Lab 2

Lab 2: Paper Folding

I ask you to do the following folding problems by using only the properties that paper seems to have when folded and creased. The idea is to construct "lines" by creasing the paper and construct points from the intersection of two creases or by marking with a small pencil/pen dot. The term construct in this lab means by folding.

Materials:

You should have three 8.5"x 11" rectangles, a "scrap" of paper, a square, and a sheet of patty paper.

Using one of the 8.5"x 11" rectangles:

1. Draw any two points p1 and p2 by making dots with a pencil.

2. Construct a line L through points p1 and p2.

3. Draw any point p by making a dot with a pencil.

4. Construct a line L1 through point p and perpendicular to L.

Using the scrap:

5. Construct a rectangle. You need not cut or tear it out of the scrap.

Using the second 8.5"x 11" rectangle:

6. Construct a square. You need not cut or tear it out of the rectangle.

Using the square given to you:

7. Construct an equilateral triangle. Construct the folds so that they assure that the triangle is equilateral. You need not cut or tear the triangle out of the square.

Using the third 8.5"x 11" rectangle:

8. Draw a line M and a point q not on M. Then construct a line N that passes through q and is parallel to M. Construct the folds so that they assure that the line N is parallel to M.

Using the sheet of patty paper:

9. (Tangent Envelope) Mark a point P around halfway on the paper in a left-right direction and somewhere in the lower half of the sheet. Now, repeatedly do the following: Pick any old point on the bottom edge of the paper and fold it onto P. Then unfold. Choose a different point on the bottom edge of the paper and fold it onto P - Unfold. Repeat this procedure for enough different points on the bottom edge until the creases in the paper form a pattern. Describe the image formed.