Less notorious, but still important numbers

[Jenab]

Everybody knows about pi and e. They are important numbers. They are famous for having the importance they do.

But there are others, such as the golden mean, which are only semi-famous, but have loads of physical significance, perhaps recognized in nature.

Other important numbers, which have mathematical significance, which have not received their due recognition, should be belaureled in this thread. The number does not have to be transcendental, but should not be an integer or a simple fraction.

Jerry Abbott

 

[TenaliRaman]

1>e^pi and pi^e
2>Euler's constant , or gamma
3>Catalan's constant
4>Chaitin's constant
5>Feigenbaum's numbers

-- AI

 

[robert Ihnot]

Liouville's number proven transcendental in 1850, and the first such decimal fraction number proven transcendental.

\sum_{n=1...\infty}(10)^{-n!} =.110001...

 

[arivero]

1>e^pi and pi^e

Why should they be important? Specially, what does it matter about e^pi (and by the way, e^(1/pi) )

 

[CRGreathouse]

Why should they be important? Specially, what does it matter about e^pi (and by the way, e^(1/pi) )

Well, e^pi is used when dealing with complex numbers. I can't think of a use for pi^e offhand, but I'm sure there is a good one somewhere.

 

[Muzza]

Well, e^pi is used when dealing with complex numbers.

That's e^(i * pi).

 

[arildno]

I think 0 is a very important number.

 

[synergy]

e^(i*pi)+1=0
has e,i,pi,1, and 0 in it.
Aaron

 

[geraldmcgarvey]

1. sqrt(2), sqrt(3), sqrt(5)
2. Apery's constant i.e. zeta(3), and zeta(2)
3. Khinchin-Levy constants
4. Madelung's constant (related to 3D NaCl crystal)

 

[disregardthat]

42 is in fact the most important number, if you care about such things.

 

[Dosmascerveza]

Avogadro's constant 6.0221415 × 1023 mol-1

 

[confinement]

The fine structure constant alpha = 0.007297351.

 

[Pjennings]

I've been thinking about pi^e lately, and trying to prove that it is irrational. By rewriting e as 1+1+1/2+1/3!+...+1/n! I got it to pi^2*pi^(1/2)*pi^(1/3!)*...*pi^(1/n!), and proved that each of these terms is irrational. I'm stuck when it comes to showing that multiplied together these numbers are irrational. Any ideas?