Here is a way to fold a pentagon from a circle that mimics the steps used in a traditional compass and straightedge construction. I took this from Oschene's marvelous blog of origami. The compass and straightedge construction isn't intuitive, but I think that folding removes some of the complexities. It seems like folding such things as angle bisectors and perpendicular lines is more intuitive than constructing them.

- Fold a circle in half twice. Line up the first crease when you make the second fold so the creases are perpendicular. Open.
- Fold the top of the circle down to the center of the circle creating the midpoint of the top radius.
- Fold a crease from the midpoint you just created to the rightmost point of the circle. Open.
- Bisect the angle between the new crease and the vertical crease by folding the new crease along the vertical one. Make sure the crease goes through the midpoint of the top radius. Open.
- Create a vertical fold where the latest crease touches the horizontal line. Two of the pentagon's vertices are defined by the points where this line touches the circle.
- Fold two edges of the pentagon. Open.
- Fold the circle in half along the line that connects the center of the circle to the vertex. Swing the left half of the circle behind the right.
- Transfer the vertices to the other half of the circle by folding along the edges again.
- Finish by folding the remaining edge.

- Oschene (aka Philip Chapman-Bell) blogs about origami. His site is full of fun and fabulous creations, often using curved folds.

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