Geography, geometry...

I don't know how many football pitches there are on the planet, but they are reassuring in their uniformity. As your plane comes in to land, in whichever town or city you might be, then sooner or later you will see a football pitch.

When the Laws of Association Football were first codified in 1863 the pich was a rather simple rectangle, albeit potentially a rather large one. There were two goal lines and two touchlines. The only other embellishments to the oblong, which could be up to 200 x 100 yards, were the goalpoasts (as now 8 yards apart) and the corner flags.
In 1865 a tape was introduced, stretched across the goal posts at a height of 8 feet.
In 1875 this tape was replaced by the crossbar.

By the time penalties were introduced in 1891, the halfway line and the centre circle had appeared.  The introduction of the penalty rule led to further markings on the pitch, as the original penalty-kick ruling was that the kick had to be taken from any point 12 yards from the goal line. All of the players – except the player taking the kick and the goalkeeper who could not advance more than six yards from the goal line – had to stand at least six yards from the ball. Thus a twelve yard line that covered the whole width of the pitch with a dotted 18 yard line. 
The curious 6 yard semi circles at the foot of each goal post marked an area in  which the goalkeeper might not be charged unless he was holding the ball or obstructing an opponent.
The goal net also appeared in 1891.


In 1902 the picture was almost completed as the penalty box and penalty spot are introduced after it was decided penalties would be awarded for fouls committed in an area 18 yards from the goal line and 44 yards wide. The six-yard box was also introduced (Hitherto, the area in which the goalkeeper might not be charged unless he was holding the ball or obstructing an opponent was bounded by semi-circles defining six yards from the goalposts. In future these will disappear and instead of them, lines will be drawn six yards into the field of play, and being joined together by a line drawn parallel to the goalline.
The space thus bounded off will be known as the ”goal area”. It will be seen that it is somewhat larger than the space which it replaces, so that the goalkeeper’s immunity from attack is slightly increased.
Eastern Daily Press of Monday 8 September 1902).


From 1905 Goalkeepers were  ordered to stay on their goal line for penalty kick and in 1907 the half way line became significant in the offside law for the first time.

Interestingly the introduction of the penalty area did not confine the handling activities of goalkeepers. Up until 1912 they could handle the ball (but not run with it rugby fashion) anywhere in their own half!
The pitch did not attain it's thoroughly modern appearance until 1937, when the arc at the edge of the penalty area was introduced to ensure players remained ten yards from the ball when a penalty was taken.