The circumference of the center circle of a soccer field is pi times its diameter (which is 10 yards). It could also be expressed as 2 times pi times its radius (which is 5 yards). It's about 31.416 yards.
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The diameter of the center circle on a regular soccer field (100x60 yards) is 20 yards.
So soccer has the circle in the middle of the field. That is related to pi because it is a circle. That is how they are related!
Given a positive charge the electric field lines are drawn starting from the charge and pointing radially outward, ending in principle at infinity, according to the electric field strength being proportional to the inverse square of distance. From the definition of electric field we know that the modulous of the electric field is greater for smaller distances from the field generating charge. Since the electric field lines point radially outward we consider the density of lines an indication of the strength of the electirc field. If we immagine to trace a circle around the electric field generating charge, of radius slightly greater than the radius of the object which holds the charge and therefore generates the electric field, such circle will be crossed by a number 'n' of lines. The density of lines crossing the cirle will then be the circumference of the circle divided by the number 'n' of lines. For a larger circle we will have a greater circumference, but same number of lines 'n', and therefore a smaller density of lines crossing it, which idicates a lower intesity of electric field for a greater distance from the charge.
The outer circle of a football field is the border of the field. When the players step outside of the border, the play stops.
I'm not sure of the proof. Wikipedia has an extensive article on pi, it's history and calculation methods. Pi is the ratio of a circle's circumference to its diameter. It is an irrational number, so it cannot be represented exactly as a decimal or a fraction, but only carried out to a decimal approximation. The decimal 3.14 is a pretty good approximation to the true value. If you take a circle with a diameter of 100 yards (the length of a football field), then calculate the circumference using the approximation of 3.14, you will be off from the actual length of the circumference by about 5 3/4 inches. Using another popular approximation [22/7] will get you within 4 9/16 inch of the actual circumference. Using the popular approximation of 3.1416 will arrive at a calculation which is within 1/32 inch of the actual circumference.