Readers are offered a deep and comprehensive study of the Pythagorean theorem, one of the most famous and important theorems in geometry. The article presents twenty-five different ways to prove this theorem, covering a wide range of mathematical methods and concepts. It actually demonstrates how the Pythagorean theorem can be proven using classical geometric approaches, as well as using modern mathematical tools. Readers will be able to get acquainted with proofs based on metric relations in a triangle, trigonometric properties of angles, elements of vector algebra, properties of a circle, tangent, chord and secant, as well as more complex proofs using differential equations and mechanics. The article will be interesting and useful for a wide range of readers, including high school students, students of mathematical specialties, mathematics teachers and everyone who is interested in the history and development of mathematical knowledge.
Lebedyeva et al. (Wed,) studied this question.
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