1. Ancient Mathematics – Straightedge and Compass Geometry
Math Circles
Ancient Mathematics – Straightedge and Compass Geometry

2. 1. Creating a Perfect Square.
Create two perpendicular lines.
Draw a circle centered at their intersection.
Connect the four intersections of the circle with the two lines.
Congratulations, you have a square!

3. 2. Creating Parallel Lines.
Create two perpendicular lines.
Create another line which is perpendicular to either of the other two lines!
Congratulations, you have two parallel lines!

4. 3. Bisecting an Angle. Draw any two lines to create an angle.
Draw a circle centered at the vertex of the angle.
Draw two more identical circles at the intersections of the circle and angle arms.
Connect the vertex of the angle to the intersection of the two circles from the previous step.

5. 4. Creating a Regular Hexagon
Draw a circle and mark where the center is.
Draw a straight line at least as long as the diameter through the center of the circle.
Draw two more equally sized circles at the intersections of the circle with this line.
Connect all of the intersections as shown.

6. 5. Creating a Circle From Three Points
Draw any three points and connect to make a triangle.
Draw three identical circles, with their radii being more than half the length of the longest side of the triangle, each centered at one of the vertices of the triangle.
Connect the intersections of these circles with lines as shown.
Draw a circle centered at the intersection of these lines. You should be able to make it pass through all three points!

7. 6. Creating a Regular Pentagon