Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Continuous Numbers
Name: Jenny
Status: student	
Age:  N/A
Location: N/A
Country: N/A
Date: N/A 


Question:
What does it mean seeing as both Pi and e are both continuous numbers that when you take the equation:

Pi^E^Pi=319442279626

Does that mean something? Did I stumble upon the meaning of life? pi^e^pi is a meaningful number. It might be a little clearer with a couple of brackets though. You could write it (pi)^[e^pi] for example. Not too surprising that it appears to be irrational, i.e. cannot be written as a ratio of integers, which is the same thing as saying the digits never repeat. One can show that every fraction n/d where n and d are integers can be written as a repeating number. And the converse, every repeating number -- take for example -- 0.123123123123123... is a rational number i.e. is the ratio of two integers n/d.



Replies:
There are a whole bunch of numbers that are irrational, i.e. cannot be written as a ratio of integers. For example sqrt(2) to mention one example. It is the solution of the algebraic equation X^2 = 2.

There is another whole class of numbers that never repeat -- called transcendental numbers -- which like irrational numbers never repeats digits. But these numbers, like pi or e are not the solution to any algebraic equation. There is no general "test" by which to determine whether or not a number is transcendent.

Vince Calder



Click here to return to the Mathematics Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (help@newton.dep.anl.gov), or at Argonne's Educational Programs

NEWTON AND ASK A SCIENTIST
Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory