Where “a” and “b” are the lengths of the two shorter sides (called the legs) of the right triangle, and “c” is the length of the hypotenuse. The theorem holds true for all right triangles.
The Pythagorean theorem has numerous applications in various fields, including geometry, trigonometry, physics, engineering, and more. It is one of the foundational principles in mathematics and has been extensively studied and utilized throughout history.」
数学的に、ピタゴラスの定理を表してみると：「a」と「b」が直角三角形の2つのより短い側（足という）の長さの二乗の和は斜辺「c」の二乗と等しくであって、a^2 + b^2 = c^2とあらわされます。
Life of Pythagoras: The details of Pythagoras’ life are often difficult to separate from myth and legend due to the lack of reliable historical records from that time. According to traditional accounts, Pythagoras was born on the island of Samos in Greece. He traveled extensively throughout his life, visiting Egypt, Babylon, and India, where he is said to have studied with various scholars and priests to gain knowledge.
After his travels, Pythagoras settled in the city of Croton (now Crotone) in southern Italy, where he founded a school known as the Pythagorean Brotherhood. The school emphasized the pursuit of knowledge, intellectual and moral development, and the belief in the harmony of the universe. It also had a secretive and mystical aspect, with members following strict rules and rituals.
Character of Pythagoras: Pythagoras was not only a mathematician but also a philosopher and spiritual teacher. He believed in the immortality of the soul and the concept of reincarnation. He taught his followers that the soul goes through a cycle of rebirths, and that achieving purity and enlightenment could lead to liberation from this cycle.
Pythagoras advocated for a disciplined and ascetic lifestyle, promoting vegetarianism, abstinence from certain foods, and adhering to strict ethical principles. He believed in the importance of moderation, self-control, and harmony in all aspects of life. Music and mathematics were integral to his teachings, as he believed they revealed the underlying order and structure of the universe.
Pythagoras was known to be an influential and charismatic leader. He attracted many followers to his school, and his teachings had a profound impact on subsequent philosophical and mathematical developments in ancient Greece.
It is important to note that due to the scarcity of reliable historical information, some details of Pythagoras’ life and character might be subject to debate and interpretation. Nevertheless, his contributions to mathematics and his philosophical ideas continue to influence various fields of study to this day.」