跟讀練習: Extras ArcLength YouTube - 通過影片學習英語口語

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Have you ever heard of an arc?
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No, I’m not talking about a boat full of animals.
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I’m talking about a shape  you encounter in geometry.
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An arc is a basically just part of a circle.
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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.
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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.
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The endpoint traces a full circle.
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But what if you don’t rotate  the line a full 360 degrees?
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What if you do the same thing  but only rotate it 45 degrees?
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In that case you’d only trace out  a small segment of a circle.
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That’s what an arc is.
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It’s a segment of a circle’s circumference.
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And just like with a straight line segment, an arc is bound by two endpoints.
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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.
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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.
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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.
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The bigger the central angle,  the longer the arc will be.
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In fact, the distance that  you’d travel if you walked along the curved path of the  arc is called the “arc length”.
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That length is always longer  than the distance you would walk if you traveled along a straight line  between the endpoints of the arc.
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You might say that the arc takes you  on a more “round-about path” haha.
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Get it? …round-about …cuz it’s a circle?
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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.
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Let’s be clever and figure  out what that formula is.
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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?
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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.
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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).
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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.
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But we should use a different  letter for arc length since ‘c’ is used for a full circumference.
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Mathematicians seem to like the letter ’s’.
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Let’s try using that formula to  calculate the length of an actual arc.
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Suppose we’re given an arc that was  made by rotating a 4 cm long radius across a central angle of 36 degrees.
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What is its arc length?
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Well, you just substitute those values  into the formula and then simplify.
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The central angle, theta, is 36 degrees  and the radius is 4 centimeters.
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Simplifying, we get 36 divided by 360 is 0.1 and 2 times Pi times 4 is 8Pi.
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Pi can be estimated as 3.14 and 8 times 3.14 equals 25.12 cm.
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Finally 0.1 times 25.12 = 2.512 cm.
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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.

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推薦影片

背景與上下文

在這段影片中,講解者探討了數學中的“弧”這一概念。他通過簡單明瞭的例子,向觀眾解釋了圓的構成以及弧的特性。影片中的內容不僅適合數學學生,同時也為學習英語的觀眾提供了良好的學習材料。通過觀看這樣的YouTube影片,觀眾可以提高他們的英語理解能力,尤其是與幾何學相關的詞彙和表達方式。

日常交流的五個重要短語

  • arc(弧)—— 指的是圓的一部分。
  • circumference(周長)—— 圓的外圍長度。
  • central angle(中心角)—— 定義弧長的重要角度。
  • arc length(弧長)—— 沿著弧的曲線行走的距離。
  • rotate(旋轉)—— 使線段旋轉以形成弧。

這些短語可以幫助學習者在數學討論中進行有效的溝通,尤其是在準備雅思口語練習時,這些術語能夠提升他們的專業性和流利度。

逐步模仿指導

要有效地學習和掌握影片中的內容,可以按照以下步驟進行模仿練習(shadow speak):

  1. 首先,觀看整個影片,不看文字字幕,這樣你可以專注於聽力。
  2. 第二次觀看時,開啟字幕,仔細閱讀每個短語的發音和意思。
  3. 接下來,暫停影片,重複講解者的每一句話。注意發音的細節,用 shadowspeak 方法進行模仿。
  4. 練習完成後,嘗試自己用所學的短語造句,把新的詞彙融入日常交流中。
  5. 最後,找一個可以交流的夥伴,利用你學到的內容進行對話練習,以增強記憶和理解。

通過這種方法,你可以提升你的聽力和口語能力,同時為雅思口語練習打下堅實的基礎。在這個過程中,記得多看YouTube學英語,不斷吸收新知識。通過 shadowspeaks 的實踐,你將會發現自己的進步。

什麼是跟讀法?

跟讀法 (Shadowing) 是一種有科學依據的語言學習技巧,最初開發用於專業口譯員的培訓,並由多語言者Alexander Arguelles博士普及。這個方法簡單而強大:您在聽英語母語原聲的同時立即大聲重複——就像是一個延遲1-2秒緊跟說話者的影子。與被動聽力或語法練習不同,跟讀法強迫您的大腦和口腔肌肉同時處理並模模擬實的講話模式。研究表明它能顯著提高發音準確性,語調,節奏,連讀,聽力理解和口語流利度——使其成為雅思口語備考和真實英語交流最有效的方法之一。

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