(I’m a retired professional seamstress, and…)
The term “Clothoid loop” caught my attention (introduced at 5:04 in the video). And now I know a little more about it…
A curve with so many names …
The clothoid equations were first defined by Leonhard Euler; this is why, in general Physics the curve is often called Euler spiral. The French physicists Augustin-Jean Fresnel and, later, Alfred Cornu, rediscovered the curve and defined its parametric equations – hence the curve is sometimes called Fresnel or Cornu spiral.
In 1890, Arthur N. Talbot, Professor of Municipal and Sanitary Engineering at the University of Illinois, defined for civil engineering the “railway transition curve” (Talbot – 1912), with similar equations as Euler did for elasticity and Fresnel and Cornu for optical applications.
The name clothoid was suggested by the Italian mathematician Ernesto Cesàro. The word clothoid comes from klothos, the Greek word for spin (wool) the shape of the curve thread that wraps around the spindle. The same root appears in the name of Clotho (The Spinner), one of the three Fates who holds the thread of human destiny.
