This paper examines how bichromatic separability problems, a classic topic in computational geometry, can be adapted for secondary mathematics education through the use of BichromaticSolver. The software computes simple or convex polygons that separate two finite sets of points under different optimisation criteria, including maximum area, minimum area, maximum perimeter, or minimum perimeter. Unlike traditional approaches, the number of polygon sides k is not fixed in advance but chosen by the user, enabling the exploration of diverse and potentially more effective configurations. Three classroom tasks were designed in which students alternated between paper-and-pencil methods and digital exploration with the software. This two-phase structure encouraged them to verify constructions, compare alternative outcomes, and refine their strategies. Classroom observations from this exploratory study document how these activities created opportunities for students to express and refine geometric reasoning while making computational thinking (CT)-related practices visible, for example decomposition, abstraction, strategic planning, and comparative evaluation of solutions. The findings suggest that integrating computational geometry problems with digital tools can enrich traditional mathematics instruction, highlight the relevance of geometry in authentic contexts, and offer a promising and transferable context for developing CT alongside core geometry content in secondary mathematics education.
R. Molano, MohammadHossein Homaei, M. Ávila et al.· International Electronic Jou...· 0 citations
Uncrewed aerial vehicles (UAVs) are increasingly deployed for autonomous navigation in complex outdoor environments, where dynamic conditions and mission requirements require intelligent adaptive decision-making. Existing optimization-based, Machine Learning (ML), and Reinforcement Learning (RL) approaches often rely on predefined models or task-specific training, limiting their generalization and adaptability in uncertain scenarios. Recent Large Language Model (LLM)-assisted approaches offer promising reasoning capabilities but remain constrained by limited agentic functionality, including insufficient memory, planning, and tool interaction mechanisms.This paper proposes an LLM-Agent-Based Path Finder (LAPF) framework for autonomous UAV navigation in town-scale outdoor environments. LAPF extends LLM-assisted navigation by integrating perception, memory, planning, and action modules into a closed-loop cognitive architecture. The proposed agent leverages prior navigation experiences, performs Chain-of-Thought (CoT) reasoning, couples each detected hazard to a bounded corrective action, and dynamically refines waypoint decisions based on environmental feedback.The three independent trials per method demonstrate that LAPF achieves mean path lengths of 512.83 m and 506.37 m, compared to the straight-line optimum of 497.33 m, corresponding to path length reductions of 17.2% and 15.6% relative to CoT prompting and absolute path efficiencies of 97.1% and 98.1% in open-field and obstacle-injected scenarios, respectively. Furthermore, LAPF is the only evaluated approach that couples every detected hazard to a bounded, metric-neutral corrective action while maintaining near-goal stability, with zero clamp events in both scenarios, whereas CoT prompting increases from 9.7 to 14.0 events.
Yousef Emami, MohammadHossein Homaei, Hao Zhou et al.· 0 citations