Perhaps in the clutches, Nobel Prize-winning physicist Stephen Weinberg formulated the essence of Bolyai-Lobachevsky's geometry when he said that Bolyai- Lobachevsky's geometry does not fit into our 3-dimensional world, which is our experience. Indeed, this is the reason why we know little about the Bolyai geometry and we have so many difficulties to illustrate it. The Bolyai geometry is only understood by professionals even today. Today, 180 years after its creation, a lot of inaccurate statements are made about it. For example, we encounter such things: "he Bolyai geometry, where the parallels meet," or "the Bolyai geometry is realized on the Pseudosphere" or "an architect built a church on the basis of the Bolyai geometry in the world" and so on. These statements are wrong!