[KS2s]Prove pi>3.05[Entrance Examination]

There is a YouTuber that explains the math entrance exam questions of Japanese universities. There is a video that made him more famous. Since he is Japanese, he only has explanations in Japanese. His son is bilingual and he publishes an English version of the video. It’s a very interesting problem, so I recommend it to those who like math.

日本の大学の数学の入試問題を解説するYouTuberがいます。その方がブレイクするきっかけとなった動画があります。彼は日本人なので日本語の解説しかありません。彼の息子がバイリンガルで、彼が英語版の動画を公開しています。なかなか面白い問題ですので数学が好きな方におすすめします。
（英語の表現が拙いことですがご了承ください。）

Prove $\pi\ > 3.05 $

鈴木貫太郎さんって誰？という方はこちらへ

埼玉県出身の50代男性
数学系YouTubeチャンネルを運営
ロードバイク、将棋、料理など多趣味
アタック25に出場経験あり。トップ賞を獲得。

家族4人で暮らしていたが2人の子供たちの大学進学で
時間ができたことで一念発起してYouTubeをはじめる。

数学系YouTuber鈴木貫太郎とは何者？【アタック25トップ賞】

毎朝6時30分に数学の受験問題をYouTubeに投稿している鈴木貫太郎さんという方がいます。気になる問題があるとついクリックしてしまうのですが、数学の勉強をする方にとってはとてもいい教材になります。ただひたす...

Prove $\pi\ > 3.05 $

次男、結構評判いいじゃん！是非観て下さい。https://t.co/nCzYjac4J0
Prove π is larger than 3.05 ~Tokyo University Entrance Examination~https://t.co/palG1XyWWd
What is e?? The essence of e. Why (e^x)’=e^xhttps://t.co/3GNvsgcTRt pic.twitter.com/VleIaKD0hM
— 鈴木貫太郎 (@Kantaro196611) June 18, 2019

Hi, it’s me again.
And today I’m going to talk about one of the most famous Entrance Examination
in the history of Tokyo University and the question is very simple
prove that $\pi$ is larger than 3.05 .
And we the Japanese students have been taught that $\pi$ is nearly equal to 3.14
and since middle school we’ve been calculating like area of a circle or
you know circumference of a circle with using 3.14.
So we are not allowed to use calculators.
So that’s how we’ve been calculating you know everything
that’s related to circles.

In this question Tokyo University is challenging you with a number
that you’d been you took it for granted for like more than ten years.
But they’re asking do you know the exact definition of $\pi$
or how you derive you know number 3.14
and it’s a very interesting question.

The definition of $\pi$

So let’s get on with it
so first we have to understand the definition of $\pi$
and suddenly not many people know the exact definition of $\pi$
so if you draw a circle there will be a diameter and a circumference, right?

So $\pi$ is defined as the circumference divided by the diameter

$$\pi = \frac{\rm circumference}{\rm diameter}$$

Well, with me if the spelling was wrong though this is definition of $\pi$
and because every single circle would look exactly the same
so even if you have a diameter of one centimeters
or even if you have a diameter of 500 meters,
the ratio of the around circumference will be exactly the same
so fly will be a constant and that constant that isn’t nothing
to be a 3.1415…
You know infinitely continuing
so that’s the basic I mean that’s definition of $\pi$.

Solution

Okay so now on to the solutions this looks a little bit weird.

But how the ancient people like you know making
Greek people derived $\pi$ without you know super computers
that we have,
right now the strategy those ancient people were using is a very simple
and straightforward
so what doing what they were doing back then is that
they would draw a rough perhaps I can
you know for example that they would plug draw a rough square
that would politically fit the circle and
also they would draw example of a hexagon inside
inside a circle, inside this circle soon
and what they would do is that they would you know measure
the perimeter of the square
so what they would do is that they would measure the perimeter
of the square and also they would measure the perimeter of this hexagon inside.
And because this hexagon’s perimeter is a little bit lessen
and because this square’s perimeter is a little bit more than this circle
if they divide both perimeter is the diameter
they would be able to you know like sandwich the puppet like pioneer deacon
you know roughly speculate the amount of $\pi$.
So perimeter of square divided by the diameter radius
so to our perimeter
thanks again divided it by the diameter must sandwich the $\pi$, right?

circumference of a circle 円周
took it for granted 当たり前の事と思う
derive 引き出す、得る
let’s get on with it　それ（問題）をやっていこう（解いていこう）
diameter 直径
now on to それでは
weird 奇妙な
straightforward 簡単
perimeter 周囲
lessen 減らす
speculate 推測する

Click here for the Japanese version of the video

His father is Kantaro Suzuki.
He released the following video as an entrance exam question in Japan. This was a big hit and established the position of mathematics YouTuber.

YouTubeチャンネル「鈴木貫太郎」をもっと知りたい

これらの動画はYouTubeチャンネル「鈴木貫太郎」でご覧いただけます。

数学系YouTuber鈴木貫太郎とは何者？【アタック25トップ賞】

著書

中学の知識でオイラーの公式がわかる

【書評】中学の知識でオイラーの公式がわかる【鈴木貫太郎著】

オイラーの公式として知られる$ e^{i\pi}= -1$を証明するための本です。そのためには高校数学で習う三角関数、対数、虚数、微分などの広範囲な基礎知識を習得する必要があります。この本を一冊勉強す...

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大学入試数学　不朽の名問１００　大人のための“数学腕試し”

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中学生の知識で数学脳を鍛える

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公式ページなど

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鈴木貫太郎

人類の至宝と言われているオイラーの公式を中学生の知識で理解するシリーズ動画をきっかけにYou Tube投稿をはじめました。今は、毎朝６:３０に大学入試問題を紹介しています。仕事の依頼、コラボはこちらまで→kantaro@momo.so-net.ne.jp 当サイトは Amazon.co.jpを宣伝しリンクするこ...

Twitter

とっても面白かったので動画の冒頭で紹介した本です。学問に対して向き合う姿勢を学べる本。キリン解剖記　https://t.co/HEYj4ozvyj @AnatomyGiraffe 千葉大　n次方程式の整数解 https://t.co/lEFsiqXxJk

— 鈴木貫太郎 (@Kantaro196611) September 22, 2020

[KS2s]Prove pi>3.05[Entrance Examination]

鈴木貫太郎さんって誰？という方はこちらへ

Prove \(\pi\ > 3.05 \)