The Experts below are selected from a list of 579 Experts worldwide ranked by ideXlab platform
Needscompilation Yes - One of the best experts on this subject based on the ideXlab platform.
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License file LICENSE Date 2009-06-15 Repository CRAN Date/Publication 2012-10-31 14:23:07
2013Co-Authors: R. J. Renka, Albrecht R Gebhardt, Stephen Eglen, Sergei Zuyev, Denis White, Maintainer Albrecht Gebhardt, Needscompilation YesAbstract:R topics documented: add.constraint........................................ 2 cells............................................. 4 circles............................................ 5 circtest............................................ 6 circum............................................ 6 Circumcircle......................................... 7 convex.hull......................................... 9 identify.tri.......................................... 10 in.convex.hull........................................ 1
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License file LICENSE Date 2009-06-15 Repository CRAN
2013Co-Authors: R. J. Renka, Albrecht R Gebhardt, Stephen Eglen, Sergei Zuyev, Denis White, Maintainer Albrecht Gebhardt, Needscompilation YesAbstract:R topics documented: add.constraint........................................ 2 cells............................................. 4 circles............................................ 5 circtest............................................ 6 circum............................................ 6 Circumcircle......................................... 7 convex.hull......................................... 9 identify.tri.......................................... 10 in.convex.hull........................................ 1
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License ACM | file LICENSE Date 2013-09-16
2013Co-Authors: R. J. Renka, Denis White, Maintainer Albrecht Gebhardt, Functions Albrecht R Gebhardt, From Stephen Eglen, Needscompilation YesAbstract:R topics documented: add.constraint........................................ 2 cells............................................. 4 circles............................................ 5 circtest............................................ 6 circum............................................ 6 Circumcircle......................................... 7 convex.hull......................................... 9 identify.tri.......................................... 10 in.convex.hull........................................ 1
Warendorff Jay - One of the best experts on this subject based on the ideXlab platform.
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The perpendicular bisectors of a triangle
Wolfram Demonstrations Project, 2016Co-Authors: Warendorff JayAbstract:Knowledge about Plane Geometry and TrianglesThe perpendicular bisectors of the sides of a triangle intersect in a single point, called the circumcenter. The circumcenter is equidistant from the vertices of the triangle. The Circumcircle passes through the three verticesComponente Curricular::Ensino Fundamental::Séries Iniciais::Matemátic
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Two triangles of equal area on either side of an angle bisector
Wolfram Demonstration Project, 2016Co-Authors: Warendorff JayAbstract:Let ABC be a triangle and let the angle bisector at vertex C intersect the Circumcircle at R and the perpendicular bisectors of BC and AC at P and Q, respectively. Let the midpoints of BC and AC be S and T, respectively. Then RQT and RPS have equal areaComponente Curricular::Ensino Médio::MatemáticaComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic
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A concurrency from Circumcircles of subtriangles
Wolfram Demonstration Project, 2016Co-Authors: Warendorff JayAbstract:Let ABC be a triangle and let the incircle intersect BC, CA, and AB at A', B', and C', respectively. Let the Circumcircles of AB'C', A'BC', and A'B'C intersect the Circumcircle of ABC (apart from A, B, and C) at A'', B'', and C'', respectively. Then A'A'', B'B'', and C'C'' are concurrentComponente Curricular::Ensino Médio::MatemáticaComponente Curricular::Educação Superior::Ciências Exatas e da Terra::Matemátic
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Angle bisectors on the Circumcircle
Wolfram Demonstrations Project, 2016Co-Authors: Warendorff JayAbstract:Knowledge about plane geometryExtend the angle bisectors of the triangle ABC to meet the Circumcircle at A', B' and C'. Then AA' ┴ B'C', BB' ┴ A'C', and CC' ┴ A'B'Componente Curricular::Ensino Fundamental::Séries Finais::Matemátic
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Products determined by a point on the Circumcircle
Wolfram Demonstration Project, 2016Co-Authors: Warendorff JayAbstract:Let ABC be a triangle and P be a point on the Circumcircle of circumradius R. Let A' and B' be the perpendicular projections of P onto BC and CA, respectively. Let Q be the perpendicular projection of P onto A'B'. Then PAxPA'=2RxPQComponente Curricular::Ensino Médio::Matemátic
R. J. Renka - One of the best experts on this subject based on the ideXlab platform.
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License file LICENSE Date 2009-06-15 Repository CRAN Date/Publication 2012-10-31 14:23:07
2013Co-Authors: R. J. Renka, Albrecht R Gebhardt, Stephen Eglen, Sergei Zuyev, Denis White, Maintainer Albrecht Gebhardt, Needscompilation YesAbstract:R topics documented: add.constraint........................................ 2 cells............................................. 4 circles............................................ 5 circtest............................................ 6 circum............................................ 6 Circumcircle......................................... 7 convex.hull......................................... 9 identify.tri.......................................... 10 in.convex.hull........................................ 1
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License file LICENSE Date 2009-06-15 Repository CRAN
2013Co-Authors: R. J. Renka, Albrecht R Gebhardt, Stephen Eglen, Sergei Zuyev, Denis White, Maintainer Albrecht Gebhardt, Needscompilation YesAbstract:R topics documented: add.constraint........................................ 2 cells............................................. 4 circles............................................ 5 circtest............................................ 6 circum............................................ 6 Circumcircle......................................... 7 convex.hull......................................... 9 identify.tri.......................................... 10 in.convex.hull........................................ 1
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License ACM | file LICENSE Date 2013-09-16
2013Co-Authors: R. J. Renka, Denis White, Maintainer Albrecht Gebhardt, Functions Albrecht R Gebhardt, From Stephen Eglen, Needscompilation YesAbstract:R topics documented: add.constraint........................................ 2 cells............................................. 4 circles............................................ 5 circtest............................................ 6 circum............................................ 6 Circumcircle......................................... 7 convex.hull......................................... 9 identify.tri.......................................... 10 in.convex.hull........................................ 1
Reznik Dan - One of the best experts on this subject based on the ideXlab platform.
