Final answer:
The Pythagorean theorem in geometry establishes a relationship between the sides of a right-angled triangle. The Pythagoreans were a community of philosophers who believed in the unified, rational structure of the universe, guided by mathematical regularities. They also explored the connection between mathematics, music, and the soul. Women, such as Theano and Myia, made significant contributions to the Pythagorean community.
Step-by-step explanation:
The Pythagorean theorem is a key principle in geometry that establishes a relationship between the sides of a right-angled triangle. It states that the square formed by the hypotenuse (the side opposite the right angle) is equal to the sum of the squares formed by the remaining two sides. This theorem was not only discovered by Pythagoras but also researched by other scientists. The Pythagoreans, a community of philosophers, were interested in understanding the natural world and how mathematics explained it. They believed that there was a unified, rational structure to the universe, governed by mathematical regularities. Their beliefs included the idea that the solution to the mysteries of the universe could be revealed through music and that the soul is immortal and continuously reincarnated. Another important aspect of the Pythagorean community was the inclusion and contribution of women, such as Pythagoras' wife Theano and their daughter Myia.