It was invented by a little something called, "nature," and it's everywhere you look.

它由我們稱為「自然」的東西所發明，而且它隨處可見。

In fact, there are specific numbers that we see in nature all the time.

事實上，大自然中隨時可見一些特定的數字。

Together, they're called "The Fibonacci Sequence" and it goes something like this: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.

它們被稱為「費波那契數」，看起來像這樣：1、1、2、3、5、8、13、21、34、55。

You may know this pattern.

你或許知道它的規律。

The first and second add up to the third, and the second and the third add up to the fourth, the fourth and the fifth add up to the sixth, and so on.

第一和第二項加總為第三項，第二和第三加起來是第四項，第四和第五加起來是第五項，第四和第五則是第六，以此類推。

The sequence was first described by mathematicians in India about 1300 years ago.

這組數列最早由印度數學家在 1300 年前寫下。

And it was introduced to the west in 1202 by Leonardo of Pisa, aka Fibonacci, who was also responsible for introducing Arabic numerals to Europe, which, yeah, if hadn't done that we'd still be counting in Roman numerals which would be terrible.

然後在 1202 年被比薩的里奧納多 (也就是費波那契) 引進西方，他也是把阿拉伯數字帶入歐洲的人，要不是他我們現在或許還在用羅馬數字算數，真恐怖。

Fibonacci was a mathematician and in his book, Liber Abaci, he described the sequence with a thought experiments about a family of incestuous bunnies.

費波那契是一位數學家，在著作《計算書》中，他用一個假想的亂倫兔子家庭來描述這個數列。

If you put one boy bunny and one girl bunny together, that's two.

如果你把一隻公兔子和母兔子放在一起，就有了兩隻。

And those two together will make a third, and those three when they're done, you know, taking turns will make five. Et cetera.

那兩隻在一起會產生第三隻，而那三隻 …… 額你知道的，之後會產生出五隻。之類的。

But, the easiest place to find these numbers in nature isn't in bunnies.

不過在自然界中這些數字並不在兔子身上。

It's in plants.

而是在植物。

If you cut a banana into slices, you'll see it has three distinct sections; an apple has five.

如果你把香蕉切片，你會發現它有三個區塊，蘋果則是有五個。

No matter what kind of flower you're looking at, chances are it has three, five, eight, thirteen, or twenty one petals.

無論你找來的是哪種花，它很有可能有 3 片、5 片、或是 8、13、21 片花瓣。

Rows of seeds in sunflowers and pine cones always add up to Fibonacci numbers.

向日葵和松果的種子排數總數永遠會是費波那契數。

Our plants don't grow this way because they're receiving some kind of mysterious, cosmic mandate.

這些植物並不是因為收到了什麼神秘的宇宙指令才會長成這樣。

They're doing it because it's the most efficient way to pack as many seeds as possible into a small space.

之所以如此是因為這樣效率最高，小空間內能置入最多顆種子。

And if you want to see why that is, you can go watch Vi Hart's video, which is linked in the description and it's awesome.

如果你想知道這是怎麼一回事，你可以去看 Vi Hart 的影片，連結就放在描述欄裡，非常好看。

But in addition to the numbers themselves, you also see the same ratio between Fibonacci numbers showing up.

不過除了數字本身，費波那契數彼此之間還有一定的比率。

When you divide almost any Fibonacci number by the one before it in the sequence, especially the larger ones, you get the same number: 1.618... lots of numbers.

當你將幾乎任何一個費波那契數除以它後面一個數，得出的結果都是同一個：1.618... 後面很多數。

The Greeks discovered this long before Fibonacci, and they called it Phi.

希臘人早費波那契發現這個定理，他們稱之為 Phi ( Ø )。

Today, it's sometimes known as the Golden Ratio.

在今日，它亦被稱為黃金比率。

Phi was purportedly used by the ancient Greek sculptor Phidias to illustrate the idea of physical perfection.

據傳 Phi 被古希臘雕刻家菲迪亞斯用來描述人體完美的比例。

He is said to have used Phi as a ratio between the statue's total height and the distance from the bottom of its feet to its navel, for instance.

舉個例子，據說他以 Phi 作為雕塑身高與腳底至肚臍間的距離比例。

And also the length of a face divided by its width.

同時也是臉部長度和寬度的比例。

There's a whole other set of patterns in nature that are based on what's called the Golden Rectangle - a rectangle whose sides lengths are successive Fibonacci numbers, like 8x13.

自然界中還有另一個模式是根據「黃金矩形」—— 一個邊長為連續的費波那契數的矩形，比如 8 乘 13。

This rectangle can be divided up into a series of squares whose lengths are also successive Fibonacci numbers, in this case: 1x1, 2x2, 3x3, 5x5, and 8x8.

這個矩形可以被分割為一系列方形，邊長同樣也是費波那契數，在這個例子中就是：1 乘 1、2 乘 2、3 乘 3、5 乘 5 和 8 乘 8。

When you draw an arc from one corner of each square to the other, they join to form a spiral that resembles many of the spirals we observe in nature - in the unfolding leaves of a desert succulent, the arrangement of those pine cone lobes and sunflower seeds, in the shells of some snails.

當你從每一個方形的一角畫弧線至另一個，它們會形成一個自然界常見的螺旋，例如沙漠多肉植物展開的葉片、松果片和葵花籽的排列、一些蝸牛的殼。

The math, you guys...

數學啊，跟你們說 ……

It can be beautiful, too.

也是可以很美的。

Thanks for watching this episode of SciShow.

感謝收看這集 SciShow 節目。

If you'd like to get in touch with us, leave suggestions or ideas, we'll be in the comments below or on Facebook or Twitter.

如果你想和我們聯繫、給我們建議或點子，我們會在下方留言欄，或是在臉書和推特。

And if you want to continue getting smarter with us, you can go to youtube.com/SciShow and subscribe.

如果你想和我們一起越來越聰明，你可以前往 youtube.com/SciShow 然後訂閱。