跟读练习: Extras ArcLength YouTube - 通过视频学习英语口语
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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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背景与上下文
在这段视频中,讲解者探讨了数学中的“弧”这一概念。他通过简单明了的例子,向观众解释了圆的构成以及弧的特性。视频中的内容不仅适合数学学生,同时也为学习英语的观众提供了良好的学习材料。通过观看这样的YouTube视频,观众可以提高他们的英语理解能力,尤其是与几何学相关的词汇和表达方式。
日常交流的五个重要短语
- arc(弧)—— 指的是圆的一部分。
- circumference(周长)—— 圆的外围长度。
- central angle(中心角)—— 定义弧长的重要角度。
- arc length(弧长)—— 沿着弧的曲线行走的距离。
- rotate(旋转)—— 使线段旋转以形成弧。
这些短语可以帮助学习者在数学讨论中进行有效的沟通,尤其是在准备雅思口语练习时,这些术语能够提升他们的专业性和流利度。
逐步模仿指导
要有效地学习和掌握视频中的内容,可以按照以下步骤进行模仿练习(shadow speak):
- 首先,观看整个视频,不看文字字幕,这样你可以专注于听力。
- 第二次观看时,打开字幕,仔细阅读每个短语的发音和意思。
- 接下来,暂停视频,重复讲解者的每一句话。注意发音的细节,用 shadowspeak 方法进行模仿。
- 练习完成后,尝试自己用所学的短语造句,把新的词汇融入日常交流中。
- 最后,找一个可以交流的伙伴,利用你学到的内容进行对话练习,以增强记忆和理解。
通过这种方法,你可以提升你的听力和口语能力,同时为雅思口语练习打下坚实的基础。在这个过程中,记得多看YouTube学英语,不断吸收新知识。通过 shadowspeaks 的实践,你将会发现自己的进步。
什么是跟读法?
跟读法 (Shadowing) 是一种有科学依据的语言学习技巧,最初开发用于专业口译员的培训,并由多语言者Alexander Arguelles博士普及。这个方法简单而强大:您在听英语母语原声的同时立即大声重复——就像是一个延迟1-2秒紧跟说话者的影子。与被动听力或语法练习不同,跟读法强迫您的大脑和口腔肌肉同时处理并模仿真实的讲话模式。研究表明它能显着提高发音准确性,语调,节奏,连读,听力理解和口语流利度——使其成为雅思口语备考和真实英语交流最有效的方法之一。

















