a 3-dimensional graph, but all of these solutions fail to satisfy in one respect or another.

However, there is one more dimension we can exploit: time! Used in the right way, this can produce wonderful videos like this one:

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