The area as a natural pseudo-Hermitian structure on the spaces of plane polygons and curves

López-López, Jorge L.

doi:10.1016/j.difgeo.2010.05.004

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Cited by 3 publications

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“…Taking into account the signs of the coefficients , we obtain the values * , * are the same as (8). Then the points ( * , ( * )) ( * , ( * )) are the intersection points of the parabola = ( ) with the axis OX.…”

Section: Methodsmentioning

confidence: 99%

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Flat area characteristics of polygons circumscribing parabolic figures

2020

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The works elucidates the extremum areas of the polygons circumscribing parabolic figures. It is shown that the ratio of the areas of the polygons circumscribed near parabolic figures to the areas of the corresponding figures always remains a constant value, independent of the coefficients characterizing the quadratic function. The only point at which the function under study reaches its minimum value is found. The question of the necessary conditions for the existence of a circle circumscribed about a parabolic quadrilateral found in the Ptolemy theorem is being considered.

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Section: Methodsmentioning

confidence: 99%

“…It was shown in [8] that the area function defines a pseudo-Hermitian structure in space that preserves the orientation of the similarity classes of plane closed curves, where the explicit geodesic characteristics of these figures are calculated.…”

Section: Introductionmentioning

confidence: 99%