Pi/4

Originally posted by Mephisto2
True, a beautiful combination of the most important numbers in C. But pi is already fascinating enough in R. It is not only 'irrational', but has a 'transcendental' aspect too. Unlike many other irrational numbers, like sqrt(2) for instance, it cannot be found as the result of a polynomial equation with integer coëfficients.

e is also a transcendental constant, and it is just as interesting, and useful as pi.

Originally posted by Nemesio
I, too, do not understand the concept of 'transcendental.' Can you
walk me through it?

I undersand ir/rational.

Nemesio

Transcendental constants are numbers that are not the root of any polynomial with rational coefficients.

Read "The Kingdom of the Infinite Number" by Bryan Bunch and Asimov on Numbers. Two very good books. Also, series aren't approximations of numbers, they are exact definitions of numbers, as they go towards infinity they converge on the number they define. You get an approximation when you calculate the series out part way (obviously you can't do it to infinity, finding out where they converge is part of calculus by the way).