Assignment 11. Geometric Constructions 1

For submission

1. Show that a sheet of paper can be folded into quarters under the rules of the paper folding scheme in the chapter.

2. Show that the a sheet of paper cannot be folded into fifths under the rules of the paper folding scheme in the chapter.

3. A circle can be inscribed in a square so it touches all four sides. Use this fact to determine if a circle can doubled in area, i.e. form a circle of double the area.

4. A sphere can be inscribed in a cube so it touches all 6 sides. Use this fact to determine if a sphere can be doubled in volume.