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The Long Run Guess

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Okay, hot shot. Let's see if you know this one. Is it a monomial (i.e. is it possible to reduce the expression to a monomial)?

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Well, it can essentially be reduced to a monomial because there are no unknown values within the expression, but the expression, when not simplified, can be considered to contain more than one single term.

 

I also see how it can be considered one whole term not simplified at all, as if the expression were to be equivalent to x in the expression "x + 2" or something (where this would be a binomial and upon the removal of 2 the expression is a monomial, but at the same time, I'm an idiot.

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Is there at least one pi term in the equation that is raised to some power (other than 0 or 1)?

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Can the number be expressed as a*π + b, where a and b are algebraic? (I think this is deducible from what's been asked, but i want to be sure.)

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Alright, chief. Now let's talk a little more about a. Is a the cube root of some rational number?

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Alright, this changes everything. Please, share with me... is a of the form x^(1/y), where x is some rational number, and y is an integer from 4-10 (inclusive)?

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Is a of the form x^(1/y), where x is a rational number and y is any positive integer?

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Well, Zane's number was π * 1/sqrt(27), which he just told me because this round was getting lame.

 

That being said, I have a number.

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

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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)}

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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:

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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.

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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.

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