Sqrt

What are some good rational approximations to Sqrt [2]?

Wolfram Blog : Mathematica and The American Mathematical Monthly’s “Problems and Solutions” Section 2009

I feel that in 10-20 years such problems — having solid algorithmic solutions — will be viewed as no more interesting than computing digits of Sqrt [2].

Wolfram Blog : Mathematica and The American Mathematical Monthly’s “Problems and Solutions” Section 2009

Also, I would have to respectfully disagree with your assertion that “in 10-20 years such problems … will be viewed as no more interesting than computing digits of Sqrt [2].”

Wolfram Blog : Mathematica and The American Mathematical Monthly’s “Problems and Solutions” Section 2009

Thanks to Mr. Brenkus, I now know that terminal velocity = Sqrt [(2 x mass x acceleration)/(C x rho x A)], which comes in handy when calculating the best possible times for swimmers.

Unbreakable Sports Records 2010

Curiously, we found that the sequence length seems on average to increase by exactly Sqrt [2] -1 at each step (which would be interesting to prove).

Wolfram Blog : Science: Live and in Public 2007

Sin [Pi Exp [Pi Sqrt [162]]] i.e. some mess of the same kind that you expect to get from fundamental theories.

The Reference Frame 2010

Exp [Pi Sqrt [162]] would have to be a very close to an integer.

The Reference Frame 2010

(X0, X ', Y0, Y', T0,1/Vz) where: V = Vz · Sqrt (1+X'2+Y'2) Juan A. Garzón: 2nd.

Recently Uploaded Slideshows miguelfm 2010

And for such numbers, Exp [Pi Sqrt [H]] can be re-expanded using the j-invariant functions that are known from toroidal, one-loop computations in string theory.

The Reference Frame 2010

Now, you see that Sqrt [162] is a pretty random number between 12 and 13.

The Reference Frame 2010