Results 1 to 10 of about 53 (42)
The Gergonne point generalized through convex coordinates [PDF]
International Journal of Mathematics and Mathematical Sciences, 1999 The Gergonne point of a triangle is the point at which the three cevians to the points of tangency between the incircle and the sides of the triangle are concurrent.
J. N. Boyd, P. N. Raychowdhury
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Curves Related to the Gergonne Point in an Isotropic Plane
Mathematics, 2023 The notion of the Gergonne point of a triangle in the Euclidean plane is very well known, and the study of them in the isotropic setting has already appeared earlier.
Ema Jurkin, Marija Šimić Horvath
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The role of biogeographical barriers on the historical dynamics of passerine birds with a circum-Amazonian distribution. [PDF]
Ecol EvolThis study found similarities at populational, phylogenetic, and evolutionary levels among four taxonomic groups of passerine birds with a circum‐Amazonian distribution. The presence of Refugia result of climatic oscillations during the Pleistocene was the main drive in the diversification of these circum‐Amazonian taxa.
Bolívar-Leguizamón SD +3 more
europepmc +2 more sources
Computer Investigation of Properties of the Gergonne Point of a Triangle
, 2022 The incircle of a triangle touches the sides of the triangle in three points. It is well known that the lines from these points to the opposite vertices meet at a point known as the Gergonne point of the triangle. We use a computer to discover and catalog properties of the Gergonne point.
Rabinowitz, Stanley, Suppa, Ercole
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A Simple Proof of Damien’s Theorem and Duality in Theory of the Zero‐Distance Phase Front
International Journal of Antennas and Propagation, Volume 2015, Issue 1, 2015., 2015 Duality plays the main role in all mathematical theories. In wave optics based on the concept of “the zero‐distance phase front,” duality takes the form of Damien’s theorem and the mirror symmetry between the conic refracting surfaces with the plane zero‐distance phase front and the plane refracting surfaces with the conic zero‐distance phase front.
Andrey Valerievich Gitin +1 more
wiley +1 more source
Curves of centroids, Gergonne points and symmedian centers in triangle pencils in isotropic plane
Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, 2018 In this paper we consider a triangle pencil in an isotropic plane consisting of the triangles that have the same circumscribed circle. We study the curves of centroids, Gergonne points and symmedian centers for such pencils of triangles. We also study the curves of centroids, Gergonne points and symmedian centers for tangential triangles of such a ...
Katić Žlepalo, Mirela, Jurkin, Ema
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On the Generalized Gergonne Point and Beyond
Forum geometricorum, 2008 In this paper we generalize the concept of Gergonne point which is a well-known center of the triangle. Given a triangle $V_1V_2V_3$, a point $I$ and three arbitrary directions, we find a distance $x=IQ_1=IQ_2=IQ_3$ along these directions, for which the three cevians $V_iQ_i$ are concurrent.
Hoffmann, Miklos, Gorjanc, Sonja
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Poncelet Porisms and Loci of Centers in the Isotropic Plane
MathematicsAny triangle in an isotropic plane has a circumcircle u and incircle i. It turns out that there are infinitely many triangles with the same circumcircle u and incircle i. This one-parameter family of triangles is called a poristic system of triangles. We
Ema Jurkin
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Insect Conservation and Diversity, Volume 17, Issue 6, Page 953-967, November 2024.We investigated Embiratermes neotenicus dispersal in Suriname and French Guiana, by studying genetic diversity, structure and factors influencing population differentiation. We used mitochondrial and nuclear data from 70 colonies. Significant genetic differentiation between populations was observed.
Damien Gergonne +6 more
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On Gergonne point of the triangle in isotropic plane
Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, 2013 Using the standard position of the allowable triangle in the isotropic plane relationships between this triangle and its contact and tangential triangle are studied. Thereby different properties of the symmedian center, the Gergonne point, the Lemoine line and the de Longchamps line of these triangles are obtained.
Beban-Brkić, Jelena +3 more
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