First we will need a piece of wax paper, about 12 inches by 12 inches. We will also need a ruler and a permanent marker. Don't worry, the marker is NOT for drawing the curve, just for setting up the creation surface.
Draw a segment across the wax paper. The segment should be about 3 inches above the bottom of the paper.
Draw a dot about 2 inches above the line.
Now take the left side of the paper and fold it until the leftmost point of the segment is touching the dot. Now crease this fold being careful not to rip the wax paper.
If you open the wax paper at this point, you will see that you have "drawn" a straight line without using a writing utensil.
The next "line" will be made by folding again. This time move the fold so that the point about 1/4 inch from the leftmost point on the segment is now touching the dot. Again crease the wax paper being careful not to tear it.
The third "line" will be made the same way. Slide the paper 1/4 inch along the segment, staying on top of the dot. Crease to form the line.
It will take a while, but as you continue to slide 1/4 inch and crease, your wax paper will begin to "turn". The curve will become evident after about 15 creases.
Here you can see the "turn" starting.
The sexyness is starting to appear!
After about 25 folds, your paper may get a bit tired. Be sure your hands are not moist or too rough so as to cause a rip.
You are almost there!
You are finished when you reach the rightmost point of the segment.
Assuming your segment was 12 inches long and you slid 1/4 inch each fold, you will have 48 "lines". These lines are each touching, or tangent, to the sexiest of all known curves.
You will see it when you open your wax paper. This curve is called a PARABOLA.
We will be exploring the Algebra behind this curve in the Quadratics section of our Algebra course.
You can use light in various ways to display your curve(s). A simple window works well.
Colored acetate placed on top of your curve and held up to a window creates great effects too.
Try some variations
You will get other parabolic curves if you place the dot in different spots in relation to the segment.
Here we see one placed about 7 inches from the segment.
Here the dot is placed to the right of center.
Here the dot is placed about 1 inch away from the segment.
We hope you give this a try. We are sure you will enjoy the results you get.
Have fun drawing WITHOUT A WRITING UTENSIL!
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If you are really curious as to HOW this creates a parabola, check this out.
