Minimal Path
This activity belongs to the GeoGebra book GeoGebra Principia.
The vectors governing the movements of particles can be undefined. At each step, we can try various vectors and choose the one that best suits our objective.
In this example, a simulation of the well-known soap film experiment, the particles try various movements before settling on those that minimize the total length of the profile and, therefore, the total area of the surface (in this case, they head towards the Steiner points [23] of the four vertices). The angles of the sheets are 120º due to the uniformity in the direction of the Euclidean distance.
Author of the construction of GeoGebra: Rafael Losada.