Explorations of the Circle
Date: 02/09/99 at 20:59:03 From: Garrett Hill Subject: Math I want to know what pi means. I am studying about circles, like about chords and radius. I would like to know the definition of circle and whether there is something else to use instead of radius, chord, diameter, and center. Sincerely, Garrett Hill
Date: 02/09/99 at 23:16:41 From: Doctor Kate Subject: Re: Math Garrett: You're asking some of the same questions that people have asked for thousands of years. They're very interesting questions. A long time ago the Greeks wondered what pi was, and a lot of people tried to find out, by trying to draw circles and squares with the same area. Even in this century, people have claimed that they've discovered that pi is 22 divided by 7. Pi is the ratio of the circumference of a circle to its diameter. That is, if you have a string the length of the circumference, Pi is how many times it will cover the diameter. It's a little bit more than 3. But Pi has all sorts of other strange properties. It's a number that you can never write all of. (That's why we just say "Pi" instead of writing it down.) If you start to write Pi, it looks like 3.141592653589 but that's only the beginning of it. It goes on forever. But what's the definition of a circle? Well, here's one interesting way to think of it: Put a thumbtack or a nail in a tabletop and tie a string to it. Tie the other end of the string to a pencil. Now pull the pencil as far away from the nail as you can and put the point on the table. The string will stop you from pulling too far. Now if you move the pencil while keeping the string pulled tight, you can move it around the nail and it will draw a circle. You should try this (ask before you put a nail or a thumbtack into someone's table, though.) Now, if we think of drawing a circle this way, we will realise that the pencil is always a certain distance from the nail - the distance is the length of the string. So you could define a circle this way: It's made up of all the points that are the same distance from the centre point. If you draw a point on a piece of paper (the centre point) and then use your ruler to draw other points (whichever ones you like) that are exactly 3 centimetres from the centre point, you'll find that you start to get a circle once you've drawn lots of these points. If you could draw enough points, you could "fill up" this whole circle. There are lots of ways to define a circle, but I like that one myself. Now for your last question: What else is there besides radius, chord, diameter and centre? Well, you can make up anything you like. You could draw triangles and squares inside circles, or put circles inside squares. You could make a circle inside another one with a radius half of the big one. You could make spirals instead of circles. You could try to figure out what the area of a circle is. There are always lots of things to explore. Here's something to try once you've tried making a circle with a nail and string: try putting TWO nails in a board or a tabletop, and then tying a string in a loop around the two nails. Then put your pencil in the string and pull it tight (so you have a triangle made of two nails and a pencil in a loop of string). Now try moving the pencil while keeping the string tight. What shape do you draw? Have fun! - Doctor Kate, The Math Forum http://mathforum.org/dr.math/
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