In this paper, we use a property of the centroids to study two general types of geometric loci: one in the plane and one in the space. Then from this result, we examine in detail the case of quadrilaterals and tetrahedra and, in particular, we determine some properties of the nine-point circle of a triangle. The study of those geometric loci is carried out by means of the homothetic transformations that facilitate and make more immediate the proofs of the properties.

Geometric loci and homothetic transformations

FERRARELLO, DANIELA;MAMMANA, MARIA FLAVIA;PENNISI, Mario
2014-01-01

Abstract

In this paper, we use a property of the centroids to study two general types of geometric loci: one in the plane and one in the space. Then from this result, we examine in detail the case of quadrilaterals and tetrahedra and, in particular, we determine some properties of the nine-point circle of a triangle. The study of those geometric loci is carried out by means of the homothetic transformations that facilitate and make more immediate the proofs of the properties.
2014
geometricloci; homothetic transformations; quadrilaterals ; tetrahedra
File in questo prodotto:
File Dimensione Formato  
Geometric loci and homothetic.pdf

solo gestori archivio

Tipologia: Versione Editoriale (PDF)
Licenza: Non specificato
Dimensione 503.93 kB
Formato Adobe PDF
503.93 kB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/14215
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 4
  • ???jsp.display-item.citation.isi??? ND
social impact