A Kepler triangle is a right-angled triangle whose sides sa- tisfy a geometric progression whose mean is the square root of the golden ratio. Presumably such triangles were already considered in antiquity. It is known that if Kepler’ triangles are suitably positioned, then it is obtained a polygon who- se vertices belong to an important logarithmic spiral: the famous Spira Solaris. Kepler triangles are special kind of continue triangles, which are triangles whose sides satisfy a geometric progression. Recent studies prove that continue triangles can be related to special families of logarithmic spirals. Here we highlight that every logarithmic spiral can be described by an appropriate chain of continue triangles.
Triangoli continui e spirali logaritmiche
Vincenzi Giovanni
2018
Abstract
A Kepler triangle is a right-angled triangle whose sides sa- tisfy a geometric progression whose mean is the square root of the golden ratio. Presumably such triangles were already considered in antiquity. It is known that if Kepler’ triangles are suitably positioned, then it is obtained a polygon who- se vertices belong to an important logarithmic spiral: the famous Spira Solaris. Kepler triangles are special kind of continue triangles, which are triangles whose sides satisfy a geometric progression. Recent studies prove that continue triangles can be related to special families of logarithmic spirals. Here we highlight that every logarithmic spiral can be described by an appropriate chain of continue triangles.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
