What Is the Circumference of a Circle?

Learn how and why the equation for the circumference of a circle works. Plus -- how is this formula used in the Olympic Games?

Jason Marshall, PhD
5-minute read
Episode #116

Circles in Olympic Track and Field Events

The farther out you are, the longer the distance you have to run to make it around the track.

If you’re looking for a great real world example of the use of the formula for the circumference of a circle, look no further than Olympic track and field. In particular, have you ever noticed how the runners in some track and field races start at different places on the track? If you think about it for a minute, it’s pretty easy to figure out that this type of staggered starting is necessary to compensate for the differences in how far the runners in different lanes have to run when going around curves. 

So, how do the people laying out the track figure out where to draw the different starting lines? Well, if you look at a track, you’ll see that it’s really just made of 2 semi-circles connected to 2 straightaways. If you measure the radius of the semi-circle made by each lane of the track, you can use the circumference formula to calculate the distances that the runners in each lane travel. The farther out you are, the longer the distance you have to run to make it around the track—which is precisely why the runner in the outside lane starts in front, followed by the runner in the next most outside lane, then the next, and so on. And you can calculate exactly what the distances between each runner should be at the start just by applying the formula for the circumference of a circle.

Bonus Tip: How to Easily Convert From KPH to MPH

Before we finish up for today, I want to share a quick and dirty tip that math fan Dan sent me in response my tip in last week’s Olympic-themed episode about converting from kilometers to miles (and kilometers per hour to miles per hour) in your head. Dan points out that it’s kind of tough to divide by 1.6 in your head as I suggested. And he’s definitely right—it’s fairly easy to multiply numbers in your head, but doing division is tough. 

So Dan suggests that instead of dividing by 1.6 to convert from kilometers to miles, we instead multiply by 5/8 (which, as you can check, really is doing the same thing). How is that better? Because multiplying some number by 5/8 is the same as adding 1/2 of that number to 1/4 of 1/2 of that number. Think about it for a few minutes, try it out, and I think you’ll agree with me that Dan’s tip is a good one.

Wrap Up

Okay, that’s all the math we have time for today. Please become a fan of the Math Dude on Facebook where you’ll find lots of great math content posted throughout the week. And if you’re on Twitter, please follow me there too. Finally, please send your math questions my way via Facebook, Twitter, or email at mathdude@quickanddirtytips.com.

Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!


About the Author

Jason Marshall, PhD

Jason Marshall is the author of The Math Dude's Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.

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