- #1
Aditya89
- 23
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Is e^pi rational? I seem to have heard from one of my tacher that research was going. How far we have gone?
Is e^pi Rational? - Research Progress
- Thread starter Aditya89
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The discussion centers on the rationality of e^pi, with participants noting that it is transcendental, a status that can be established through Gelfond's theorem. Euler's formula, which connects the numbers 0, e, pi, and i, is highlighted as a significant mathematical relationship. A reference to a comment by Gauss emphasizes the importance of understanding this formula for aspiring mathematicians. The conversation seeks to clarify the current research progress on the topic. Overall, the thread underscores the complexities surrounding the nature of e^pi in mathematical theory.
- #2
devious_
- 312
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It's transcendental. This can be proved using Gelfond's theorem.
- #3
jim mcnamara
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Since you seem to be going in this direction, you might like Euler's formula
which relates 0, e, pi, i
http://mathworld.wolfram.com/EulerFormula.html
which relates 0, e, pi, i
http://mathworld.wolfram.com/EulerFormula.html
- #4
devious_
- 312
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From the link jim posted:
"Gauss is reported to have commented that if [e^{i \pi} + 1 = 0] was not immediately obvious, the reader would never be a first-class mathematician."
...
"Gauss is reported to have commented that if [e^{i \pi} + 1 = 0] was not immediately obvious, the reader would never be a first-class mathematician."
...
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