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Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

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Open Access Research Article

Use of homogeneous coordinates in the study of graves triad and related results

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pp. 2067–2078Vol. 29Issue 6June 2026DOI: 10.47974/JIM-2666XML
Received:
01 Mar 2026
Published Online:
30 Jun 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2666
Pages:
2067–2078

Abstract

A matrix of order three is used to represent a triangle for real projective space of dimension two, here vertices of the triangle’s with respect to a frame of reference are represented  as rows of a matrix. Suppose there are three triangles such that the first is circumscribing the second, the second is circumscribing the third, and the third is circumscribing the first, forming a cyclic order and satisfying the Pappus configuration; then the triad of triangles is called a graves triad. The three triangles forming graves’ triad give rise to three pairs of perspective triangles, called the perspective graves triad. This triad contributes to various results. The existence of the graves triad was already proven. In this paper, the existence of the perspective graves triad is established by using homogeneous coordinates. The related results are interesting because here a well-defined system of reference has been used. Some results of the perspective graves triad are discussed in relation to co-linearity. 

Keywords

Subject Classifications

51N15

References

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