Shadowing-Übung: Extras ArcLength YouTube - Englisch Sprechen Lernen mit Video

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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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Über Diese Lektion

In dieser Lektion wirst du das Konzept des Bogens in der Geometrie kennenlernen und verstehen, wie man die Länge eines Bogens berechnet. Ein Bogen ist ein Teil eines Kreises und wird durch einen zentralen Winkel sowie den Radius des Kreises definiert. Du wirst lernen, wie man den Bogen berechnet und die Beziehung zwischen dem zentralen Winkel und der Bogenlänge verstehen. Diese Fähigkeiten sind wichtig, um mathematische Konzepte präzise im Englischen zu beschreiben und anzuwenden. Zudem bietet dir das Verfolgen des Videos die Möglichkeit, deine Fähigkeiten im Englisch sprechen üben durch shadow speak zu verbessern.

Wichtiges Vokabular & Phrasen

  • Bogen (arc)
  • zentraler Winkel (central angle)
  • Radius (radius)
  • Bogenlänge (arc length)
  • Umfang (circumference)
  • Kreise (circles)
  • drehen (to rotate)
  • Gleichabstand (equidistant)

Übungstipps

Um das Englisch lernen mit YouTube effektiv zu gestalten, empfehle ich dir, das Video mehrmals anzusehen. Achte darauf, die wichtigen Phrasen laut nachzusprechen. Versuche beim shadow speech, synchron mit dem Sprecher zu sprechen, um deinen Sprachfluss und deine Aussprache zu verbessern. Beginne mit langsamem Nachsprechen, bevor du das Tempo erhöhst. Dieser shadowing-Ansatz wird dir helfen, die spezifische Geometrie-Vokabeln in einem natürlichen Kontext zu verinnerlichen. Achte darauf, Pausen im Video zu nutzen, falls du mehr Zeit benötigst, um die Phrasen zu üben. Indem du diese Techniken anwendest, wirst du mit der Zeit dein Englisch sprechen üben noch effektiver gestalten können.

Was ist die Shadowing-Technik?

Shadowing ist eine wissenschaftlich fundierte Sprachlerntechnik, die ursprünglich für die professionelle Dolmetscherausbildung entwickelt und durch den Polyglotten Dr. Alexander Arguelles populär gemacht wurde. Die Methode ist einfach aber wirkungsvoll: Du hörst englisches Audio von Muttersprachlern und wiederholst es sofort laut — wie ein Schatten, der dem Sprecher mit nur 1–2 Sekunden Verzögerung folgt. Anders als passives Hören oder Grammatikübungen zwingt Shadowing dein Gehirn und deine Mundmuskulatur, gleichzeitig echte Sprachmuster zu verarbeiten und zu reproduzieren. Studien zeigen, dass es Aussprachegenauigkeit, Intonation, Rhythmus, verbundene Sprache, Hörverständnis und Sprechflüssigkeit signifikant verbessert — was es zu einer der effektivsten Methoden für die IELTS Speaking-Vorbereitung und reale englische Kommunikation macht.

Shadowing-Technik: die vollständige Schritt-für-Schritt-Anleitung lesen →