Аннотация
The study examines the problem of non-multiplicity of systematic errors in geometric constructions of regular polygons. Systematic errors resulting from the inaccuracy of drawing tools, limitations arising from user inexperience, and the presence of errors in geometric constructions significantly affect the accuracy of geometric tasks. This study suggests a new approach that includes the principles of geometric progression to reduce these errors and avoid multiplying repetitive systematic errors, offering an optimal solution to this problem to achieve highly accurate results. The methodology proposed in the article includes an analysis of systematic errors in the construction of regular polygons, optimization of the construction stages, and reasoned analysis using manual drawing. The main innovations include dividing circles into equal parts, ensuring the accuracy of geometric constructions. The analysis presented by the scheme confirms the reliability of the methods, reducing deviations from theoretical values. The results show an approximate value of the regular polygons [7(3,4); 9(4,5); 13(6,7)] The effectiveness of the proposed method in geometric light construction is expressed by solving problems. These methods are universal and redefine long-standing problems of geometric constructions, as well as expand the fundamental work of mathematicians such as Al-Farabi and Gauss.