For distances >600km, flying is usually 4x-10x faster at a similar price. At least in and around Germany. I assume in the US trains compare way worse, also because the distances are way larger.
Examples: "Normal" example: Stuttgart (Germany) -> Amsterdam (Netherlands) Train: 11h 10min - 241€ Plane: 1h 20min - 225€
Best case scenario for train in Germany at around that distance (because there's a direct connection): München -> Berlin Train: 3h 54min - 167€ Plane: 1h 5min - 226€
You can approximate the length of any path (including circles) by adding the lengths of many small line segments that follow that path. Making a line segment bigger by some factor, will increase it's length by the same factor. Therefore, scaling the circle by any factor, increases it's circumference by the same factor. Scaling a circle is just scaling it's radius so: Scaling the radius by some factor, changes the circumference by the same factor. That means the ratio between radius and circumference is always constant.
I hope this is decipherable :D