POLYGONS AND CIRCLES Section: Geometry

1. CIRCLES AND POLYGONS (5-sided)

In the following window you can see that a regular polygon is found inside a circle that passes through all its vertices. This circle is called the circumscribed circle. There is also a circle which forms a tangent with the midpoints (M) of the sides which is called the inscribed circle.

1.- Rotate this polygon until the circumscribed and inscribed circles are drawn.
 The Init button will restore the initial values.

2. CIRCLES AND POLYGONS (4 and 8-sided)

In the following window you can see the circumscribed and inscribed circles of two polygons: a 4-sided one and an 8-sided one.

1.- Note that the more sides the polygon has, the closer it is in shape to the circle that circumscribes it.

2.- What are the circles like that circumscribe the square and the octagon?

 The Init button will restore the initial values.

3. CIRCLES AND POLYGONS (20-sided)

In the following window you can see the circumscribed and inscribed circle of a 20-sided polygon.

1.- Rotate the 20-sided polygon until the circumscribed and inscribed circles are drawn.

2.- Don't you think the polygon looks like a circle? It almost fits perfectly between the circumscribed and inscribed circles.

 When computers draw circles they are actually drawing many-sided polygons.
 The Init button will restore the initial values.

 Agustín Muñoz Núñez Spanish Ministry of Education. Year 2001