I have been a enthusiast of geometry for a long time and over the years some friends and I developed a "Construction by Folding program for solid forms. The idea that I would like to showcase is this:
"In the process of spinning an axis in defined, there is the truest form of the straight line you can have and it is the quickest way to it".
For this work, it really is play, we need a standard circle size, one that can be produced with ease over and over. I suggest the use of a dinner plate or something that will not be misplaced and always handy.
Circles can then be traced on a blank page as needed with a #10 coffee can for instance.
The circle after it is cut out can be folded in half, this develops two semicircles
and a diameter. Please notice that if the two semicircles are equal then the
line separating them is the longest possible cord that can cut the circle.
Conversely only the longest possible cord can be the diameter and cut the
circle into two equal parts.
The CENTER is not yet defined, this can be done in two ways. Spin the circle or fold the circle twice thus two diameters cross.
The act of folding is a rotation. The straight lines are axis and are artifact of the fold (spin). Any two diameters so defined will mark off the corners of a rectangle at the circumference. When the folds occur at right angles thus a SQUARE is defined.
