Geometric Expansion of a Curve


A math-free, fun way to scale up (or down) a curved line without changing its proportions.



During the layout of a cabinet with curved surfaces, I ran into a situation where I needed to scale up a curve. (It involved developing a curved surface on a flat plane). I looked into some of my pre-WWII source literature and could only find some rather complex and vague instructions for doing so. After a couple of sleep-disturbed nights thinking about it, I woke up realizing I already knew the solution: I could employ the fundamental geometry of the ancient sector! Basically, you construct an isosceles triangle around the chords of the two curves–which allows you to employ the constant proportionality of the base of the triangle with its two equal-length sides. This download walks you through the process.