Name: 【TED-Ed】達文西密碼之一《維特魯威人》中的神聖幾何圖形 (【TED-Ed】Da Vinci's Vitruvian Man of math - James Earle)
Uploaded: 2022-05-31T21:01:20.000Z
Duration: 3 min 21 s

分詞構句

This image of the "Vitruvian Man", taken from Leonardo's sketches, has become one of the most recognizable symbols of the Renaissance.

這幅《維特魯威人》是達文西・李奧納多的著作之一，也是文藝復興時期，最廣為人知的一個標誌。

It's a simple pen-and-ink drawing, right?

它就是個簡單的鋼筆畫，不是嗎？

Let's start to answer this question with a math problem.

讓我們從數學的角度來回答這個問題。

I know how to calculate the area of a circle; I take the value for pi and multiply it by the radius squared.

我們都知道如何計算元的面積；用pi 乘以半徑的平方。

I also know how to take the area of a square; I multiply the base by itself.

我們也都知道如何計算正方形的面積；邊長乘以邊長。

But how can I take the area of a circle and create a square with an equal area?

但是我們如何才能得到一個與原面積相等的正方形呢？

This is a problem often called "squaring a circle" that was first proposed in the ancient world.

這個問題一般稱作「化圓為方」，早在古代就被提出。

And like many of ideas of the ancient world, it was given new life during the Renaissance.

也像許多其他古人留下來的問題一樣，這個問題在文藝復興時期得到了新生。

As it turns out, this problem is impossible to solve because of the nature of pi, but that's another story.

儘管結果顯示，這個問題是無解的，原因在於圓周率pi 的性質，但我們今天先不討論這個。

Leonardo's sketch, which is influenced by the writings of the Roman architect, Vitruvius, places a man firmly at the center of a circle and a square.

達文西・李奧納多的這幅素描，受到一位古羅馬建築師維特魯威的著作啟發，將一個男人同時放在圓形與正方形裡。

Vitruvius claimed the navel is the center of the human body and that if one takes a compass and places the fixed point on the navel, a circle can be drawn perfectly around the body.

維特魯威提出人的肚臍是人體的正中心，如果把圓規的一端，固定在肚臍上，以此為圓心，可以圍繞人體畫出一個完美的圓。

Additionally, Vitruvius recognized that arm span and height have a nearly perfect correspondence in the human body, thus placing the body perfectly inside a square as well.

此外，維特魯威也提出人張開雙臂的距離，與人的身高近乎相等，所以人體也就能被恰好放入一個正方形。

Leonardo used the ideas of Vitruvius to solve the problem of squaring a circle metaphorically using mankind as the area for both shapes.

達文西・李奧納多借用了維特魯威的想法，利用人體比例，將兩個圖形面積間的關係，對「化原為方」問題，提出了一個間接解法。

Leonardo wasn't just thinking about Vitruvius, though.

達文西・李奧納多不單只受了維特魯威的啟發。

There was an intellectual movement in Italy at the time called Neoplatonism.

當時的義大利，興起了一股叫做新柏拉圖主義的思潮。

This movement took an old concept from the 4th century developed by Plato and Aristotle called "The Great Chain of Being".

這股思潮建立在公元四世紀由柏拉圖和雅里斯多德提出的「存在巨鏈」的概念之上。

This belief holds that the universe has a hierarchy resembling a chain, and that chain starts at the top with God, then travels down through the angels, planets, stars, and all lifeforms before ending with demons and devils.

此一概念為：宇宙是一個像鏈條一樣環環相扣的系統，鏈的頂端是等級最高的上帝，再來是天使、星體、恆星以及所有生物，最後以惡魔收尾。

Early in this philosophic movement, it was thought that mankind's place in this chain was exactly in the center.

在這個哲學思潮的早期，人被放在這條巨鏈正中間。

Because humans have a mortal body accompanied by an immortal soul, we divide the universe nicely in half.

因為人類同時擁有會消亡的身軀和永生的靈魂，我們剛好將宇宙一分為二。

Around the time Leonardo sketched the "Vitruvian Man", however, a Neoplatonist named Pico della Mirandola had a different idea.

但是，在達文西・李奧納多畫這幅素描《維特魯威人》的前後，一個叫皮科．德拉．米蘭多拉的新柏拉圖主義者，提出了不同的想法。

He pried mankind off the chain and claimed that humans have a unique ability to take any position they want.

他將人類從巨鏈中分離出來，因為人類有特殊的能力，能夠在巨鏈中佔據任何位置。

Pico claimed that God desired a being capable of comprehending the beautiful and complicated universe he had created.

皮可提出，上帝希望能有一種生物能夠欣賞他所創造的美麗而複雜的宇宙。

This led to the creation of mankind, which he placed at the center of the universe with the ability to take whatever form he pleases.

上帝由此創造了人類，祂將人類放在了宇宙的中心，同時讓人類具有選擇各種型態的能力。

Mankind, according to Pico, could crawl down the chain and behave like an animal or crawl up the chain and behave like a god; it's our choice.

皮可認為，人類可以墜落到巨鏈底端並表現出獸性，也可以昇華至巨鏈頂端，表現出神性；這些都是我們的選擇。

Looking back at the sketch, we can see that by changing the position of the man, he can fill the irreconcilable areas of a circle and a square.

回到這幅素描上，我們可以看到，只要改變這個人的姿勢，他就可以同時裝入兩個等面積的圓和正方形這兩個原本無法得的相同面機的形狀。

If geometry is the language the universe is written in, then this sketch seems to say we can exist within all its elements.

如果幾何是書寫宇宙的語言，那麼這幅素描就暗示了我們可以與宇宙內所有的元素協調共存。

Mankind can fill whatever shape he pleases geometrically, and philosophically, as well.

人類可以變成任何形狀，無論是幾何意義上或哲學意義上。

In this one sketch, Leondardo was able to combine the mathematics, religion, philosophy, architecture, and artistic skill of his age.

達文西・李奧納多在此素描裡結合了他同一時代的數學、宗教、哲學、建築和藝術靈感。

No wonder it's become such an icon for the entire time period.

難怪這幅素描成為了歷史長流間的標誌。