[br][color=#999999]This activity belongs to the [i]GeoGebra book[/i] [url=https://www.geogebra.org/m/sw2cat9w]GeoGebra Principia[/url].[/color][br][br][br]In this example, we start with a thread without appreciable mass from which weights hang (the vertices of the polyline). The script of slider-associated animation causes these vertices to vertically move downwards, simulating gravity (external force), while the cohesive forces between neighboring vertices (internal forces of the thread) limit this movement.[br] [br]As we can observe, after a few seconds, the polyline takes on the shape of the resulting [i]funicular polygon [/i][url=https://encyclopedia2.thefreedictionary.com/Funicular+Polygon][img]https://www.geogebra.org/resource/scjbyz2p/0tuzuVw455vxurEw/material-scjbyz2p.png[/img][/url]. The vertices align themselves quite well with an ellipse. If we add more vertices, the alignment will come closer and closer to the theoretical parabola (infinite point loads uniformly distributed horizontally). The catenary is not far off either (it would be the result of removing the weight from the vertices and adding uniform weight to the polyline thread: the loads are uniformly distributed but not horizontally, rather along the curve, that is, separated by the same arc length instead of the same horizontal length).

[color=#999999]Author of the construction of GeoGebra: [url=https://www.geogebra.org/u/rafael]Rafael Losada[/url].[/color]