In ancient China, the Pythagorean theorem developed independently and was known as the Gougu theorem. The Chinese mathematician and philosopher, Zhou Bi Suan Jing, introduced this theorem during the Western Zhou Dynasty around 1046-771 BCE. However, the most comprehensive Chinese work on the Gougu theorem can be found in the book "The Nine Chapters on the Mathematical Art" (Jiuzhang Suanshu), which was written during the Han Dynasty around 200 BCE.

The Gougu theorem in ancient China has the same principle as the Pythagorean theorem, stating that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Mathematically, it can be represented as:

c² = a² + b²

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

In "The Nine Chapters on the Mathematical Art," a problem is solved using the Gougu theorem, demonstrating its practical application in Chinese mathematics. This problem, known as "Gougu Problem 9," is about determining the height of an object when the shadow length and the angle between the shadow and the object are given.

The development of the Pythagorean theorem in ancient China demonstrates that this fundamental principle was recognized and utilized independently in different cultures around the world. The fact that the theorem was discovered in multiple civilizations reflects its universal importance in mathematics and its practical applications in various fields.