The Folding Circle

©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources

1. Fold the circle in half.What the name is for half a

circle?

©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources

2. Fold the circle into fourths.3. Unfold the circle and mark the center.4. Draw a line from one edge of their circles

through the center to the other edge. What is the term for this line?

5. Draw a line from the center of the circle to one edge.

What is the term for this line?6. Fold the edge of the circle down so that it

meets the center.7. Draw a line on the resulting fold.

What is the term for this line?

©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources

8. Fold down another edge to the center so that the resulting shape looks like an ice-cream cone.

9. Fold down the final edge. What shape have you created?

©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources

10.Fold one vertex of the triangle down so that it touches the center of the opposite side. What shape have you created?

11.Fold one of the acute vertices of the trapezoid over so that it meets one of the obtuse vertices.

What shape have you created?12. Even numbers: Fold one of the acute

vertices of the rhombus so that it touches the other acute vertex. Odd numbers: Unfold that shape back to the original triangle.

Compare the two shapes.

©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources

13. Unfold the circles back to the original large triangle.

14. Fold the three vertices of that triangle in so that each is in contact with the center point. What shape have you created?

©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources

Folding 3 diameters

A. Fold circle in half. B. Fold one corner point over making 2 equal parts. C. Fold unfolded part behind and even up points and edges. Crease only when the edges, points and circumference are even. One fold on top, in middle, and one on the bottom, like a “Z”.D. This folds the semi-circle into thirds. Open to find 3 diameters.

1

11

A.

B. C.

D.

©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources

Make a sphere

A. Bring 2 end points of one diameter together, hold them closed with a bobby pin..B. Bobby pin 2 of these folded circles together in the same way, on the straight edges showing a square, or quadrilateral pattern that moves on perpendicular axis, reflecting first fold of circle. C. Join 2 sets of 2 together, straight edges joined with bobby pins. This makes a sphere of open triangles and squares, a Vector Equilibrium, traditionally called a cuboctahedron.

+

bobbypin

bobby pin

A. B.

+C.

©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources

Make a tetrahedron

1.Fold 3 diameters into the circle. 2.Fold 3 alternate points on circumference (ends of diameters) to the center point. Crease well. 3.Fold each end point of the triangle to the midpoint on the opposite side. Do all 3 points separately. Do not overlap these folds. Crease well each fold with a straight edge. 4.Bring end point together forming a tetrahedron. Tape along edges to hold together.

tape

End point Edge line

Surface plane

Viewing symmetry of the tetrahedron

Fold over 3 points to center point

Fold over 3 points to center of opposite side

Bring 3 points together

©2009, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia Adapted from Various Sources