Now, in modern times, we call this Pythagoras' theorem.

在现代，我们称之为毕达哥拉斯定。

And I have tried to apprehend the Pythagorean power by which number holds away above the flux.

同时我解毕达哥拉斯的力量，通过它的力量，数驾驭了万物的变化。

Pythagoras, a Greek philosopher who lived around 500BC, is said to have discovered that notes that sound harmonious together have simple ratios between their frequencies: for example, one that is an octave higher than another has double the frequency.

据说公元前500年左右，希腊哲学家毕达哥拉斯已经发现了发音和谐的音符在频率之间成简单比例：例如，高一个八度的音符具有两倍的频率。

STEP 5 Give them a who’s who of notable vegetarians, including the Greek mathematician Pythagoras, Leonardo da Vinci, Mahatma Gandhi, and Sir Paul McCartney.

告诉他们一些奉行素食主义的名人，包括希腊数学家毕达哥拉斯，著名艺术家达·芬奇，印度民族主义运动先锋地，英国音乐家詹姆斯·保罗·麦卡特尼爵士。

Pythagoras didn't write down his beliefs but communicated them orally to a select few men, so it's hard to know if what we have is his original teachings.

毕达哥拉斯并没有把他的信仰写下来，而是把它们口头传达给少数几个人，所以很难知道我们所拥有的是否是他的原始教义。

For instance, the Greek philosopher Pythagoras noticed that if you pluck a string, the sound that it makes depends on how long or short it is.

例如，希腊哲学家毕达哥拉斯注意到，如果你拨动一根绳子，它发出的声音取决于它的长短。

Pythagoras was misunderstood, and Socrates, and Jesus, and Luther, and Copernicus, and Galileo, and Newton, and every pure and wise spirit that ever took flesh.

毕达哥拉斯被误解了，苏格拉底、、路德、哥白尼、伽利略、牛顿，以及所有有史以来纯洁与睿智的灵魂都被误解过。

According to the converse of the Pythagorean theorem, that has to make a right triangle, and, therefore, a square corner.

根据毕达哥拉斯的逆定，这就可以形成一个直角三角形，因此，便可形成直角。

Pythagoras was born the longest time ago in 570 B.C. and might have had the first laboratory ever recorded.

毕达哥拉斯出生于公元前570年，可能是有史以来第一个拥有有记载的实验室的人。

Empedocles thought he was a God and jumped into a volcano. And Pythagoras had an irrational fear of beans.

恩培多克勒以为他是天神，跳进了火山，毕达哥拉斯对豆子有莫名的恐惧。

And I have tried to comprehend the Pythagorean power by which number holds sway above the flux.

同时我力图领悟毕达哥拉斯的力量，即数字驾驭一切不稳定的强大力量。

They all came up with elegant proofs for the famous Pythagorean theorem; the rule that says for a right triangle, the square of one side plus the square of the other side is equal to the square of the hypotenuse.

他们都对毕达哥拉斯定（勾股定）做出了精彩的证明；这个定是说，对于一个直角三角形，一边的平方加上另一边的平方等于斜边的平方。

Pythagorus discovered that we were wrong.

毕达哥拉斯发现我们错了。

And according to his follower Philolaus of Croton, Pythagoras believed that the planets moved in set patterns according to mathematical principles of harmony and did not " wander the sky" as their Greek name planetes meaning 'wanderer' suggests.

根据他的追随者克罗顿的菲洛劳斯的说法，毕达哥拉斯认为行星按照和谐的数学原以固定的模式运行，而不是像他们的希腊名字“漫游者”所暗示的那样“漫游天空”。

One classic proof often attributed to Pythagoras himself uses a strategy called proof by rearrangement.

经典证明是毕达哥拉斯自己做出的，他利用了一种名叫排列的证明方法。

In particular, the Mesopotamian understood Pythagorean triples at a level of sophistication that we never expected.

特别是美索不达米亚人对毕达哥拉斯三元组解的复杂程度，是我们从未预料到的。

And it wasn't until 1945 that it was revealed to contain Pythagorean triples.

直到 1945 年，毕达哥拉斯三元组才被发现。

Pythagoras, who lived between circa 571 and 497 BCE, developed a mathematical system to explain the movements of the planets, and so often, is considered the first Greek astronomer.

毕达哥拉斯生活在公元前 571 年至 497 年之间，他发明了一套数学系统来解释行星的运行，因此经常被认为是第一位希腊天文学家。

The theorem is named for Pythagoras, a Greek philosopher and mathematician in the 6th century B.C., but it was known more than a thousand years earlier.

该定是以公元前 6 世纪的希腊哲学家和数学家毕达哥拉斯命名的，但它早在一千多年前就被人所知。

Pythagoras is credited with being the person to identify Venus as one single planet, not two — one appearing in the morning and one in the evening.

毕达哥拉斯被认为是确定金星是一颗行星的人，而不是两颗——一颗在早上出现，一颗在晚上出现。