Examples
include pi and the number e that is used as the base
for natural logartihms.
But irrational surds such as root two are not transcendental since
any root is defined as the solution of a polynomial equation. (eg
root two is the positive solution of x-squared=2)
You
might find proofs that pi and e are transcendental in an introductory
Analysis text, or by exploring the links to various web-based analysis
course materials.
If you have come across any good web-based illustrations of these
and related concepts,
please do let
us know and we will add them here.