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魔數學堂
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課堂上玩數學
課堂上玩數學

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統計的開端。
【奶茶與費雪】

在某個夏天午後,某位女士說:「沖泡的順序對於奶茶的風味影響很大,把茶加進牛奶裡和把牛奶加進茶裡,這兩種沖泡方式所泡出的奶茶口味截然不同。」當時大家聽了都覺得不可思議,這兩種沖泡方式最後當然都是泡出奶茶,怎麼可能有風味的差異呢?而20世紀最偉大的統計大師羅納‧愛默‧費雪(Ronald Aylmer Fisher)在當時就透過實驗許多杯奶茶發現,下午茶的調製順序對風味有很大的影響,後來他寫了統計學偉大的巨作《試驗設計》,像這樣從一開始的假說,到設計試驗,分析試驗結果,最後下結論,這整個過程正是統計分析的精髓。
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有趣的文章。
Humans are really terrible at guessing probabilities:

https://mathwithbaddrawings.com/2018/07/11/why-its-so-hard-to-surprise-a-mathematician/

One way I like to think about the 'Birthday-Paradox' is to consider three cases:

[1] "What are the chances that in a room of 23 people some person picked at random has the same birthday as another person in the room?"

[2] "What are the chances that in a room of 23 people two of the folks in the room have the same birthday?"

[3] "What are the chances that in a room of 23 people two of the folks in the room were born on the same date?"

When we read the three questions they seem to be very simular but are instead different. And, since only ONE of the questions is the "Birthday-Paradox", and we clump all of them together we are surprised that one of the questions has a much higher probability than the other two.

[1] The chances of this occurring are VERY SMALL (6%)

[2] The chances of this occurring are VERY GOOD (over 50%) - This IS the "Birthday Paradox".

[3] We conflate "date of birth" with day of the year you celebrate the anniversary of your birth. Your date of birth includes the year you were born. The anniversary of your birth ignores the year you were born.

The chances of this occurring depend on THE GROUP. This question turns into [2] when you consider a group like a class in a school since everyone was most likely born in the same year so you can ignore the year.

And if you just pick people at random from the general population the chances go way, way down since you get many different years of birth.
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多明諾裡的數學。

其中用多明諾排魔方陣應該是最酷的!
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要怎麼轉動頭頸部呢?

我們建議的動作是頭部盡量保持端正不動,以下巴畫無限大(∞)的符號。

這個動作簡單方便,無論是工作時、看電視時都可以做。將意念放在下巴,然後開始以下巴尖端畫∞──無限大的符號。每次做時,由左到右,然後由右到左,最少各做一分鐘。

生活中的數學,無限大的實際應用!XD
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這影片太有趣了,首先用兩種平常少見的方式,定義「質數」。
在整數系中,這兩種定義是一樣的。
接下來,說明在非整數系裡,兩種定義不可互推。
影片的最後,推測費馬所說那個美妙的證明,也許就是因為費馬他以為整數系的這個特性,可以適用於任何系統裡。
這似乎給了費馬最後定理一個合理的解釋。
I've read about this result before but the explanation in the video goes much deeper than any explanation I seen so far. An excellent video. (And it is a bit too long to fit in the margin of a piece of paper :)
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漫畫數學
考拉茲猜想,亦稱3n+1問題、冰雹數列。用漫畫來表示,還蠻可愛的。
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最大質數再次被更新。
M77232917 is the new largest known prime number, which is 23 million digits long.
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圓錐體積的證明。
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公視《改變世界的符號》

介紹重要數學概念的歷史沿革,以及這些概念帶來了哪些文明科學進展。除了透過戲劇演出歷史,也借用戲劇、經典藝術作品、專家解釋、真人示範、以及電腦動畫來說明數學原理。

#數學史
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