It is reasonable to assume that some type of ball game similar to football, from which the sport we know today developed, has been played somewhere on the planet (most likely China) for more than 3,000 years. I'd imagine that during this 3,000 years time period the rules and play field had varied. It's pretty much common sense (and tradition) that most sports that contain "goals" on either end will be rectangular in shape. How else would you accommodate a sport with this much activity happening and with two teams, one on either side ? Rectangular is the only answer because a square playing field would direct too much play to the sidelines and no concentrated focus on the goal of each opposing team. It could get pretty boring if it was any other shape. The actual dimensions of a modern sized Football pitch were written out by English FA in 1863.
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Originally to avoid the sun in either team's eyes. At a point in the game which may be critical, one team should not have an unfair advantage due to the sun, so they are built north/south