square roots

[potterfan3]

whats the square root of 1,2 and pi

[Clanad]

Square root of Pi is1.7724538509055159....... however, Pi is an infinitesimal number, so there is no exact square root, just is there no exact value for Pi itself...

[Clanad]

Oh, and square root of 1 is 1, square root of 2 is 1.4142135623, unless you want to carry it to 100 digits since it is an irrational number... also known as Pythagoras' Constant, by the way...

[fo3nix]

you meant irrational number for Pi, right? ;-)

[Clanad]

While TT is certainly an irrational number, fo3nix, it is also an infinitesimal number. Unfortunately, for discussion purposes, at least in this type of forum, that argument becomes as much philosophical as it does factual since infinitesimals are non-real numbers. I probably erred in referencing the term. Thanks for the input!

[RogerWilco]

Of course, for practical purposes, instead of employing the incredible processing power of a number computers, a few routers, some firewalls, squillions of miles of cables, etc. For about 4 or 5 Euros, you could buy a calculator and type the question in there

[bernardo]

On the contrary, there is an exact value for pi and for its square root, but it is not possible to express the exact value using decimal notation. The other square roots of 1, 2, and pi are of course -1, -1.4142... and -1.7724...

[tony1941]

Clanad, I think you meant to say "irrational"; infinitesimal surely means very small. Anyway, square root of 2 and Pi are both irrational numbers, but Pi is also a member of the subset of these called "transcendental numbers". I can't argue with the figures, though! See below:- http://plus.maths.org/issue21/xfile/index-gifd.html

PS I once learned a rhyme which enables you to quote Pi to 20 figures (!!) by counting the number of letters in each word. Would anyone else like a copy of it?? It makes a good party trick.

[fo3nix]

Clanad: I disagree with you that Pi is an infinitesimal number. Can you explain to me why it is?

[spinchimp]

tony1941 - I don't think I would want to go to the sort of parties you attend.

[Clanad]

Well, fo3nix, keeping in mind that my ability to squeak through calc and trig lends new meaning to the sound coming from my grandfather's cheap shoes, my take on this question derives from the definition(s) of infinitesimal numbers. The first is the rather classical approach; less than 1/n for all n, but, however, never 0. The other being somewhat (actually a lot) more esoteric; they cannot be represented as a finite floating point number. By the way, this discussion could just as well include e and the other constants... in my opinion.
As an example; many mathmaticians do not believe infinitesimals exist since the argument, invariably centers on the area between 0.999 and 1, but not zero. Most that do support infinitesimals existence seem to agree that they can only consist of non-real numbers, only hyper-real numbers... they are a notional quantity. So, having had time to consider my statement about pi being an infinitesimal, and not having the time to accurately defend that position and considering the 2,000 character limitation of this site, I think the wisest course of action is to invoke G�del's Incompleteness Theorem which simply states that within any formal system with its own rules and conventions, there are some facts within that system that are true, but which cannot be proved to be true using the rules of the system. For now, at least let's agree that pi is transcendental, irrational and the current expansion of its value equals nearly 6 and one half billion decimal places. This, knowing all the while that pi defined to 47decimal places predicts the circumference of the universe within the diameter of a photon!

[fo3nix]

hehe. well, i agree with all of the above, except for the infinitesimal part. and while some weird maths guys may come up with some weird ideas about Pi and the other constants, I dont believe them to be true. and many other mathematicians probably dont either.