Everyone who listened attentively to a geometry teacher at the school is very familiar with what the Egyptian triangle is. It differs from other types of similar geometric figures with an angle of 90 degrees by a special aspect ratio. When a person first hears the phrase “Egyptian triangle”, pictures of the magnificent pyramids and pharaohs come to mind. And what does the story say?
As always, there are several theories regarding the name "Egyptian Triangle". According to one of them, the famous Pythagorean theorem saw the light precisely thanks to this figure. In 535 BC Pythagoras, following the advice of Thales, went to Egypt in order to fill some gaps in knowledge of mathematics and astronomy. There he drew attention to the features of the work of Egyptian land surveyors. In a very unusual way, they performed the construction of a triangular figure with a right angle, the sides of which were interconnected with each other by a ratio of 3-4-5. This mathematical series made it relatively easy to connect the squares of all three sides with one rule. That is how the famous theorem arose. And the Egyptian triangle is precisely the very figure that prompted Pythagoras to a brilliant solution. According to other historical data, the figure was given the name Greeks: at that time they often visited Egypt, where they might be interested in the work of surveyors. There is a likelihood that, as is often the case with scientific discoveries, both stories happened at the same time, so it’s impossible to say with certainty who first came up with the name “Egyptian Triangle”. Its properties are amazing and, of course, are not limited to only one aspect ratio. Its area and sides are represented by integers. Thanks to this, applying the Pythagorean theorem to it allows one to obtain integer numbers of squares of the hypotenuse and legs: 9-16-25. Of course, this may be a coincidence. But how, then, to explain the fact that the Egyptians considered "their" triangle to be sacred? They believed in its relationship with the entire universe.
After the information about this unusual geometric figure became publicly available, the search for other similar triangles with integer sides began in the world. It was obvious that they exist. But the importance of the question was not just to perform mathematical calculations, but to check the "sacred" properties. The Egyptians, with all their unusualness, were never considered stupid - scientists still can not explain how the pyramids were built. And here, all of a sudden, an ordinary figure was attributed a connection with Nature and the Universe. And, indeed, the found ancient Babylonian cuneiform script contains indications of a similar triangle with a side whose size is described by a 15-digit number. Currently, the Egyptian triangle, whose angles are 90 (straight), 53 and 37 degrees, are found in completely unexpected places. For example, when studying the behavior of the molecules of ordinary water itself, it turned out that a change in the state of aggregation is accompanied by a restructuring of the spatial configuration of the molecules, in which you can see ... the same Egyptian triangle. If we recall that a water molecule consists of three atoms, then we can talk about the conditional three sides. Of course, we are not talking about the complete coincidence of the famous ratio, but the numbers obtained are very, very close to the desired ones. Is it because the Egyptians recognized the symbolic key to the natural phenomena and secrets of the universe for their “3-4-5” triangle? After all, water, as you know, is the basis of life. No doubt, it is too early to put an end to the study of the famous Egyptian figure. Science never rushes to conclusions, seeking to prove its assumptions. But we can only wait and be surprised at the knowledge of the ancient Egyptians.