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number of rational point on circumference of a circle. (1 Viewer)

glittergal96

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A proof of this claim would also provide a proof of the algebraic independence of pi and e over Q.

This is an open problem.
 

Paradoxica

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A proof of this claim would also provide a proof of the algebraic independence of pi and e over Q.

This is an open problem.
Which would probably net you a fields medal automagically, seeing as you'd be well within the age limit. Furthermore, if you were still in high school, dozens of universities would probably be offering you scholarships for research in pure mathematics.
 

lita1000

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Integrand never said anything about if p1=p2 and q1=q2, then LHS = RHS (from sy's post). He's saying that if LHS=RHS then p1=p2, and q1=q2. Search up if and only if type arguments on wiki for details on this. Your second line makes it seem like he wasn't talking about this.

You have completely misunderstood Integrand's post.

Don't be a hayabusaboston btw, using words like "ordeal" won't make you seem any smarter.
 

Paradoxica

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Integrand never said anything about if p1=p2 and q1=q2, then LHS = RHS (from sy's post). He's saying that if LHS=RHS then p1=p2, and q1=q2. Search up if and only if type arguments on wiki for details on this. Your second line makes it seem like he wasn't talking about this.

You have completely misunderstood Integrand's post.

Don't be a hayabusaboston btw, using words like "ordeal" won't make you seem any smarter.
well then. you certainly wouldn't like me because that's how I converse. Usually. If the mood is correct, I will talk like a 7-year old with a very limited set of words.
 

dan964

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Is this solution valid?


Clarifications
1. "It follows therefore that the change in x must be positive, if x1, x2 are both rational.": This line is ignored, as it is an error and kinda of irrelevant, forgot to remove;


2. Q is the distance BC squared = (x2-x1)^2; I could have put it in earlier. If the assumption is true, it has to be rational. (I have to deal with the square of the distance because the distance may be irrational square-root)
3. pi/e is clearly irrational, since neither have any common factors. The RHS is clearly rational; as the numerator and denominator a
 

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Paradoxica

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Is this solution valid?


Clarifications
1. "It follows therefore that the change in x must be positive, if x1, x2 are both rational.": This line is ignored, as it is an error and kinda of irrelevant, forgot to remove;


2. Q is the distance BC squared = (x2-x1)^2; I could have put it in earlier. If the assumption is true, it has to be rational. (I have to deal with the square of the distance because the distance may be irrational square-root)
3. pi/e is clearly irrational, since neither have any common factors. The RHS is clearly rational; as the numerator and denominator a
http://www2.math.ou.edu/~jalbert/courses/openprob2.pdf
Refer to problem 22.
Sorry, but if you have a proof of the irrationality of pi/e, then you will have solved a massive open problem. The proof could also lead to the proof of irrationality of the other operations involving pi and e. It is not known whether or not pi is a rational multiple of e. Therefore, your claim is invalid.
 

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