If any part of the football crosses the plane of the goal line it is considered a touchdown.
Nope. The ball has to cross the goal line while in the players possesion.
The line that crosses the y-axis is called the intercept.
the line that crosses the equator is called the PrimeMeridian (PM)
the goal line
The football need only "break the plane of the goal line". If any part of the ball crosses the goalline, it's a touchdown. The entire ball does not have to cross.
As long as the football crosses the plane of the goal line while legally under control in the ball carrier's possession, it's a touchdown regardless of where the player's body is (unless he goes out of bounds before the ball crosses the plane).
it is not a touchdown because the ball never broke the plane.
According to referee Ed Hochuli who is quoted in the article that you can read at the 'Touchdown or No Touchdown' link below, a player who crosses out of bounds is awarded a touchdown if a part of his body touches in the end zone, or the pylon, after the ball crosses the 'imaginary' goal line outside the pylons. I interpret the question to ask if a player lands completely out of bounds but the ball crosses the 'imaginary' goal line outside the pylon, is it a touchdown? The way I understand what I read, the answer is no since no part of the player touched inbounds. Click on the 'Touchdown or No Touchdown' link to read the article and weigh in with your opinions. If I'm understanding your question right, you're asking about the hypothetical goal line that "travels around the world" indefinitely out of bounds. The NFL just changed this rule for the 2008 season, so that the extended goal line no longer exists. The player must now break the plane of the goal line within the field of play, or press the ball against the corner pylon, for the touchdown to count.
The x intercept
Only if the kicked ball doesn't go beyond the line of scrimmage or a defensive player touches the ball after it crosses the line of scrimmage.
The point where a line crosses the x-axis is called the x-intercept.