This amazing Egyptian triangle

Everyone who listened attentively at schoolthe teacher of geometry, is very familiar with what the Egyptian triangle is. From other types of similar geometric figures with an angle of 90 degrees, it has a special aspect ratio. When a person first hears the phrase "the Egyptian triangle", the pictures of majestic pyramids and pharaohs come to mind. And what does history say?

As it always happens, with respect to the name"Egyptian triangle" has several theories. According to one of them, the famous theorem of Pythagoras saw the light precisely because of this figure. In 535 BC. Pythagoras, following the advice of Thales, traveled to Egypt to fill certain gaps in the knowledge of mathematics and astronomy. There he drew attention to the peculiarities of the work of Egyptian surveyors. They performed a very unusual way of constructing a triangular figure with a right angle, the sides of which were interconnected with one another with the ratio 3-4-5. This mathematical series made it relatively easy to relate the squares of all three sides with one rule. This is how the well-known theorem arose. And the Egyptian triangle is exactly the same figure that pushed Pythagoras to the most ingenious decision. According to other historical data, the figure was given the name of the Greeks: at that time they often stayed in Egypt, where they could become interested in the work of surveyors. There is a possibility that, as often happens with scientific discoveries, both stories occurred simultaneously, therefore it is impossible to say with certainty who invented the name "Egyptian Triangle" first. Its properties are amazing and, of course, are not exhausted by the mere correlation of the sizes of the parties. Its area and sides are represented by whole numbers. Thanks to this application of the Pythagorean theorem to it, one can obtain integers of squares of the hypotenuse and the legs: 9-16-25. Of course, this can be a mere coincidence. But how, then, to explain the fact that the Egyptians considered their "own" triangle sacred? They believed in its relationship with the whole universe.

After information about this unusualthe geometric figure became public, in the world searches for other similar triangles with integer sides began. It was obvious that they existed. But the importance of the question was not just to perform mathematical calculations, but to test "sacred" properties. The Egyptians, for all their unusualness, were never considered stupid - scientists still can not explain how the pyramids were built. And here, suddenly, the usual figure was attributed to the connection with Nature and the Universe. And, indeed, the oldest Babylonian cuneiform found contains instructions about a similar triangle with a side, the size of which 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, it turned out that the change in the aggregate state is accompanied by a rearrangement of the spatial configuration of the molecules, in which one can see ... that same Egyptian triangle. If we recall that the water molecule consists of three atoms, then we can speak of conditional three sides. Of course, there is no question of a complete coincidence of the famous relation, but the numbers obtained are very, very close to the ones sought. Is it not because the Egyptians recognized for their "3-4-5" triangle a symbolic key to the natural phenomena and mysteries of the universe? After all, water, as you know, is the basis of life. No doubt, it's too early to put an end to the study of the famous Egyptian figure. Science never rushes to conclusions, trying to prove its assumptions. And we can only wait and marvel at the knowledge of the ancient Egyptians.

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