Ellipse Paper Folding Activity - ALEX
Title: Ellipse Paper Folding Activity
Purpose: Students will use paper folding to discover an ellipse and how the distance between the foci and the shape of the ellipse are related.
Materials: Wax paper, ruler, fine-tip markers, scissors
Directions:
1. On a piece of wax paper, patty paper, or transparent paper, construct a circle using a compass or circular shaped object.
2. Label the center of your circle A.
3. Create another point INSIDE the circle, not too close to the center.
4. Label this point F. (This is your focal point.)
5. Fold the paper so that point F is anywhere on the circumference of the circle. Make a crease in the paper.
6. Open the paper and place point F on another point on the circumference of the circle. Make another crease in the paper.
7. Continue this process many times around the circle. (It is sometimes easier to slide the point around the circle, making creases every few millimeters.)
8. Once many creases are made, an ellipse should appear within your original circle. (If you cannot see an ellipse yet, continue folding, making your creases closer together.)
9. After all the folding is completed, draw the outline of the ellipse on your wax paper.
Now use your figure to answer the following questions:
1. The creases on your circle form the outline of what appears to be a /an _______.
2. Where is/are the focus/foci?
3. Fold your circle in half. Unfold, and repeat in a different direction. When it is unfolded, notice that your two folds are the diameters of the circle. Mark the point of intersection of the diameters with the permanent marker.
What is this intersection called?
4. Compare your ellipse to ellipses constructed by other students. What do you notice about the ellipse’s shape and the distance between the two points?
5. What do you think your figure would look like if the two points were on top of each other?
Each of these two points is a focus of the ellipse, and the two foci determine the ellipse. An ellipse is defined as the set of all points in a plane, the sum of whose distances from the foci are constant.
Test this with your ellipse.
1. Mark a point on your ellipse.
2. Use your ruler to measure the distance from each focus to this point.
3. Add these distances and record your results._____________
4. Repeat this for three other points on the ellipse.___________,
_____________,____________
5. What do you notice about these sums?
6. Suppose the two foci were on top of each other. Describe how the distance from the foci to a point on the edge of the figure is related to the figure.
Think About It
If you moved Point F closer to the edge of the circle and folded another curve, describe how you think the curve’s shape would change.
If you moved Point F closer the center of the circle and folded another curve, describe how you think the curve’s shape would change.
How does this paper folding construction work?
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