One of the most well–known geometric transformations, constituting an important problem solving tool, is the so-called spiral similarity of a geometric figure. It allows the transformation, by means of a spiral movement around a point, of a figure F into another similar figure F', that is generated by a rotation and a simultaneous expansion of F. Together with the rotation, the inverse transformation of spiral similarity produces, instead, a contraction of the original figure. Aim of this work isp recisely the study of properties of this inverse transformation and its links with polygonal spirals. Here, this transformation is achieved through an entirely new construction, that can be aided and eased by means of computer algebra and graphics tools.
On a particular spiral similarity
Ritelli Daniele;Spaletta Giulia
2023
Abstract
One of the most well–known geometric transformations, constituting an important problem solving tool, is the so-called spiral similarity of a geometric figure. It allows the transformation, by means of a spiral movement around a point, of a figure F into another similar figure F', that is generated by a rotation and a simultaneous expansion of F. Together with the rotation, the inverse transformation of spiral similarity produces, instead, a contraction of the original figure. Aim of this work isp recisely the study of properties of this inverse transformation and its links with polygonal spirals. Here, this transformation is achieved through an entirely new construction, that can be aided and eased by means of computer algebra and graphics tools.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
