Construct a Parabola Using Circles

Here is a novel way to construct a parabola.

Materials

• Cardboard
  
• Paper
  
• Pushpin
  
• Pencil
  

Steps

1. Cut out the circles from the pattern.
   
2. Tape a piece of paper onto cardboard.
   
3. Draw a horizontal line near the bottom of the page.
   
4. Push a pushpin into the paper at a point above the center of the line and slightly lower than the diameter of the smallest circle.
   
5. Place a circle onto the paper so that it simultaneously touches the pushpin and the line.
   
6. Poke a hole at the center of the circle. Repeat with the circle on the other side of the pushpin.
   
7. Repeat for each circle.
   
8. Connect the pinpricks to form a parabola.
   

Notes

• One definition of a parabola is the set of all points equidistant to a fixed line (called the directrix) and a fixed point (the focus.) The centers of the circles in this project ensure that this condition is met. When the circle rests on the line and touches the focus, the center of the circle is the same distance from both. After all, the radius of a circle is the same in all directions.