How Do You Draw A Pentagon

3 Answers 3

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I think this is the easiest way to draw a regular pentagon with just a compass and straightedge. enter image description here

answered Jan 18 '17 at 11:17

SeyedSeyed

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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:

grg

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answered Jan 18 '17 at 3:59

pie314271pie314271

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I only know two constructions. The first I learned in high school and involves straightedge and compass: enter image description here

The other I learned in college as I studied compass-only (Mohr-Mascheroni) constructions. Ironically the compass-only construction is one of the simplest constructions Ive seen, only requiring 10 circles, the line-segments at the end are cosmetic.

enter image description here