The classification of Pythagorean triples is based on differences in the tangents of their triangles in a certain group, the value of which tends to one divided by a prime number and has the form of a fraction. The corresponding tables containing primitive and non-primitive Pythagorean triples are constructed in accordance with the proposed visual classification. Based on the presented classification, the concept of the "parent" Pythagorean triple is introduced — a primitive triple underlying a series (table) of Pythagorean triples derived from it. The first "parent" Pythagorean triple among the set of primitive tangent values of their triangles is defined by us as "119, 120, 169". It is shown that the first "parent" Pythagorean triple on the basis of the increase of the smaller legs of their triangles — 3, 4, 5 — can be considered as the initial structural unit of a two—dimensional planar construction of a figure — a right triangle, and the product of the numbers 3, 4, 5 — equal to 60 - it is advisable to consider, in turn, as a structural unit of a three-dimensional A three—dimensional figure is a parallelogram.