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Why does pi = circumference divided by diameter?

Question #110453. Asked by kairie123.
Last updated May 13 2021.

avatar
merlin321
Answer has 7 votes
merlin321
16 year member
103 replies avatar

Answer has 7 votes.
Every circle ever drawn, regardless of its size, will always produce the magic number PI when you divide its circumference by its diameter.

link https://en.wikipedia.org/wiki/Pi#Definition

Response last updated by looney_tunes on May 13 2021.
Nov 03 2009, 2:51 PM
Watchkeeper
Answer has 8 votes
Watchkeeper
18 year member
412 replies

Answer has 8 votes.
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. "

link http://mathforum.org/dr.math/faq/faq.pi.html

Nov 03 2009, 4:54 PM
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satguru star
Answer has 5 votes
satguru star
Moderator
21 year member
1250 replies avatar

Answer has 5 votes.
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).

Nov 03 2009, 5:16 PM
queproblema
Answer has 6 votes
queproblema
19 year member
2119 replies

Answer has 6 votes.
"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."

link https://en.wikipedia.org/wiki/Pi#The_letter_.CF.80

Nov 04 2009, 11:03 AM
2NDS0N
Answer has 26 votes
Currently Best Answer
2NDS0N

Answer has 26 votes.

Currently voted the best answer.
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.

Area of a square: 4 * (apothem)^2

Area of a circle: pi * (radius)^2

Nov 27 2013, 7:37 PM
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