The Pythagorean School was an ancient Greek school of philosophy established by the mathematician, Pythagoras of Samos The Pythagoreans believed in the power of numbers and considered mathematics to be the basis of the universe. Their beliefs, principles, and theorems reflected a deep respect for the mathematical order of the universe and had a profound influence on later thinkers, particularly in the fields of mathematics, astronomy, and philosophy.
The most well-known of the Pythagorean theorems is the Pythagorean Theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. This theorem can be used to calculate the length of the sides of any right triangle, which has made it an invaluable tool in the field of mathematics.
Other famous theorems include the Pythagorean identity, which states that for any real numbers a, b, and c, a2 + b2 = c2. This theorem was a significant advance in the field of algebra and has been used in many mathematical equations.
The Pythagoreans also believed in the concept of harmony in nature, which they called the "music of the spheres". This concept states that the planets and stars in the heavens move harmoniously, following mathematical principles. This belief has had a profound influence on later philosophers, particularly on those who believed in natural law and the power of mathematics.
Finally, the Pythagoreans believed in the shaping of the soul through the study of mathematics and music. This was known as the process of purification, and it was believed to be an essential part of the development of the intellect and the soul.
These are five examples of the best Pythagorean principles, beliefs, and theorems:
1. The Pythagorean Theorem: The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
2. The Pythagorean Identity: For any real numbers a, b, and c, a2 + b2 = c2.
3. The Music of the Spheres: The planets and stars in the heavens move harmoniously, following mathematical principles.
4. The Process of Purification: The shaping of the soul through the study of mathematics and music.
5. The Golden Ratio: The ratio of two measurements that when the ratio of the sum of those measurements to the larger one is equal to the ratio of the larger one to the smaller one. This theorem was especially important to the Pythagoreans.