Circles

From EscherMath
Revision as of 07:31, 7 February 2009 by Barta (talk | contribs)
Jump to navigationJump to search

Some Examples

A circle is a set of points that all lie at the same distance from a fixed point, called center. Circles come in all different sizes. We sometimes measure the distance from the center to the point on the circle and this distance is called the radius.

Circles show up in everyday life and below are some examples. In the top row we start of with the circle we just described. It has center C, radius r and a point P on the circle. Next to it is a roud sign for a round about. this is a place where the rooad forms a circle and in the sign the circle is made up of three curved arrows. Another example of circular shapes is a coin. Here we show a quarter, but if you check any loose change you - or your friend - may have in his/her pocket you will see that all our coins are circular in shape.

In architecture and design circular chapes can be used. The example shown on the bottom row is a circular patio with a fountain in the center. If you have ever done any do-it-yourself work you will recognize the circular saw shown on the bottom row. Aas the name says, the saw is shaped as a circle. Finally on the bottom right we have included a print from MC Escher. It is called Circle Limit III and is one out of a series of 4 prints.


Circles and circular shapes
Circ1.png Circular Intersection.png Circle-Quarter.png
Circle with center C and radius r Road sign: circular intersection A Quarter
Circular-Patio.jpg Cirkelzaagblad.jpg Circle-Limit-III.jpg
Circular Patio Circle Saw Escher's Circle Limit III

Drawing Circles

We can ask several types of questions about the circle. One may be that we want to draw a circle to have one shape inside and the other outside the circle. We have done an example for you and you can see the pictures that go with it below.

What if a center is given with a triangle T and a polygon P1, and we want the circle big enough so that P1 lies inside the circle and T lies outside the circle? In this case that can be done and the circle is shown in the picture on the right.

Drawing Circles
Circle-poly1.svg Circle-poly2.svg
Triangle T, Polygon P1 and the center The circle drawn in so that T lies outside and P1 inside the circle