Approximating Pi and e with Linear Algebra

[derekmohammed]

I was wondering if there are any formulations of Pi or e that use "n-euclid space" to approximate it? Or really just the use of any linear algebra to approximate Pi or e?

Thanks...

Derek Mohammed

 

[lyapunov]

Nagell 1951), and Liouville proved in 1844 that e does not satisfy any quadratic equation with integral coefficients (i.e., if it is algebraic, it must be algebraic of degree greater than 2).

(Mathworld on e)

almost the same goes for pi.

[cutie of the month: pi(pi + 1/e - 1/(4(pi^3)))= 11.0000014549696...]

 

[HallsofIvy]

Excuse me?? I was under the impression that Liouville proved that a number (that he constructed for the purpose) was transcendental, Hermite proved that the number e was transcendental in 1873 and Lindeman proved that pi was transcendental in 1882.

 

[lyapunov]

You're excused...

The somewhat mangled quote (I see now) was from Mathworld, that has oodles of info of why pi and e are not algebraic, but are transcendental.

No contradictions, there... Maybe some first reading on algebraic, irrational and transcendental would be useful here:

http://mathworld.wolfram.com/AlgebraicNumber.html
http://mathworld.wolfram.com/e.html