In this article, we propose a method for solving extremal problems in algebra and stereometry. The method is applied to problems that can be addressed using basic elementary inequalities and trigonometric equalities in triangles. These problems are reduced to finding the minimum or maximum value of a function. The aim of the method is to construct a systematic algorithm for solving extremal problems.
The article is devoted to the Twenty-second International Linguistics Olympiad held in 2025. It presents the results of the Bulgarian participants, a chart of the awards from past years, one of the problems from the qualification tests and its solution.
This article presents the results of a survey conducted among 50 computer science teachers in Bulgarian secondary schools, aiming to identify the main challenges in computer science education and to propose practical guidelines for addressing them. Through quantitative and qualitative analysis of the collected data, key problem areas were identified: outdated curriculum, insufficient technical resources, the need for professional development, and difficulties in motivating students. Seven recommendations for improvement are proposed, including curriculum reform, investment in technology, teacher training, the implementation of innovative teaching methods, and collaboration with the IT industry.
Dynamic Geometry Systems have advanced considerably in recent years, yet the lack of open-source solutions that can automatically verify answers and provide feedback on geometric construction exercises still limits their wider use in education. This challenge arises from the inherent difficulty of assessing complex geometric constructions with computational methods. GeoTry was designed to address this need as an interactive digital learning resource developed with GeoGebra. It supports both teachers and learners by automatically verifying geometric construction exercises and offering structured guidance based on Polya's problem-solving approach. We investigate how automatic verification can be meaningfully embedded in geometric construction exercises, focusing on the underlying design principles and technical considerations.
This work is dedicated to problems involving plane figures defined by points related to conic sections. The presented problems involve finding elements or areas of convex polygons whose vertices lie on ellipses, hyperbolas, and parabolas. Extremal area problems are also considered.
