This monograph explores the previously unexplored aspects and properties of the Egyptian triangle, as well as the ideas of finding the sizes of other geometric figures drawn inside and outside the Egyptian triangle, the magnitudes of these triangles and the calculation formulas and their practical application. The book also publishes information on an entirely new system of formulas and new constants for today's science. For the first time in science, the concept of "Egyptian triangle chain" was introduced. This concept is explained, instructions and procedures for its use are shown and analyzed.