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2021 | OriginalPaper | Chapter

12. Loci in the Triangle

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

It is known that bisectors, medians, mediators, heights can be drawn in a triangle. If two heights are taken, for example, they intersect at a point if the triangle is static. However, if the triangle moves, having a single fixed side, several variants of equivalent mechanisms are obtained, resulting in the trajectories of the points of intersection of different shapes. The resulting curves and successive positions are given. Some mechanisms are very complicated, only that they are used only as calculation artifices, not being necessary to build them and only in real cases when it is necessary to draw these trajectories on pieces. The resulting curves are of a great diversity of shapes.

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Literature
1.
go back to reference Mică enciclopedie matematică (1980) Editura tehnică, Bucureşti Mică enciclopedie matematică (1980) Editura tehnică, Bucureşti
2.
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
Metadata
Title
Loci in the Triangle
Authors
Iulian Popescu
Xenia Calbureanu
Alina Duta
Copyright Year
2021
DOI
https://doi.org/10.1007/978-3-030-63079-9_12

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