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  • After many adventures in Wonderland,

    在仙境中經歷了許多冒險之後。

  • Alice has once again found herself in the court

    愛麗絲又一次發現自己在法庭上

  • of the temperamental Queen of Hearts.

    的喜怒無常的紅桃皇后。

  • She's about to pass through the garden undetected,

    她就要穿過花園而不被發現了。

  • when she overhears the king and queen arguing.

    當她無意中聽到國王和王后在爭吵時。

  • It's quite simple,” says the queen. “64 is the same as 65, and that's that.”

    "這很簡單,"女王說。"64和65是一樣的,就是這樣。"

  • Without thinking, Alice interjects. “Nonsense,” she says.

    愛麗絲不假思索地插了一句。 "胡說八道。"她說。

  • If 64 were the same as 65, then it would be 65 and not 64 at all.”

    "如果64和65一樣,那就是65,根本就不是64。"

  • What? How dare you!” the queen huffs.

    "什麼,你怎麼敢!"女王氣急敗壞。

  • “I'll prove it right now, and then it's off with your head!”

    "我現在就證明給你看,然後就把你的頭砍下來!"

  • Before she can protest,

    在她抗議之前。

  • Alice is dragged toward a field with two chessboard patterns

    愛麗絲被拖向一個有兩個棋盤圖案的領域----------。

  • an 8 by 8 square and a 5 by 13 rectangle.

    一個8乘8的正方形和一個5乘13的長方形。

  • As the queen claps her hands, four odd-looking soldiers approach

    當王后拍手時,四個長相怪異的阿兵哥走了過來

  • and lie down next to each other, covering the first chessboard.

    並挨著躺下,蓋住第一塊棋盤。

  • Alice sees that two of them are trapezoids with non-diagonal sides measuring 5x5x3,

    愛麗絲看到,其中有兩個是非對角線邊長為5x5x3的梯形。

  • while the other two are long triangles with non-diagonal sides measuring 8x3.

    而另外兩個是非對角線邊長為8x3的長三角形。

  • See, this is 64.”

    "看,這是64號。"

  • The queen claps her hands again.

    女王又拍了拍手。

  • The card soldiers get up, rearrange themselves,

    卡牌兵們起身,重新佈置。

  • and lie down atop the second chessboard.

    並躺在第二張棋盤上。

  • And that is 65."

    "那就是65歲。"

  • Alice gasps. She's certain the soldiers didn't change size or shape

    愛麗絲喘息著。她確定那些阿兵哥沒有改變大小和形狀。

  • moving from one board to the other.

    從一個板塊移動到另一個板塊。

  • But it's a mathematical certainty that the queen must be cheating somehow.

    但從數學上來說,皇后一定是在作弊,這是一種數學上的肯定。

  • Can Alice wrap her head around what's wrongbefore she loses it?

    愛麗絲能不能在她失去理智之前想明白什麼是錯的?

  • Pause the video to figure it out yourself. Answer in 3.

    暫停視頻,自己想辦法。回答在3。

  • Answer in 2

    答覆2

  • Answer in 1

    回答1

  • Just as things aren't looking too good for Alice, she remembers her geometry,

    就在愛麗絲的情況不怎麼好的時候,她想起了自己的幾何。

  • and looks again at the trapezoid and triangle soldier

    又看了看梯形和三角形的戰士

  • lying next to each other.

    躺在旁邊的。

  • They look like they cover exactly half of the rectangle,

    它們看起來像正好覆蓋了長方形的一半。

  • their edges forming one long line running from corner to corner.

    它們的邊緣形成一條長線,從角到角。

  • If that's true, then the slopes of their diagonal sides

    如果是這樣,那麼它們的對角線的斜率為

  • should be the same.

    應該是一樣的。

  • But when she calculates these slopes

    但當她計算這些斜坡時

  • using the tried and true formula "rise over run,"

    利用屢試不爽的公式 "漲過跑"

  • a most curious thing happens.

    一件很奇怪的事情發生了。

  • The trapezoid soldier's diagonal side goes up 2 and over 5,

    梯形兵的對角線面上升2,超過5。

  • giving it a slope of two fifths, or 0.4.

    使其斜率達到五分之二,即0.4。

  • The triangle soldier's diagonal, however, goes up 3 and over 8,

    而三角兵的對角線,則上升3個,超過8個。

  • making its slope three eights, or 0.375.

    使其斜率達到了八分之三,即0.375。

  • They're not the same at all!

    他們根本就不一樣!

  • Before the queen's guards can stop her,

    在女王的衛兵阻止她之前

  • Alice drinks a bit of her shrinking potion to go in for a closer look.

    愛麗絲喝了一點她的縮小藥水,要進去仔細看看。

  • Sure enough, there's a miniscule gap between the triangles and trapezoids,

    果然,三角形和梯形之間的差距微乎其微。

  • forming a parallelogram that stretches the entire length of the board

    形成一個平行四邊形,延伸整個板子的長度。

  • and accounts for the missing square.

    並交代了缺失的方。

  • There's something even more curious about these numbers:

    這些數字還有更奇怪的地方。

  • they're all part of the Fibonacci series,

    它們都是斐波那契系列的一部分。

  • where each number is the sum of the two preceding ones.

    其中每一個數字都是前面兩個數字之和。

  • Fibonacci numbers have two properties that factor in here:

    斐波那契數有兩個特性,在這裡也是一個因素。

  • first, squaring a Fibonacci number gives you a value

    首先,對斐波那契數進行平方化處理,就會得到一個值。

  • that's one more or one less

    孰多孰少

  • than the product of the Fibonacci numbers on either side of it.

    比它兩邊的斐波那契數的乘積。

  • In other words, 8 squared is one less than 5 times 13,

    換句話說,8的平方是13的5次方少一個。

  • while 5 squared is one more than 3 times 8.

    而5的平方則是8的3倍多1。

  • And second, the ratio between successive Fibonacci numbers is quite similar.

    其次,連續的斐波那契數之間的比例也很相似。

  • So similar, in fact, that it eventually converges on the golden ratio.

    如此相似,事實上,它最終趨於黃金比例。

  • That's what allows devious royals to construct slopes

    這就是讓狡猾的王室成員建造斜坡的原因。

  • that look deceptively similar.

    看起來很相似的。

  • In fact, the Queen of Hearts could cobble together an analogous conundrum

    事實上,紅桃皇后可以湊出一個類似的難題

  • out of any four consecutive Fibonacci numbers.

    在任何四個連續的斐波那契數中。

  • The higher they go, the more it seems like the impossible is true.

    越是往高處走,越是覺得不可能的事情是真的。

  • But in the words of Lewis Carrollauthor of Alice in Wonderland

    但用《愛麗絲夢遊仙境》的作者劉易斯-卡羅爾的話說就是:

  • and an accomplished mathematician who studied this very puzzle

    和一位研究這個謎題的傑出數學家-----。

  • one can't believe impossible things.

    人不能相信不可能的事情。

After many adventures in Wonderland,

在仙境中經歷了許多冒險之後。

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B2 中高級 中文 愛麗絲 對角線 女王 王后 仙境 三角形

你能解開愛麗絲夢遊仙境的謎語嗎?- Alex Gendler (Can you solve the Alice in Wonderland riddle? - Alex Gendler)

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    林宜悉 發佈於 2020 年 11 月 18 日
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