Recent content by MevsEinstein

  1. MevsEinstein

    Undergrad Rewriting the Toeplitz Conjecture

    The Toeplitz Conjecture (better known as the inscribed square problem) states that all Jordan curves have an inscribed square. It has been stated in the early 1900's and remains an open problem. I drew a square and then making a ton of curves that touch its four vertices: This shows that the...
  2. MevsEinstein

    Undergrad Defining a function for prime gaps using the prime counting function

    I thought I didn't put the definition for R(x) so I typed it again on accident
  3. MevsEinstein

    Bad Math Jokes

    I saw this one on a shirt:
  4. MevsEinstein

    High School Can this decomposition of zeta relate to the Riemann hypothesis?

    Oops, sorry about that.
  5. MevsEinstein

    Dardistan, one of the world’s most multilingual places

    There's a ton of "Stans" that aren't there own nations. Here are a few more: Dagestan, Tatarstan, Khusestan, Nuristan, Baluchistan, and Sistan. The region of Afghanistan, Pakistan, and Kashmir are very ethnically diverse themselves. I have a theory that this happens because of the numerous...
  6. MevsEinstein

    How did Columbus predict the Jamaica lunar eclipse of 1504?

    He probably did know in his heart since he didn't find any spices or valuables like in China. But if he said that he didn't go to China and went to somewhere else, then Spain won't fund his voyages. I have also heard that he made his crew swear that one of the landmasses he visited (which we now...
  7. MevsEinstein

    Undergrad Defining a function for prime gaps using the prime counting function

    I am getting dizzy
  8. MevsEinstein

    Undergrad Defining a function for prime gaps using the prime counting function

    I'm not even in high school yet :-p
  9. MevsEinstein

    Undergrad Defining a function for prime gaps using the prime counting function

    Thanks! So $$R(x)= \min{y \in \mathbb{N}$$
  10. MevsEinstein

    Undergrad Defining a function for prime gaps using the prime counting function

    This is why PF is amazing the people keep giving out resources. TYSM!
  11. MevsEinstein

    Undergrad Defining a function for prime gaps using the prime counting function

    Thanks! So $$R(x)= \min \lbrace y \in \mathbb{N} \, : \, \pi(y) = \pi(x) + 1 \rbrace - x$$
  12. MevsEinstein

    Undergrad Defining a function for prime gaps using the prime counting function

    I don't know how to write the smallest value of ##\pi^{-1}(x)## in set notation. But I did go ahead and graph a few values of ##R(x)##: https://www.desmos.com/calculator/vacrq5jxg1
  13. MevsEinstein

    Undergrad Defining a function for prime gaps using the prime counting function

    OH. Well, the inverse prime function actually doesn't exist since ##\pi(x)## is a step function. So now what? Maybe if we think of ##\pi^{-1}## as a set of numbers and take the smallest one then we are fine?
  14. MevsEinstein

    Undergrad Defining a function for prime gaps using the prime counting function

    That's fine since we are only looking at positive integers.
  15. MevsEinstein

    Undergrad Defining a function for prime gaps using the prime counting function

    I asked Wolfram to find the inverse function of ##\frac{x}{\ln (x)}## (which is an approximation for ##\pi (x)##) and it gave me ##-xW(-\frac{1}{x})##. So an approximation for ##R(x)## is ##-(\pi(x)+1)W(-\frac{1}{\pi(x)+1}) - x##
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