What major concept is derived from the Pythagorean Theorem?

The major concept derived from the Pythagorean Theorem is focused on right triangles. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This crucial relationship allows for various applications in mathematics, particularly in geometry, where understanding the properties of right triangles is foundational for further concepts.

The Pythagorean Theorem specifically applies to Euclidean geometry, which deals predominantly with flat surfaces and does not extend to triangles in three-dimensional space, spherical geometry, or calculus integration. Instead, it is a fundamental tool for solving problems involving right triangles and serves as a stepping stone to more advanced mathematical concepts and applications.