Circle with Center π, e
The circle with center at π and e is a circle in the Cartesian coordinate system centered at the point (π, e). The equation of this circle is given by (x - π)^2 + (y - e)^2 = r^2, where r is the radius of the circle.

Rational Points on the Circumference
To find the rational points on the circumference of this circle, we need to consider the coordinates of points that lie on the circle and have rational values for both x and y. In other words, we are looking for points with coordinates (x, y) such that x and y are both rational numbers.

Analysis of Rational Points
Since the center of the circle is at the point (π, e), any rational point on the circumference will have coordinates that are a rational distance away from this center. This means that the radius of the circle must also be a rational number in order for there to be rational points on the circumference.

Conclusion
In conclusion, the number of rational points on the circumference of a circle with center at π and e will depend on the radius of the circle. If the radius is a rational number, there will be infinitely many rational points on the circumference. If the radius is an irrational number, there will be no rational points on the circumference.