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Properties of Parabola-Inscribed Poncelet Polygons
2021Co-Authors: Bellio Filipe, Garcia Ronaldo, Reznik DanAbstract:We investigate properties of Poncelet $N$-gon families inscribed in a parabola and circumscribing a focus-centered circle. These can be regarded as the polar images of a bicentric family with respect to the Circumcircle, such that the bicentric incircle contains the circumcenter. We derive closure conditions for several $N$ and describe curious Euclidean properties such as straight line, circular, and point, loci, as well as a (perhaps new) conserved quantity.Comment: 21 pages, 17 figure
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Family Ties: Relating Poncelet 3-Periodics by their Properties
2021Co-Authors: Garcia Ronaldo, Reznik DanAbstract:We compare loci types and invariants across Poncelet families interscribed in three distinct concentric Ellipse pairs: (i) ellipse-incircle, (ii) Circumcircle-inellipse, and (iii) homothetic. Their metric properties are mostly identical to those of 3 well-studied families: elliptic billiard (confocal pair), Chapple's poristic triangles, and the Brocard porism. We therefore organized them in three related groups.Comment: 20 pages, 10 figures, 4 tables, 18 video link
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Invariant Center Power and Elliptic Loci of Poncelet Triangles
2021Co-Authors: Helman Mark, Garcia Ronaldo, Laurain Dominique, Reznik DanAbstract:We study center power with respect to circles derived from Poncelet 3-periodics (triangles) in a generic pair of ellipses as well as loci of their triangle centers. We show that (i) for any concentric pair, the power of the center with respect to either Circumcircle or Euler's circle is invariant, and (ii) if a triangle center of a 3-periodic in a generic nested pair is a fixed linear combination of barycenter and circumcenter, its locus over the family is an ellipse.Comment: 25 pages, 16 figures, 6 tables, 8 video links, 7 live app link
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Related by Similarity II: Poncelet 3-Periodics in the Homothetic Pair and the Brocard Porism
2020Co-Authors: Reznik Dan, Garcia RonaldoAbstract:Previously we showed the family of 3-periodics in the elliptic billiard (confocal pair) is the image under a variable similarity transform of poristic triangles (those with non-concentric, fixed incircle and Circumcircle). Both families conserve the ratio of inradius to circumradius and therefore also the sum of cosines. This is consisten with the fact that a similarity preserves angles. Here we study two new Poncelet 3-periodic families also tied to each other via a variable similarity: (i) a first one interscribed in a pair of concentric, homothetic ellipses, and (ii) a second non-concentric one known as the Brocard porism: fixed Circumcircle and Brocard inellipse. The Brocard points of this family are stationary at the foci of the inellipse. A key common invariant is the Brocard angle, and therefore the sum of cotangents. This raises an interesting question: given a non-concentric Poncelet family (limited or not to the outer conic being a circle), can a similar doppelg\"anger always be found interscribed in a concentric, axis-aligned ellipse and/or conic pair?Comment: 13 pages, 5 figures, 3 tables, 5 video
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Related by Similiarity: Poristic Triangles and 3-Periodics in the Elliptic Billiard
2020Co-Authors: Garcia Ronaldo, Reznik DanAbstract:Discovered by William Chapple in 1746, the Poristic family is a set of variable-perimeter triangles with common Incircle and Circumcircle. By definition, the family has constant Inradius-to-Circumradius ratio. Interestingly, this invariance also holds for the family of 3-periodics in the Elliptic Billiard, though here Inradius and Circumradius are variable and perimeters are constant. Indeed, we show one family is mapped onto the other via a varying similarity transform. This implies that any scale-free quantities and invariants observed in one family must hold on the other.Comment: 19 pages, 13 figures, 5 tables, and 11 video
Denis White - One of the best experts on this subject based on the ideXlab platform.
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License file LICENSE Date 2009-06-15 Repository CRAN Date/Publication 2012-10-31 14:23:07
2013Co-Authors: R. J. Renka, Albrecht R Gebhardt, Stephen Eglen, Sergei Zuyev, Denis White, Maintainer Albrecht Gebhardt, Needscompilation YesAbstract:R topics documented: add.constraint........................................ 2 cells............................................. 4 circles............................................ 5 circtest............................................ 6 circum............................................ 6 Circumcircle......................................... 7 convex.hull......................................... 9 identify.tri.......................................... 10 in.convex.hull........................................ 1
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License file LICENSE Date 2009-06-15 Repository CRAN
2013Co-Authors: R. J. Renka, Albrecht R Gebhardt, Stephen Eglen, Sergei Zuyev, Denis White, Maintainer Albrecht Gebhardt, Needscompilation YesAbstract:R topics documented: add.constraint........................................ 2 cells............................................. 4 circles............................................ 5 circtest............................................ 6 circum............................................ 6 Circumcircle......................................... 7 convex.hull......................................... 9 identify.tri.......................................... 10 in.convex.hull........................................ 1
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License ACM | file LICENSE Date 2013-09-16
2013Co-Authors: R. J. Renka, Denis White, Maintainer Albrecht Gebhardt, Functions Albrecht R Gebhardt, From Stephen Eglen, Needscompilation YesAbstract:R topics documented: add.constraint........................................ 2 cells............................................. 4 circles............................................ 5 circtest............................................ 6 circum............................................ 6 Circumcircle......................................... 7 convex.hull......................................... 9 identify.tri.......................................... 10 in.convex.hull........................................ 1