ANGLE TRISECTION PROBLEM AS A TOOL FOR INQUIRY-BASED GEOMETRY LEARNING
DOI:
https://doi.org/10.32999/ksu2413-1865/2026-115-7Keywords:
dynamic mathematical modelling, GeoGebra, digital experiment, absolute angular error, mathematical reasoning, problem-solving activityAbstract
The study aims to substantiate the didactic potential of the classical mathematical problem of dividing an arbitrary angle into three equal parts as a research-oriented learning case and to demonstrate how geometric construction, digital experimentation, quantitative error analysis, and mathematical reasoning can be combined in mathematics education. Methods. The study employed theoretical analysis and generalization of scientific and methodological literature, analysis and modelling of geometric constructions, a digital experiment in GeoGebra, measurement and comparison of angular values, quantitative analysis of absolute angular error, elements of correlation analysis, pedagogical interpretation, and structural-logical modelling of research-oriented learning activity. The authors’ construction was treated as a research hypothesis rather than as a proven universal method for an exact solution of the classical problem. Results. Digital verification was conducted for 18 selected initial angles ranging from 25.6° to 90°. The mean absolute error was 0.0815°, while the maximum recorded deviation of an individual part from the theoretically exact value α/3 was approximately 0.267°. No pronounced linear relationship was found between the initial angle and the mean absolute error (r ≈ −0.12). A characteristic symmetry of the results was identified: the two outer angles coincided within the precision of digital measurement, whereas the deviation was mainly manifested in the central angle. The pedagogical interpretation of the study resulted in a four-component model comprising problem-search, constructive, experimental-analytical, and reflective-proof components. Conclusions. The proposed construction should be interpreted as an approximation. Its didactic value lies in enabling a complete cycle of mathematical investigation, from problem formulation and hypothesis generation to digital verification, error assessment, critical interpretation, and a reasoned conclusion. The approach can be applied in mathematics lessons and extracurricular activities, particularly when working with mathematically gifted students, and supports the distinction between visually convincing experimental evidence and rigorous mathematical proof
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