Skill 8 of 13
In Progress

The radian unit

Mathematical skill ●●●○○

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


In fact, she could do it even more quickly by simply 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 long2 or ‘2\pi radiuses long’.3

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  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,