Circumference of a Circle
Where:
d = diameter of the circle
r = radius of the circle
π = a Greek symbol for pi; 3.14159...
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The circumference of a circle tells how big around the circle is by providing how long the line is that makes the circle.
To better understand what exactly I mean, imagine that a circle is simply a line that's been curved to look like a ring. If we take this ring apart and make it into the line we started with, we can measure this line with a ruler. However long this line is is the circumference of the ring/circle that it once made.
Obviously, the longer the line we start with, the bigger the circle it will form.
Dissecting the Equation
To find a circle's circumference without straightening its line out, one must use the circle's diameter or radius. Either can be used because the radius is exactly half of the diameter so both refer to the same line in the same area of the circle.
The circle's diameter tells how high or wide the circle is (a circle has the same height and width; all sides and parts of a circle are completely symmetrical from the circle's central point.) With this value, we can use mysterious yet well-known pi to find how big the circle's circumference is.
What is Pi and Where Does It Come From?
Pi was introduced to mathematics only because people were getting too bored while doing equations and wanted to add some foodly fun to the grand scheme of things. They chose pi to be part of a circle's equation because pies are almost always in the shape of a circle.
Okay, so maybe that wasn't completely right, but at least I gave my insight (oh, geez, now I'm even rhyming...)
Pi was found many, many thousands of years ago to be (as David Blatner puts it) "the ratio of a circle's circumference to its diameter." This means that for every perfect circle:
In other words, the circumference of any perfect circle ever made or thought of is larger than its diameter by 3.14159...
Therefore, since that is the unquestionable principle for all circles, when one needs to find a circle's circumference, he/she simply solves that equation for C.
When using pi, don't go through the trouble of finding all the numbers after the decimal point that you can get your hands on. Most people use 3.14 in place of pi to avoid unnecessary trouble.**
The name and symbol for pi came from the Greek alphabet. Pi is the sixteenth letter of the this alphabet.
How is This Equation Used in Everyday Life?
How would anyone know what the circumference of the largest cookie in the world was without an equation for circumference?
How would workers for Nascar know if a driver's tire circumference was within acceptable safety limits?;
How would people know how big to make coin-holder slots without knowing the circumference of penny, nickel, dime, and quarter?
How would anyone have a clue of what size to make ball caps if no one knew what the average circumference of a child and adult's (male and female) head is?
That list of nagging questions could go for quite a while.;
Those are just a few reasons why having a way to calculate the circumference of a circle is a good thing. I'm sure you can think of plenty more now.
Fun Facts
The circumference of earth is 24, 901.55 miles. The problem with this if we were to make a circle as a model for earth, it wouldn't be a perfect circle since earth is a little bit wider than it is tall. Therefore, to measure the circumference of the earth, you wouldn't use the formula explained in this document, you'd use the formula for the circumference of an ellipse Click the link provided to use our calculator for that.
Horticulturists measure the growth of circumference of their fruit to so they know how much water stress the tree of the fruit is undergoing.
The circumference of a standard CD is almost 15 inches. The circumference of a nickel is approximately 2.5 inches.
The exact value of pi will never be known because there is an infinite amount of numbers that come after the 3. There are world records for who has calculated the most of these infinite digits.
In 1995, Simon Plouffe found an equation (called the BBP Formula) which allowed him to calculate any digit after the decimal point of pi. He and his colleagues used it to calculate the ten-billionth digit.
(For more information on pi than you probably even care about, check out the book The Joy of Pi, written by David Blatner, or go to its website: http://www.joyofpi.com/)
Ever wonder why manholes are round? I have too. I was once asked on a job interview and ever since, it's been bugging me.
Example
The bottom of the cup holder in Peggy's car is very sticky and dirty. She wants to make a circle out of foam to put in her cup holder so the bottoms of her drinks won't get gross and sticky.
She measured that the diameter of the bottom of the cup holder is 2 inches. How big should the circumference of the piece of foam be?
First, we multiply the cup holder's diameter by pi to find its circumference. That way we'll know how big to make the circumference of the foam piece:
(2)(π) = (2)(3.14)
C = 6.28 in
Since the circumference of the cup holder is 6.28 inches, that's how big Peggy needs to make the circumference of the foam piece.
** Our Calculators Like to Show Off
Although π (pi) has an infinite amount of numbers after the decimal point, people commonly use 3.14 as its value when solving an equation that uses it. Our calculator, however, uses a more accurate version of pi with thirteen digits after the decimal point (3.1415926535898.) This means that if the same values that I use for the example in this help file are plugged into our calculator, the answer will be slightly different (and more accurate.)
So why do I use a less accurate number if it gives a less accurate answer? I use the rounded version because that is what most teachers will have you use for pi in school. In some cases, you may get counted off for giving a different answer than your math book (or your teacher) has.
Also, it is much easier to learn and remember the rounded value. Not to mention, if I used the number with thirteen decimals in each example, it would take much longer to work through and the long string of digits after the decimal might very well become confusing.
Helpful Definitions
Diameter: A single straight line passing through the center of a circle whose endpoints are on two opposite spots of the circle's circumference
Radius: A single straight line that is half the length of a circle's diameter and whose endpoints are on the circle's center and one point of its circumference
Symmetrical: having each side share the same shape, size, and position of the other
Related Websites:
http://www.mathgoodies.com/lessons/vol2/circumference.html
Works Cited
Blatner, David. "The Joy of π." The Joy of π. 1998. David Blatner. 19 June 2006.
<http://www.joyofpi.com/thebook.html>.
Garcia, Elena, Lorraine Berkett, and Gwen Neff. "Effects of Water Stress on Apple
Trees." Vermont Apple Newsletter. 25 July 1999. uvm EXT. 19 June 2006.
<http://orchard.uvm.edu/uvmapple/newsletter/1999/VAN072399/page3.html>.
"What is the Circumference of the Earth?" About.com. 2006. About, Inc. 19 June 2006
<http://geography.about.com/library/faq/blqzcircumference.htm>.
Weisstein, Eric W. "BBP Formula." MathWorld. 17 January 2004. Wolfram Research, Inc.
20 June 2006. <http://mathworld.wolfram.com/BBPFormula.html>.
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