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2021 | OriginalPaper | Chapter

13. Loci of Points Belonging to a Quadrilateral

Authors : Iulian Popescu, Xenia Calbureanu, Alina Duta

Published in: Problems of Locus Solved by Mechanisms Theory

Publisher: Springer International Publishing

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Abstract

If in a triangle there are few usual lines that can intersect, in a quadrilateral there are many more possibilities. Thus, heights intersecting perpendicular from each corner on the opposite sides, as well as bisectors, medians, non-curves, diagonals, can intersect here as well. For each case the synthesis of the equivalent mechanism is made and then the intersection curve of the considered lines is determined. You get lots of curves, of a great diversity of shapes. By changing some lengths of some sides, other curves are obtained. In many cases, two curves plotted by two points on the mechanism were represented. The successive positions of some generating mechanisms are also given. Particular cases of the quadrilateral are also analyzed: square, rectangle, rhombus, parallelogram. The trajectory of the point of intersection of the diagonals of a quadrilateral is searched, when one side of the quadrilateral moves, dragging them on two other sides. The trajectory of a point on the connecting rod is also given for comparison. Woody curves were obtained. Next, two lengths of the mechanism were modified, resulting in other curves, some quite interesting.

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Literature
1.
go back to reference Popescu I (2016) Locuri geometrice şi imagini estetice generate cu mecanisme. Editura Sitech, Craiova Popescu I (2016) Locuri geometrice şi imagini estetice generate cu mecanisme. Editura Sitech, Craiova
2.
go back to reference Sass L, Popescu I, Luca L (2003) Determinarea traiectoriei punctului de intersecţie a diagonalelor unui patrulater. În: Construcţia de maşini, nr. 11/2003 Sass L, Popescu I, Luca L (2003) Determinarea traiectoriei punctului de intersecţie a diagonalelor unui patrulater. În: Construcţia de maşini, nr. 11/2003
Metadata
Title
Loci of Points Belonging to a Quadrilateral
Authors
Iulian Popescu
Xenia Calbureanu
Alina Duta
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-63079-9_13

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