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  • Suppose you have a ball covered entirely with hair and you're trying to comb the hair so

    假設你有一個完全用頭髮覆蓋的球,你'試圖梳理頭髮,所以。

  • that it lies flat everywhere along the surface. If the ball were a donut, or it existed in

    它沿著表面到處都是平的。如果球是一個甜甜圈,或者它存在於

  • two dimensions, this would be easy! But in three dimensions? Well, you're going to run

    二維空間,這很容易!但在三維空間裡呢?那麼,你將會運行

  • into trouble. A lot of trouble. A big hairy ball of trouble.

    陷入了麻煩。很多麻煩。一個大毛球的麻煩。

  • That's because of a theorem in algebraic topology called the "Hairy Ball Theorem" (and yes,

    那是因為代數拓撲學中的一個定理,叫做"毛球定理"(沒錯。

  • that's it's real name) which unequivocally proves that at some point, the hair must stick

    那是它的真名),這明確地證明,在某些時候,頭髮必須堅持。

  • up. Now don't go wasting your time playing around with a hairy ball trying to prove the

    了。現在,不要去浪費你的時間玩周圍的毛球試圖證明的毛球

  • theorem wrong - this is math we're talking about. It's proven - done - QED!

    定理錯了--這是我們正在談論的數學。它'的證明--完成--QED!

  • Technically speaking, what the Hairy Ball theorem says is that a continuous vector field

    從技術上講,毛球定理說的是,一個連續的向量場的

  • tangent to a sphere must have at least one point where the vector is zero.

    與球體相切,至少有一點矢量為零。

  • So what does this have to do with reality apart from uncombable hairy balls? Well, the

    那麼,除了無法梳理的毛球,這和現實有什麼關係呢?嗯,這個

  • velocity of wind along the surface of the earth is a vector field, so the Hairy Ball

    風沿地球表面的速度是一個矢量場,所以毛球的

  • Theorem guarantees that there's always at least one point on earth where the wind isn't

    該定理保證了地球上總有至少一個點的風不是'的。

  • blowing.

    吹。

  • And it doesn't really matter that the object in question is ball-shaped. As long as it

    而且它並不'有關物體是球狀的,這並不重要。只要它

  • can be smoothly deformed into a ball without cutting or sewing edges together, the theorem

    可以順利地變形為一個球,而不需要切割或縫合邊緣,定理為

  • still holds. So the next time a mathematician gives you trouble, ask them if they can comb

    仍然成立。所以,下次有數學家給你添麻煩的時候,問問他們能不能梳理一下。

  • a hairy banana.

    一根毛茸茸的香蕉。

Suppose you have a ball covered entirely with hair and you're trying to comb the hair so

假設你有一個完全用頭髮覆蓋的球,你'試圖梳理頭髮,所以。

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B1 中級 中文 毛球 定理 梳理 麻煩 頭髮 證明

看動畫理解毛球定理!(The Hairy Ball Theorem)

  • 134 10
    Calvin Chen 發佈於 2013 年 01 月 01 日
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