Задача Пифагора и ее применение

Using the example of one of the most ancient number-theoretic problems – the Pythagorean problem – schoolchildren can demonstrate the connections between various mathematical disciplines, at first glance, completely unrelated to each other. The Pythagorean problem establishes a connection between number theory, geometry, and mathematical analysis. The paper considers a brief history of the Pythagorean problem, provides arithmetic and geometric ways of solving it, the connection with Diophantine equations, the use of solutions to the Pythagorean problem to obtain rational parametrization of conic sections, as well as for calculating integrals containing irrationality.