What is the Pythagorean theorem?

The Pythagorean theorem is a fundamental principle in geometry that relates the lengths of the sides of a right-angled triangle. It states that in such a triangle, the square of the length of the hypotenuse (the side opposite the right angle and the longest side) is equal to the sum of the squares of the lengths of the other two sides. Mathematically, it’s expressed as: \[ c^2 = a^2 + b^2 \] where \( c \) is the hypotenuse, and \( a \) and \( b \) are the other two sides. This theorem is widely used to calculate the distance between two points, determine the length of a side when the other two are known, and solve various practical problems involving right triangles. For example, it’s useful in construction when ensuring structures are properly aligned, in navigation to find the shortest path between points, and in computer graphics for calculating distances on screens. Understanding this theorem also provides a foundation for more advanced math topics, such as trigonometry and algebra.