You are really just "drawing" a bunch of tangents to the parabolic curve. When there are sufficiently many of them "drawn" the curve becomes evident. If you don't put enough creases in the paper, you will think the trick doesn't work, keep folding!

Mathematically the reason this works is because you are creating perpendicular bisectors for each of the segments that connect a point on segment to point B. These perpendicular bisectors are each at slightly different slopes within limits determined by the angles "n" formed at the endpoints of .

Here is a more visual description of what happens.

As the base angles approach 90 degrees, the tangents, or perpendicular bisectors, will approach 180 degrees. This is what gives you that gentle curve. Hopefully you see now why it is so important to "draw" lots of tangents.

The exact same thing happens on the other side as long as point B is above the center of .

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If you really want to understand why this works and you are still a bit confused, we strongly recommend playing with this. Experiment with placement of point B and the length of . As you experiment, you may come up with a better way to explain why it works. If you do, please let us know. We will publish your explanation with your name.

Hope this helped.

themathlab.com staff