The scariest part of all is that someone thought it was a good idea.
One lecture during my calculus course was used to prove that pi was irrational. For e, the Euler number, the proof that it is irrational takes me about half a page and 5min - 1 min to think about the structure of the proof and 4 min to write it down correctly. For pi, the effort is much larger, and, as better mathematicians have written, this says something about the depth of irrationality of pi compared with e. pi "behaves" more like a rational number while e is more deeply irrational. Some of the most deeply irrational numbers have the form: sum of 10^(-n^2) with n from 0 to infinite, that is1.10010000100000010...with the number of zeros between the ones increasing from 2 to 4 to 6 and so on. There is no further proof needed to see that this number is irrational, there is obviously no periodicity in the decimal representation.
Post a Comment