Here are some ideas about ways to draw polygons and stars within polygons.
You will need:
- Paper - such as firm card stock.
- Drawing and colouring pencils.
- A ruler.
- A protractor - a circular one is easier to use.
- Compasses.
- Scissors.
Draw a circle using the compasses, make sure that the radius is at least 10 centimetres so that your design is large enough to see clearly.
Decide how many sides you would like your polygon to have.
Divide the 360 degrees of the full circle by the number of sides you have decided upon. This will allow you to divide the circle into equal sectors. (E.g. If I decide on 5 sides - a pentagon, then 360/5 equals 72 degrees.)
Using your protractor, mark off your circle by the required number of degrees. For my pentagon, I would mark off a point at every 72 degrees.
Next join the points together to form your polygon. Here is my pentagon.
Draw a line, using the ruler, to connect alternate (every other) angles or corners.
The five-pointed star in my pentagon is called a pentagram. Do you think the star inside an octagon will have five points?
Inside the centre of the pentagram is a smaller polygon, what shape is it?
Repeat the steps of joining the angles. What do you think will happen?
Keep repeating the steps until you have the smallest polygon you can draw.
Try experimenting with some other polygons and stars. Next time you join the corners of the polygon try skipping a different number of points, perhaps joining every third one instead of second one together.
You can draw different types of polygons inside each other within the same circle and get some very interesting results.