How to draw a regular pentagon with compass and straightedge I remember reading that Gauss managed to construct a regular pentagon with just a compass and straightedge, but I don't remember the particulars of how he did this. Could someone help me out and give me instructions on how to do this?

I'm not sure if this one is Gauss', but here's the one I use:


*

*Draw a circle. Let the center be $O$.

*Define a direction as "left" and draw a line from the center going "left" until you hit the circle. This segment is $OA$.

*Draw another line segment, this time going "up" (this is perfectly legal - you should know how to construct a perpendicular line to a segment). This segment is $OB$.

*Find the midpoint of $OA$, calling it $M$.

*Draw $BM$.

*Find the angle bisector of $BMO$ and draw until you hit $OB$. Call this intersection $I$.

*Draw a perpendicular line to $OB$ going "left" until you hit the circle at a point $C$. $BC$ is now one line segment of the pentagon and the rest is relatively simple (just draw circle centered around $C$ passing through $B$ to get third vertex, etc.)
Something like this:

