A Geometria de Distâncias como uma Proposta para o Ensino Médio no Contexto da Base Nacional Comum Curricular

Distance Geometry offers an alternative approach to analytically studying geometry: it explores a metric space based on distance information between points, rather than their coordinates. Although it is a relatively recent field, DG has already made significant contributions to Mathematics and Computer Science, with various applications in Robotics, Inverse Kinematics, Proteomics, Engineering, and other areas. However, this approach is still absent in basic mathematics education, where teachers generally present content in traditional ways with limited connections to student's real-world experiences or to current innovations. This work investigates the feasibility of incorporating Distance Geometry problems into the curriculum, aiming to modernize basic Mathematics education through new perspectives that foster problem-solving and integrate technologies in developing the skills defined in the Brazilian National Common Core Curriculum (BNCC). Based on a case study with activities conducted at Feliciano Pires School in Brusque, Santa Catarina, this paper suggests activities to enrich teaching practices and enhance student learning through this new perspective.