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Drawing Conic Sections with Push Pins and String

I already shared how to make conic sections with clay. Here is another fun way to make conic sections. In this activity, we draw conic sections using:

  • thick cardboard, cork board, or other surface that you can put a push pin into (I’ve tried foam board insulation, and that works well.)
  • paper
  • push pins
  • loops of thread or string
  • pens or pencils

Before doing this activity at my after-school math club, I asked the kids to describe how to draw a circle without using the word “round”. They struggled with this, so we talked about the fact that every point on a circle is equidistant from the center.

To draw a circle, place your paper on top of the cardboard and put a push pin in the center. Place a loop of string around the push pin and the pencil.  Pull the loop tight and draw a circle around the push pin as shown in the video below.  Make sure you string isn’t too long or you will run off the paper, and be careful that the loop doesn’t slip off of the push pin.

Vary the length of the string to see how that changes the circle.

Now, place two push pins on the board, and loop the string around both pins. The resulting shape is an ellipse. The two push pins are the foci of the ellipse.  Try varying the distance between the push pins and the length of the string.

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The circle is the case where both foci are in the same spot. Moving the foci apart, give the ellipse. Now, imagine moving one of the foci out to infinity. Of course, this isn’t possible in practice, but you can move one end of the loop far away. Make a long loop of string, and attach one end to a chair or table, or have a friend hold it, making it almost tight. Now use your pen to pull it tight to the side of the paper and draw around the other push pin. This creates a parabola – the conic section with one foci at infinity.

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Test Your Hand and Eye

Ready to see how good you are at drawing circles and finding the center of circles and angles, or making 90o angles? Here are two online games to try.

The Circle Drawing Experiment allows you to draw circles and then gives you a score based on how well the relationship between perimeter and area of your circle matches a perfect circle. And, it includes cute cat pictures! Hint: larger circles give better scores.

CircleDrawingExp

The Eyeballing Game asks you to use your “eyeballing” skills to make parallelograms, find midpoints of lines, bisect angles, and more.

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Just be careful! These games can be addictive!