The fact that this apparatus draws a straight line is the subject of Problem 3.3b . But, as pointed out above, straightness is a local property in that whether a segment of a line is straight depends only on what is near the segment and does not depend on anything happening away from the line. This will become particularly important later when we investigate straightness on the cone and cylinder. Think about what is important near the crease in order to have reflection symmetry. Figure 1.14 .
Reflection symmetry is local.
When we talk about straightness as a local property, you may bring out some notions of scale. For example, if one sees only a small portion of a very large circle, it will be indistinguishable from a straight line. This can be experienced easily on many of the modern graphing programs for computers. Also a microscope with a zoom lens will provide an experience of zooming. This property is called infinitesimally straight , or in more standard terminology, differentiable .