Jump to content
Chipwoodstock

The Long Run Guess

Recommended Posts

Assuming you mean a is an irrational real number (because otherwise it's a repeat of your previous question), no.

Share this post


Link to post
Share on other sites

r exp(iφ), r∈ℕ, φ∈ℝ
still an infinite amount of possibilities for r as well as φ :rolleyes:
 
I'll anyhow take a shot in the dark:
r∈{5,10}, φ∈{±atan(3/4),±atan(4/3)}

Share this post


Link to post
Share on other sites

If abs(a),abs(b) ≤ 100 there are some more simple possibilities:

φ∈{±atan(x±1):x∈{5/12, 7/24, 8/15, 9/40, 11/60, 12/35, 13/84, 16/63, 20/21, 20/99, 28/45, 33/56, 36/77, 39/80, 48/55, 60/91, 65/72}}

(of course these can lead to a, b way bigger than 100, but not every possibility has to be covered above 100) if φ is not an element of this set, either a or b are irrational (since you wrote in a previous answer, b isn't the irrational part, a is irrational), or you constructed the numbers some other way, but without knowing the algebraic curve you've chosen to do so, this wouldn't help anyhow, however as they are constructed to have this form in either way, it would be basically impossible to guess them... :unsure:

Share this post


Link to post
Share on other sites

Is it related to Pi?

Nope.

This may have been before i understood the polar form of complex numbers. π does show up in the number if written in the form re. Apologies for any confusion.

 

abs(a),abs(b) ≤ 100

Yes.

 

φ∈{±atan(x±1):x∈{5/12, 7/24, 8/15, 9/40, 11/60, 12/35, 13/84, 16/63, 20/21, 20/99, 28/45, 33/56, 36/77, 39/80, 48/55, 60/91, 65/72}}

φ is none of those numbers.

 

(since you wrote in a previous answer, b isn't the irrational part, a is irrational)

I said the number is not of the form a*i, where a is rational or real. That means, in a+bi, where a,b∈ℝ, one or both of a and b is irrational.

Share this post


Link to post
Share on other sites

Recap:

  • The number is algebraic and irrational.
  • The number is not real or imaginary (i.e. in rectangular form [a+bi, a∈ℝ, b∈ℝ], a and b are both non-zero).
  • The number, written in polar form (re, r∈ℝ, 0≤θ<2π), contains π.
  • r∈ℤ, r ≠ 5, r ≠ 10, |a| ≤ 100, |b| ≤ 100.
  • tan(|θ|) ∉ A and cot(|θ|) ∉ A, where A = {3/4, 5/12, 7/24, 8/15, 9/40, 11/60, 12/35, 13/84, 16/63, 20/21, 20/99, 28/45, 33/56, 36/77, 39/80, 48/55, 60/91, 65/72}.

 

New hint: the number is a root of a non-zero polynomial in one variable with integer coefficients and degree no greater than 5.

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!

Register a new account

Sign in

Already have an account? Sign in here.

Sign In Now

×