After enjoying the summer, I got to thinking about a 20° angle I ran into last year, which had an arc length of π. I wondered, "Would it really be so impossible to straighten out an arc and geometrically produce a line segment the length of pi?" If 2πr equals the length of a circle’s circumference, then a semicircle with a radius of 1 would have a 180° arc equal to π. My 20° angle goes into 180° nine times, so by having a radius of nine, its arc also equals π, right?  A 20° angle with a radius of 9 has an arc length of π. And the longer the radius, the shorter the angle’s arc and the less curvature it has. So in GeoGebra I explored how close to linear π the arc of an angle could get by going long on the radius and short on the arc. To do this properly, I could only use conventionally constructible angles for a geometric solution.  Last Tuesday, September 1st, I managed to geometrically construct a line segment the length of π to 15 decimal places, GeoGebra's maximu...