Folding Polygons From a Circle. A circle cut from a regular sheet of typing paper is a marvelous manipulative for the mathematics classroom. Instead of placing an emphasis on manipulating expressions and practicing algorithms, it provides a hands-on approach fro the visual and tactile learner. .
A circle cut from a regular sheet of typing paper is a marvelous manipulative for the mathematics classroom. Instead of placing an emphasis on manipulating expressions and practicing algorithms, it provides a hands-on approach fro the visual and tactile learner.
1. Mark the center of your circular disk with a pencil. Fold the circle in half. What is the creased line across the disk called? Fold in half again to determine the true center. What are these two new segments called? What angle have you formed? Unfold the circle. How many degrees are there in a circle? Was your estimate of the center of the circle a good one? Compare your result with that of your neighbor.
2. Place a point on the circumference of the circle. Fold the point to the center. What is this new segment called?
3. Fold again to the center, using one endpoint of the chord as an endpoint for your new chord.
4. Fold the remaining arc to the center. What have you formed? Compare your equilateral triangle with that of your neighbor. Throughout of the rest of this activity suppose that the area of your triangle is one unit.
5. Find the midpoint of one of the sides of your triangle. Fold the opposite vertex to the midpoint. What have you formed? What is the area of the isosceles trapezoid if the area of the original triangle is one unit?
6. Notice that the trapezoid consists of three congruent triangles. Fold one of these triangles over the top of the middle triangle. What have you formed? What is its area?
7. Fold the remaining triangle over the top of the other two. What shape do you now have? What is its area? The triangle is similar to the unit triangle we started with.
8. Place the three folded over triangles in the palm of your hand and open it up to form a three dimensional figure. What new shape have you made? What is its surface area?
9. Open it back up to the large equilateral triangle you first made. Fold each of the vertices to the center of the circle. What have you formed? What is its area?
10. Turn the hexagon over and with a crayon, pen, or pencil shade the hexagon. Remember what the area of this hexagon is when compared to the original equilateral triangle. Turn the figure over again. Push gently toward the center so that the hexagon folds up to form a truncated tetrahedron. What is its surface area?
11. Using only the fold lines already determined, create different polygonal figures and determine their area. Using only the existing fold lines, can you construct figures with the following areas? Are there any others? If so, sketch them.
1 , 1 , 19 , 2 , 3 , 7 , 8 , 7 , 23
4 2 36 3 4 9 9 18 36
12. You can tape twenty truncated tetrahedra together to make an icosahedron. There will be five on the top, five on the bottom, and ten around the middle.
Other vocabulary that might be used: