Drawing an ellipse with string and pins

After doing this	Your work should look like this
Start with the height and width of the desired ellipse. The two lines are the major and minor axes of the ellipse. The major axis is the longer one.
1.  With the compasses' point on the center, set the compasses' width to half the width (major axis) of the desired ellipse. (This is called the ellipse semimajor axis).
2.  Move the compasses' point to one end of the minor axis of the desired ellipse and draw two arcs across the major axis.
3.  Where these arcs cross the major axis are the foci of the ellipse. Label them F1, F2.
4.  Put a pin in each end of the major axis (they will be moved later), and tie a string to them so that the string between them is taut. The best way to do this is to push the pin through the string itself if possible, rather than tying a knot.
5.  Leaving the string attached, move the pins to the focus points F1, F2. Put a pencil point against the string and pull the string taut with the pencil.
6.  Keeping the string taut, move the pencil in a large arc. The pencil will draw out the desired ellipse. To avoid the string catching on the pins, you may find it better to draw the upper and lower halves of the ellipse separately.
7.  Done. The ellipse will pass through the four initial points defining the ends of the major and minor axes.

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Other constructions pages on this site

• List of printable constructions worksheets

Lines

• Introduction to constructions
• Copy a line segment
• Sum of n line segments
• Difference of two line segments
• Perpendicular bisector of a line segment
• Perpendicular from a line at a point
• Perpendicular from a line through a point
• Perpendicular from endpoint of a ray
• Divide a segment into n equal parts
• Parallel line through a point (angle copy)
• Parallel line through a point (rhombus)
• Parallel line through a point (translation)

Angles

• Bisecting an angle
• Copy an angle
• Construct a 30° angle
• Construct a 45° angle
• Construct a 60° angle
• Construct a 90° angle (right angle)
• Sum of n angles
• Difference of two angles
• Supplementary angle
• Complementary angle
• Constructing  75°  105°  120°  135°  150° angles and more

Triangles

• Copy a triangle
• Isosceles triangle, given base and side
• Isosceles triangle, given base and altitude
• Isosceles triangle, given leg and apex angle
• Equilateral triangle
• 30-60-90 triangle, given the hypotenuse
• Triangle, given 3 sides (sss)
• Triangle, given one side and adjacent angles (asa)
• Triangle, given two angles and non-included side (aas)
• Triangle, given two sides and included angle (sas)
• Triangle medians
• Triangle midsegment
• Triangle altitude
• Triangle altitude (outside case)

Right triangles

• Right Triangle, given one leg and hypotenuse (HL)
• Right Triangle, given both legs (LL)
• Right Triangle, given hypotenuse and one angle (HA)
• Right Triangle, given one leg and one angle (LA)

Triangle Centers

• Triangle incenter
• Triangle circumcenter
• Triangle orthocenter
• Triangle centroid

Circles, Arcs and Ellipses

• Finding the center of a circle
• Circle given 3 points
• Tangent at a point on the circle
• Tangents through an external point
• Tangents to two circles (external)
• Tangents to two circles (internal)
• Incircle of a triangle
• Focus points of a given ellipse
• Circumcircle of a triangle

Polygons

• Square given one side
• Square inscribed in a circle
• Hexagon given one side
• Equilateral triangle inscribed in a given circle
• Hexagon inscribed in a given circle
• Pentagon inscribed in a given circle

Non-Euclidean constructions

• Construct an ellipse with string and pins
• Find the center of a circle with any right-angled object