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regular pentagon
The film strip shows the steps in the construction of the regular pentagon.

Copy this straight edge and compass construction for yourself and explain why it produces a regular pentagon.

The description of the construction below, and the information in the notes, should help you to explain the construction.
Full Screen Version
This text is usually replaced by the Flash movie.
Here are the steps shown in the film sequence:

1. Draw a circle $C_1$ centre $O$ diameter $PQ$.

The circle $C_1$ has radius 1 unit; what is its equation?

2. Draw the perpendicular bisector of $PQ$ cutting $PQ$ at $O$ and $C_1$ at $A$ and $Y$.

3. Draw perpendicular bisectors of $PO$ and $OQ$ cutting $PQ$ at $R$ and $S$.

Find the length $YS$

4. Draw circles $C_2$ and $C_3$ centres $R$ and $S$ and radii $RO$ and $SO$.

5. Join $R$ and $S$ to the point $Y$ cutting $C_2$ at $T$ and $U$ and $C_3$ at $V$ and $W$.

6. Draw circle $C_4$ centre $Y$ radius $YW=YU$ cutting $C_1$ at $D$ and $C$.

What is the equation of $C_4$? Find the value of $y$ at the intersection of $C_1$ and $C_4$ .

7. Draw circle $C_5$ centre $Y$ radius $YT=YV$ cutting $C_1$ at $E$ and $B$.

What is the equation of $C_5$ ?

Find the value of $y$ at the intersection of $C_1$ and $C_5$.

At $B$ and $E$ $x^2 + y^2 +2y +1 = 2y + 2 = (3 + \sqrt 5)/2$ so

8. Join $AB$, $BC$, $CD$, $DE$, $EA$.

How would you adapt this construction to produce a regular decagon?