But who was Pythagoras, and what more did he contribute to the world?

畢達哥拉斯是誰，他對世界還有什麼貢獻？

Let's explore the life and legacy of this Ancient Greek philosopher and mathematician. Pythagoras was born around 570 BCE on the island of Samos in the Aegean Sea.

讓我們一起來探索這位古希臘哲學家和數學家的生平和遺產。 畢達哥拉斯於公元前 570 年左右出生在愛琴海上的薩摩斯島。

From a young age, he was fascinated by the mysteries of the world.

他從小就對世界的奧祕著迷。

His early education was influenced by various teachers, including the philosopher Thales of Miletus, who sparked Pythagoras' interest in mathematics and astronomy. Seeking greater knowledge, Pythagoras traveled extensively in his youth.

他的早期教育受到不同老師的影響，其中包括米利都的哲學家泰勒斯，泰勒斯激發了畢達哥拉斯對數學和天文學的興趣。為了尋求更多的知識，畢達哥拉斯年輕時四處遊歷。

He visited Egypt, where he studied geometry and the mysteries of the pyramids.

他訪問了埃及，在那裡研究了幾何學和金字塔的奧祕。

He also journeyed to Babylon, absorbing their mathematical knowledge, and possibly even traveled to India. Around 530 BCE, Pythagoras settled in Croton, a Greek colony in southern Italy.

他還曾前往巴比倫，吸收他們的數學知識，甚至可能去過印度。公元前 530 年左右，畢達哥拉斯定居在意大利南部的希臘殖民地克羅頓。

Here, he founded a religious and philosophical school known as the Pythagorean Brotherhood.

在這裡，他創建了一個宗教和哲學學校，即畢達哥拉斯兄弟會。

This community was dedicated to the study of mathematics, philosophy, and music, and it followed strict rules regarding lifestyle and behavior. Pythagoras' teachings extended beyond mathematics.

這個團體致力於研究數學、哲學和音樂，並嚴格遵守有關生活方式和行為的規定。畢達哥拉斯的學說超越了數學。

He believed in the transmigration of souls, a method that influenced his views on vegetarianism and the treatment of animals. However, his mathematical contributions are what he is best known for today.

他相信靈魂的轉世，這種方法影響了他對素食主義和對待動物的觀點。然而，他在數學方面的貢獻才是他今天最為人熟知的。

The most famous of these contributions is the Pythagorean Theorem.

其中最有名的貢獻是勾股定理。

This theorem states that in a right-angled triangle, the square of the hypotenuse—the side opposite the right angle—is equal to the sum of the squares of the other two sides.

該定理說明，在直角三角形中，斜邊（與直角相對的一邊）的平方等於其他兩邊的平方和。

This principle has become a fundamental part of geometry, but Pythagoras' influence went beyond just geometry. He and his followers discovered the mathematical relationships in musical harmony, noting that the lengths of strings vibrating at harmonious intervals are proportional to whole numbers.

這一原理已成為幾何學的基本組成部分，但畢達哥拉斯的影響卻不僅限於幾何學。他和他的追隨者發現了音樂和聲中的數學關係，指出在和諧音程中振動的弦的長度與整數成正比。

This discovery laid the groundwork for the mathematical study of music and acoustics. Despite his significant contributions, much of Pythagoras' life remains shrouded in mystery.

這一發現為音樂和聲學的數學研究奠定了基礎。儘管畢達哥拉斯做出了重大貢獻，但他的生平仍被蒙上了一層神祕的面紗。

He left no writings of his own, and much of what we know about him comes from his disciples and later philosophers.

他沒有留下自己的著作，我們對他的瞭解大多來自他的弟子和後來的哲學家。

His school was eventually dissolved due to political conflicts, but his ideas endured. Pythagoras passed away around 495 BCE, but his legacy lived on through his students and the enduring impact of his teachings.

他的學校最終因政治衝突而解散，但他的思想卻流傳了下來。畢達哥拉斯於公元前 495 年左右去世，但他的遺產通過他的學生和他的學說的持久影響流傳了下來。

The Pythagorean Theorem remains a fundamental concept in mathematics, and his ideas on the harmony of numbers continue to inspire mathematicians, scientists, and philosophers. Pythagoras once said, "Number rules the universe." His life and work remind us of the profound connections between mathematics and the natural world, and his contributions continue to resonate through the centuries.

畢達哥拉斯定理仍然是數學中的一個基本概念，他關於數的和諧的思想繼續激勵著數學家、科學家和哲學家。畢達哥拉斯曾經說過："數主宰宇宙"。他的生平和工作提醒我們數學與自然世界之間的深刻聯繫，他的貢獻在數個世紀中繼續引起共鳴。