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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