In mathematics, in geometry, a cyclogon is the curve traced by a vertex of a polygon that rolls without slipping along a straight line. There are no restrictions on the nature of the polygon. It can be a regular polygon like an equilateral triangle or a square. The polygon need not even be convex: it could even be a star-shaped polygon. More generally, the curves traced by points other than vertices have also been considered. In such cases it would be assumed that the tracing point is rigidly attached to the polygon. If the tracing point is located outside the polygon, then the curve is called a prolate cyclogon, and if it lies inside the polygon it is called a curtate cyclogon.

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  • En matemàtiques, en geometria, un ciclògon és la corba traçada per un vèrtex d'un polígon que roda sense lliscar al llarg d'una línia recta. No hi ha restriccions a la naturalesa del polígon. Pot ser un polígon regular, com un triangle equilàter o un quadrat. El polígon ni tan sols ha de ser convex; fins i tot podria ser un polígon en forma d'estrella. De manera més general, també s'han considerat les corbes traçades per punts diferents dels vèrtexs. En aquests casos, se suposa que el punt de traça està connectat rígidament al polígon. Si el punt de traça es troba fora del polígon, llavors la corba s'anomena ciclògon prolat, i si es troba dins del polígon s'anomena ciclògon curtat. Al límit, a mesura que el nombre de costats augmenta a l'infinit, el ciclògon es converteix en una cicloide. El ciclògon té una propietat interessant pel que fa a la seva àrea. Sigui la zona de la regió situada per sobre de la línia i per sota d'un dels arcs, fem que denoti l'àrea del polígon rodant i que denoti l'àrea del disc que circumscriu el polígon. Per a cada ciclògon generat per un polígon regular, (ca)
  • In mathematics, in geometry, a cyclogon is the curve traced by a vertex of a polygon that rolls without slipping along a straight line. There are no restrictions on the nature of the polygon. It can be a regular polygon like an equilateral triangle or a square. The polygon need not even be convex: it could even be a star-shaped polygon. More generally, the curves traced by points other than vertices have also been considered. In such cases it would be assumed that the tracing point is rigidly attached to the polygon. If the tracing point is located outside the polygon, then the curve is called a prolate cyclogon, and if it lies inside the polygon it is called a curtate cyclogon. In the limit, as the number of sides increases to infinity, the cyclogon becomes a cycloid. The cyclogon has an interesting property regarding its area. Let A denote the area of the region above the line and below one of the arches, let P denote the area of the rolling polygon, and let C denote the area of the disk that circumscribes thepolygon. For every cyclogon generated by a regular polygon, (en)
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  • En matemàtiques, en geometria, un ciclògon és la corba traçada per un vèrtex d'un polígon que roda sense lliscar al llarg d'una línia recta. No hi ha restriccions a la naturalesa del polígon. Pot ser un polígon regular, com un triangle equilàter o un quadrat. El polígon ni tan sols ha de ser convex; fins i tot podria ser un polígon en forma d'estrella. De manera més general, també s'han considerat les corbes traçades per punts diferents dels vèrtexs. En aquests casos, se suposa que el punt de traça està connectat rígidament al polígon. Si el punt de traça es troba fora del polígon, llavors la corba s'anomena ciclògon prolat, i si es troba dins del polígon s'anomena ciclògon curtat. (ca)
  • In mathematics, in geometry, a cyclogon is the curve traced by a vertex of a polygon that rolls without slipping along a straight line. There are no restrictions on the nature of the polygon. It can be a regular polygon like an equilateral triangle or a square. The polygon need not even be convex: it could even be a star-shaped polygon. More generally, the curves traced by points other than vertices have also been considered. In such cases it would be assumed that the tracing point is rigidly attached to the polygon. If the tracing point is located outside the polygon, then the curve is called a prolate cyclogon, and if it lies inside the polygon it is called a curtate cyclogon. (en)
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  • Ciclògon (ca)
  • Cyclogon (en)
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