We compare the performance of two systems, ChatGPT 3.5 and GeoGebra 5, in a restricted, but quite relevant, benchmark from the realm of classical geometry: the determination of geometric loci, focusing, in particular, on the computation of envelopes...
A general algorithm to determine the coupler link geometric loci, such as centrodes, inflection and return circles, as well as circling-point and centering-point curves, is formulated to analyze any type of four-bar linkages with the main target to f...
In this work, we developed a software tool for the simplified, automated definition and viewing of loci in the plane, an essential task in the design, engineering and architectural fields. The process was started by identifying the most salient geome...
Since Darwin, biologists have sought to understand the evolution and origins of phenotypic adaptations. The skull is particularly diverse due to intense natural selection on feeding biomechanics. We investigated the genetic and molecular origins of t...
The advancement of technology influenced the development of mechanical and mechatronic systems. This article presents the integration of new technologies into traditional mechanics. Specifically, it presents a flexible interactive software for dynami...
Let X be a smooth projective variety and f:X→Pr a morphism birational onto its image. We define the Terracini loci of the map f. Most results are only for the case dimX=1. With this new and more flexible definition, it is possible to prove stron...
We study the Terracini loci of an irreducible variety X embedded in a projective space: non-emptiness, dimensions and the geometry of their maximal dimension’s irreducible components. These loci were studied because they describe where the diff...
This paper explores the application of automated reasoning tools, specifically those implemented in GeoGebra Discovery, to the perimeter-area inequality in triangles. Focusing on the computational complex and real algebraic geometry methods behind th...
In Minkowski 3-space, we establish a geometric framework to osculate Type-II ruled surfaces by utilizing the Type-II Bishop frame in (E13). Our analysis extends to higher-order singularities such as butterflies and pyramids, including explicit singul...
The western corn rootworm (WCR), is one of the most serious pests of maize in the United States. In this study, we aimed to find a reliable pattern of difference related to resistance type using population genetic and geometric morphometric approache...
Seed geometric parameters are important in yielding trait scorers, quantitative trait loci, and species recognition and classification. A novel method for automatic measurement of three-dimensional seed phenotypes is proposed. First, a handheld three...
Faults between stator winding turns of synchronous generators have led to specific changes in the harmonic content of currents. In this paper, these changes are used to detect faults in variable-speed synchronous generators connected to three-level c...
The classical fiber product in algebraic geometry provides a powerful tool for studying loci where two morphisms to a base scheme, ϕ:X→S and ψ:Y→S, coincide exactly. This condition of strict equality, however, is insufficient for d...
The nominate subgenus Lyponia Waterhouse, 1878 from China is reviewed, with two new species described and named L. (s. str.) ruficeps sp. n. (China, Yunnan) and L. (s. str.) zayuana sp. n. (China, Xizang). A distribution map and a key to all species...
The soft-shell clam Mya arenaria is one of the most ancient invaders of European coasts and is present in many coastal ecosystems, yet little is known about its genetic structure in Europe. We collected 266 samples spanning a latitudinal cline from t...
Black-spotted pond frogs (Pelophylax nigromaculatus), widely distributed in East Asia, can be suitably used for the study of population genetic patterns and ecosystem monitoring. To systematically manage, conserve, and study this species, it is neces...
Airborne GNSS-R campaigns are crucial to the understanding of signal interactions with the Earth’s surface. As a consequence of the specific geometric configurations arising during measurements from aircraft, the reflected signals can be difficult to...
Plant species complexes represent a particularly interesting example of taxonomically complex groups (TCGs), linking hybridization, apomixis, and polyploidy with complex morphological patterns. In such TCGs, mosaic-like character combinations and con...
This article proposes a possible path devoted to upper secondary school and early university students, as well as training teachers, with the aim to build a conscious approach to the learning/teaching of the conics, which uses, for an educational pur...