- #1
FUNKER
- 121
- 0
is this correct
-(pi) + (1 - 2i)((pi)^2) = i^2
i = (-1)^(1/2)
(pi)= 3.142...
peace
-(pi) + (1 - 2i)((pi)^2) = i^2
i = (-1)^(1/2)
(pi)= 3.142...
peace
Is Pi Actually Transcendental?
- Thread starter FUNKER
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In summary, the conversation discusses the correctness of an equation involving pi and imaginary numbers. The expert suggests that the equation is not correct and offers a simpler solution. The conversation also mentions the concept of transcendental numbers and a humorous discussion about mathematicians doing math in the bathroom. A link is provided for further reading.
- #2
suyver
- 248
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No, this is not correct. You are saying that
[tex]\pi + (1-2 i)\pi^2=-1[/tex]
which would imply that
[tex]\pi=\left(\mp\frac{1}{10}\pm\frac{i}{5}\right)\left(\mp 1+\sqrt{8i-3}\right)[/tex]
which is clearly not the case...
[tex]\pi + (1-2 i)\pi^2=-1[/tex]
which would imply that
[tex]\pi=\left(\mp\frac{1}{10}\pm\frac{i}{5}\right)\left(\mp 1+\sqrt{8i-3}\right)[/tex]
which is clearly not the case...
Last edited:
- #3
matt grime
Science Advisor
Homework Helper
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Saying pi is transcendental would have saved you all that latexing...
- #4
suyver
- 248
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But I like LaTeX'ing! :)
- #5
moshek
- 265
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matt:
saying only that pi is transcendental
could make suvey feel more good
with his nice effort to explain the answer.
Moshek
saying only that pi is transcendental
could make suvey feel more good
with his nice effort to explain the answer.
Moshek
- #6
matt grime
Science Advisor
Homework Helper
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Erm, what the heck does that mean? Perhaps I was offering a tongue in cheek way of pointing out that the answer could be done in far fewer steps, and without making a statement that needs to be checked. Algebraic expressions don't always look like they ought to; I can think of several expressions that appear to have non-zero imaginary part, yet are real.
- #7
moshek
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Matt:
I am still thinking about your question to me if a mathematician is going to the toilet is he also doing mathematics by this.
Until I will have the exact answer for you
you may enjoy to read this:
https://www.physicsforums.com/showthread.php?t=17243
Moshek
I am still thinking about your question to me if a mathematician is going to the toilet is he also doing mathematics by this.
Until I will have the exact answer for you
you may enjoy to read this:
https://www.physicsforums.com/showthread.php?t=17243
Moshek
1. What does it mean for pi to be transcendental?
A number is considered transcendental if it cannot be expressed as a root of any polynomial equation with rational coefficients. In simpler terms, pi cannot be written as a fraction or ratio of two whole numbers, making it an irrational number.
2. How was it proven that pi is transcendental?
In 1882, German mathematician Ferdinand von Lindemann proved that pi is transcendental by showing that it cannot be a root of any polynomial equation with rational coefficients. This proof is known as the Lindemann-Weierstrass theorem.
3. Are there any other transcendental numbers besides pi?
Yes, there are infinitely many transcendental numbers. Other well-known examples include e, the base of the natural logarithm, and the square root of 2.
4. Why is it important to know that pi is transcendental?
Knowing that pi is transcendental has significant implications in mathematics and science. It means that pi cannot be calculated or approximated precisely, making it an infinitely long and non-repeating decimal. This has applications in fields such as geometry, physics, and engineering.
5. Can we ever know the exact value of pi?
No, we cannot know the exact value of pi due to its transcendental nature. However, with the help of advanced computing technology, we can calculate its decimal representation to millions or even billions of digits.
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