Dividing the circumference of a circle by its diameter will always give pi because that's how pi is defined.
"By definition, pi is the ratio of the circumference of a circle to its diameter. Pi is always the same number, no matter which circle you use to compute it. "
I'll just add if you want an illustration of putting the cart before the horse that is quite a good one. As stated, Pi is a result, not a cause. Being of fixed design all circles must share the same properties, only varying in size but no other qualities. (see above references, they'll include this I'm sure).
"The constant is named "π" because "π" is the first letter of the Greek words περιφέρεια (periphery) and περίμετρος (perimeter), probably referring to its use in the formula to find the circumference, or perimeter, of a circle."
People aren't understanding the intent behind the question here.
The number pi has the same relationship to a circle as the number 4 does to a square. Just as if you were to divide the perimeter of a square by its width you would always get the number 4, dividing the circumference of a circle by its diameter you will always get the number pi. This relationship can be used to determine other properties of the square or circle such as the square area.
To further understand the relationship between the number pi and a circle:
Try using the apothem (the distance from the center of a square to the mid-point of any side) of a square to get the area of the square. The formula is similar to that of the formula used to get the area of a circle.
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