My wife is putting together a simple gift for our niece. Lest I spoil a surprise, I'll be vague about the specifics. It required some hexagons. We started, logically, with an octagon.
I approached this mathematically. Find the midpoint on one edge, work an equal distance out either side, then connect the dots. Bam.
Wait...that didn't work.
So, I moved to a circle that represented the diameter of the octagon pieces. Well, a circle was hard because I didn't have a protractor to get the angles right. So, I moved to a rectangle with some right triangles taken out.
Well, with no protractor, it's hard to draw a 120 degree angle. I could do a mean 45 with the quilting square, though.
Admitting defeat, I jumped to the Google and found a number of posts by searching, "draw regular hexagon." The image searches were promising: one linked to a post from New Mexico State University which described how to draw a regular hexagon using a circle and a compass.
I went out to the garage and found a compass my grandfather probably had since before I was born that I snagged while cleaning out mom and dad's garage last year. It sat contentedly in our garage until called upon, after which it performed wonderfully.
This provided me a quick reminder on the mental dissonance between thinking I know how something should work and being able to describe how it actually works. The best thing is that the number of points on the circle is infinite, as long as the radius is known. The more points I draw, the closer I get to another circle. This blew my mind in Flatland, (apparently, there's now a movie?) and it blew my mind again when I did Saturday afternoon.
We're on our way to one sweet gift (all planned and executed by my talented wife).