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Skill 8 of 13
In Progress

The radian unit

To measure how long the Roman Colosseum is around (circumference), the archaeologist can with a measuring wheel choose to walk all the way around. But she could also just measure the distance across (diameter) and use the formula:1

$$\text{circumference}=\pi\;\text{diameter}$$

In fact, she could do it even quicker by just measuring the distance to the centre (radius), since two of those distances give the diameter:

$$ \text{circumference}=\pi \;\overbrace{2\;\text{radius}}^\text{diameter}$$

So, the circumference (the full round) is ‘$\pi$-times-the-diameter long’, or in other words: ‘$\pi$ diameters long’.2 Or it is ‘$2\pi$ radiuses long’.3

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References:

  1. Sears and Zemansky’s Univesity Physics with Modern Physics’ (book), Hugh D. Young & Roger A. Freedman, Pearson Education, 13th ed., 2012
  2. Online Etymology Dictionary’ (dictionary), Douglas Harper, www.etymonline.com