シャドーイング練習: Extras ArcLength YouTube - 動画で英語スピーキングを学ぶ
レッスンを作成中...
1
Have you ever heard of an arc?
2
No, I’m not talking about a boat full of animals.
3
I’m talking about a shape you encounter in geometry.
4
An arc is a basically just part of a circle.
5
In our video lesson called “Circles: What is Pi?”, you learned that a circle is the set of all points that are equidistant from a central point.
6
A good way to draw a circle on the coordinate plane is to first draw a horizontal line segment from the origin to some point on the x-axis and then rotate that segment 360 degrees around the origin, leaving a trail from the endpoint as you go.
7
The endpoint traces a full circle.
8
But what if you don’t rotate the line a full 360 degrees?
9
What if you do the same thing but only rotate it 45 degrees?
10
In that case you’d only trace out a small segment of a circle.
11
That’s what an arc is.
12
It’s a segment of a circle’s circumference.
13
And just like with a straight line segment, an arc is bound by two endpoints.
14
We can make arcs of different lengths just by choosing different angles to rotate our line, which you may have realized is the radius of the full circle.
15
Rotating only 10 degrees gives you this short, slightly curved line, while rotating 100 degrees gives you this much longer arc; more than one-fourth of a full circle.
16
The angle you choose to rotate is called the “central angle” of the arc and it, along with the radius, determines the length of the arc.
17
The bigger the central angle, the longer the arc will be.
18
In fact, the distance that you’d travel if you walked along the curved path of the arc is called the “arc length”.
19
That length is always longer than the distance you would walk if you traveled along a straight line between the endpoints of the arc.
20
You might say that the arc takes you on a more “round-about path” haha.
21
Get it? …round-about …cuz it’s a circle?
22
And here’s something handy, there’s actually a formula you can use to calculate the arc length if you know the radius and the central angle of the arc.
23
Let’s be clever and figure out what that formula is.
24
If you rotate the radius line a full 360 degrees, the arc length would just be the same as the full circumference of the circle you make, right?
25
So if we only rotate the radius line a fraction of the amount between 0 and 360, the arc length will only be a fraction of the total circumference.
26
That fraction will be the angle we actually rotate the line (represented by the Greek letter theta) over the total angle for a full circumference (360 degrees).
27
The formula for circumference is c = 2(Pi)r So if we just multiply that amount by the fraction (theta over 360) that should give us the arc length.
28
But we should use a different letter for arc length since ‘c’ is used for a full circumference.
29
Mathematicians seem to like the letter ’s’.
30
Let’s try using that formula to calculate the length of an actual arc.
31
Suppose we’re given an arc that was made by rotating a 4 cm long radius across a central angle of 36 degrees.
32
What is its arc length?
33
Well, you just substitute those values into the formula and then simplify.
34
The central angle, theta, is 36 degrees and the radius is 4 centimeters.
35
Simplifying, we get 36 divided by 360 is 0.1 and 2 times Pi times 4 is 8Pi.
36
Pi can be estimated as 3.14 and 8 times 3.14 equals 25.12 cm.
37
Finally 0.1 times 25.12 = 2.512 cm.
38
Rounding off two two decimal places gives us an arc length ’s’ of 2.51 cm Okay, …hope that helps you understand what an arc is and how you can calculate its length.
📺 同じチャンネル
B13
Math Antics - Negative Numbers
American AccentKidsTeensHigh School Students
B1Math Antics - Finding A Percent Of A Number
American AccentKidsTeensHigh School Students
B1Math Antics - Calculating Percent Change
American AccentBusiness EnglishHigh School StudentsUniversity Students
B1Math Antics - Percents Missing Total
American AccentHigh School Students
B1Math Antics - What Percent Is It?
American AccentDaily ConversationHigh School StudentsUniversity Students
B1Math Antics - Percents And Equivalent Fractions
American AccentDaily ConversationHigh School StudentsUniversity Students
B1Math Antics - What Are Percentages?
