Finding the CircumferenceDate: 11/27/97 at 13:30:48 From: Shae Godfrey Subject: Circumference Would you be able to tell me how to work out the circumference of a circle? Date: 11/27/97 at 17:49:10 From: Doctor Luis Subject: Re: Circumference Basically, the "circumference" of a circle is the distance around it. There is a way to calculate the circumference if you know another geometric length called the radius. Here's a diagram of a circle (sort of). Okay, it's not a circle, but it's as close as I can get with these characters. :) So suppose it's a circle... * * Do you see the "+"? It represents a special point * * on the circle, called the "center." The reason it's * r * a special point is that if you make a line from *-----+ * the center to a point on the circle, that line * * is going to have the same length no matter what * * point on the circle you choose. Those special lines * * are called "radii" (pronounce the "ii" as an "e" followed by an "i"). If you're only talking about one of these lines then it is called "radius". Here, on the diagram, I called it the radius "r". (Notice that there are an infinite number of these "radii" but their lengths are the same) There is another special line that is associated with the circle, and mathematicians have called it the "diameter". It is simply a line segment from one point on the circle to another point on the circle that also passes through the center of the circle. It looks something like this, * * If you look carefully, you can see that the diameter * * (I called it D on the diagram) is in reality one * D * radius from the center to a point on the circle, *-----+----* and another radius from the center to the OPPOSITE * * point on the circle. So you see, the length of * * the diameter is twice the length of the radius. * * Now, what about the circumference? Well, that's just the curved line around the circle. This means that if you cut your circle at one point and straighten it so that it becomes a straight line, the length of that line is going to be the length of the circumference. |<--- Circumference --->| -------------------------------- It turns out that circles have a very curious property. If you take the diameter of ANY circle (no matter what size), the number of diameters that fit in the circumference will be the same for ANY circle (try to verify it yourself with two pieces of string). Actually the diameter will fit about three times into the circumference, but not EXACTLY. There will be a small part of the circumference left. diameter ---------- circumference -------------------------------- three diameters ------------------------------ Mathematically speaking, we say that the ratio of the circumference to the diameter is constant (the same number) for all circles. This constant is very famous in mathematics, and it appears unexpectedly in a lot of theorems and equations. Even the Egyptians knew about it thousands of years ago (they said it was 22/7 although we know it's a little less than that). The Greeks also knew about this constant and calculated it to better accuracy using geometrical methods. Mathematicians like to call this constant "pi" (pronounced like "pie"), after the Greek letter "p". This number pi is a very interesting number that people have studied extensively. It is an irrational number. Essentially, that means you cannot write it as a ratio (you can't get pi by dividing two integers). The implication of that is that we will never know the exact value of pi - we will always be off the true value. We can only get increasingly accurate estimates of what pi is, and people have written programs and found pi to millions of decimal places on the most powerful and fastest computers. (for most purposes we only need fewer than ten decimal places). Well, how does all of this help us calculate the circumference of a circle? Simple, you know that the circumference divided by the diameter is the number pi for any circle, and so pi = Circumference / Diameter or circumference = pi * diameter So, if you know the diameter of the circle you can get the circumference just by multiplying by pi (which is approximately 3.14159... ) . Remember that, diameter = 2 * radius and so circumference = pi * (2 * radius) = 2 pi * radius or simply C = 2 pi r This is the way you'll find it in most books, in terms of the radius. -Doctor Luis, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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