Curious Mathematical Problem

Curious Mathematical Problem

Let us consider the following equation:

Prove that

  • x = log(Pi) = 1.14472988584… is a very good approximation of a solution, up to 10 digits.
  • Using high performance computing or other means, prove that it is correct up to 1,000 digits.
  • Is x = log(Pi) an exact solution?

If the answer to the last question is positive, this would mean that log(Pi) is NOT a transcendental number, but rather, an algebraic number. A remarkable result in itself!

Source for picture: algebraic numbers

Solution

Any real number larger or equal to 1 is a solution, so there is nothing particular with log(Pi).

For related articles from the same author, click here or visit www.VincentGranville.com. Follow me on on LinkedIn, or visit my old web page here.

DSC Resources



Link: Curious Mathematical Problem