American AccentHigh School StudentsUniversity Students
✨ おすすめ動画
B214
170 文
Why a Circle Has 360 Degrees? | The History and Logic Behind 360° Explained with Animation
Cambridge Exam PrepHigh School StudentsUniversity Students
B23
163 文
My Secret Warehouse Tour
American AccentBusiness EnglishHigh School StudentsUniversity Students
B23
217 文
Why English is SO Hard to Learn!
American AccentBusiness EnglishDaily ConversationHigh School Students
C114
28 文
Introduction to high school physics | Khan Academy
American AccentHigh School StudentsUniversity Students
B157 文
Fractions
American AccentHigh School StudentsUniversity Students
B27
61 文
Character arc
Cambridge Exam PrepHigh School StudentsUniversity Students
C112
47 文
Essence of linear algebra preview
American AccentBusiness EnglishUniversity StudentsWorking Adults
B11
33 文
Composite Area Example 1
High School StudentsUniversity Students
B21
25 文
What's Inside My Spherical Die?
American AccentUniversity Students
B21
535 文
Stroll Through the Playlist (a Biology Review)
Cambridge Exam PrepHigh School StudentsUniversity Students
C11
74 文
The Science Behind The Odyssey's Greatest Challenge
American AccentIELTS PrepTOEFL PrepUniversity Students
B12
74 文
Elements | Middle school chemistry | Khan Academy
American AccentHigh School StudentsUniversity Students
この動画で話す練習をする理由
この動画では、アークとその長さの計算について学ぶことで、数学的な概念を英語で表現する力を養えます。特に、アークの定義や計算式は、実際の会話やIELTS スピーキング対策に役立つ重要な内容です。英語の発音を良くするためには、理論だけでなく、実際に声に出して練習することが不可欠です。話すことで自分の理解を深め、英語スピーキング練習の効果を最大化できます。また、複雑な表現を含んだ内容を話すことで、コミュニケーション能力を高め、より豊かな会話ができるようになります。
文法と表現の文脈
この動画ではいくつかの重要な文法構造や表現が使われています。以下はその例です：
- 「What if you don’t rotate the line a full 360 degrees?」 - この表現は仮定法を使っており、仮の状況を示すのに効果的です。
- 「the distance that you’d travel if you walked along the curved path」 - 条件文の形で、異なる状況での結果を比較しています。
- 「the bigger the central angle, the longer the arc will be.」 - 比較級を使った構文で、因果関係を示しています。
- 「That length is always longer than the distance you would walk」 - 「always longer than」のような表現は、相対的な比較を行う際に有効です。
これらの文法構造をシャドーイングしながら練習することで、理解が深まり、自然な英会話が可能になります。
一般的な発音の落とし穴
この動画では、いくつかの発音上の注意点があります。特に難しい単語やアクセントに注目しましょう：
- “arc” - 発音は「アーク」と短くはっきり言いましょう。
- “circumference” - 3つの音節に分け、各音を明確に発音することが重要です。
- “central angle” - 強調する部分を意識して発音しましょう。
これらの単語を意識して練習することで、発音が向上し、英語の流暢さが増します。英語の発音を良くするためには、正しい発音を身に付けることが非常に重要です。シャドーイングサイトを活用して、実際の発音を聞きながら練習することをお勧めします。
シャドーイングとは？英語上達に効果的な理由
シャドーイング（Shadowing）は、もともとプロの通訳者養成プログラムで開発された言語学習法で、多言語習得者として知られるDr. Alexander Arguelles によって広く普及されました。方法はシンプルですが非常に効果的：ネイティブスピーカーの英語を聞きながら、1〜2秒の遅延で声に出してすぐに繰り返す——まるで「影（shadow）」のように話者を追いかけます。文法ドリルや受動的なリスニングと異なり、シャドーイングは脳と口の筋肉が同時にリアルタイムで英語を処理・再現することを強制します。研究により、発音精度、抑揚、リズム、連音、リスニング力、そして会話の流暢さが大幅に向上することが確認されています。IELTSスピーキング対策や自然な英語コミュニケーションを目指す方に特におすすめです。