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  5. Analytical solution for the problem of the optimal single-row regular cutting into the triangles

Analytical solution for the problem of the optimal single-row regular cutting into the triangles

A.I. Zinchenko
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The formula for the calculation of the number of triangles which can be placed on a rectangular sheet of metal of the given sizes, for the regular single-row placing has been obtained. The triangle is determined by radius of the circumscribed circle and angles between the vectors, which join the center of this circle and the vertices of the triangle, and the side of the sheet. The obtained results have been used to test the program, developed by the author. This program deals with the finding of the optimal cutting.
Keywords: regular cutting, material utilization ratio, triangle, circumscribed circle, the equation of the line