Textile Journal of Uzbekistan


This article is devoted on automating triangular fractal patterns and carpet design in textiles, demonstrating the classic and new arithmetic, combinatorial features of the generalized arithmetic triangles of Pascal's triangle. Binomial, trinomial and other combinatorial numbers constructed on the basis of recurrence relations were studied. The software "Pascal's Triangle" was developed in the C# programming language. A convenient user interface of the program has been developed. Based on the software implementation, arithmetic triangles are constructed from residues in the form of Pascal's triangle and combinatorial numbers. The developed software can be used in industry, when drawing patterns, for their subsequent stamping on carpets, fabrics, ceramic tiles, etc.

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