Page:Geometric Exercises in Paper Folding.djvu/19



1. The upper side of a piece of paper lying flat upon a table is a plane surface, and so is the lower side which is in contact with the table.

2. The two surfaces are separated by the material of the paper. The material being very thin, the other sides of the paper do not present appreciably broad surfaces, and the edges of the paper are practically lines. The two surfaces though distinct are inseparable from each other.

3. Look at the irregularly shaped piece of paper shown in Fig. 3, and at this page which is rectangular. Let us try and shape the former paper like the latter.

44. [sic] Place the irregularly shaped piece of paper upon the table, and fold it flat upon itself. Let X' X be the crease thus formed. It is straight. Now pass a knife along the fold und separate the smaller piece. We thus obtain one straight edge.

5. Fold the paper again as before along BY, so that the edge X' X is doubled upon itself. Unfolding the paper, we see that the crease BY at right angles to the edge X' X. It is evident by superposition that