19-Feb-1995
Unsolved Problem 8:
Is pi+e irrational?
The number pi is the ratio of a circle's circumference
to its diameter.
The number e is the base of natural logarithms
and is approximately equal to 2.71828.
It is the unique number a such that the derivative of
a^x is a^x.
A rational number is a number
that is the ratio of two integers.
All other real numbers are said to be irrational.
It is known that e is irrational and that pi is
irrational, but it is not known if their sum is
irrational.
Reference:
- [Klee 1991]
- Victor Klee and Stan Wagon,
Old and New Unsolved Problems
in Plane Geometry and Number Theory.
Mathematical Association of America. Washington, DC: 1991.
Page 243.
pi+e
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