How much longer is a Pi Day 5k?

[Andy Norton] [Steven Mackay] How much further is a Pi Day 5k? Local expert and resident mathematician, Andy Norton, has the scoop. [Andy Norton] Hi, I'm Andy Norton in the math department here. And we're trying to figure out how much longer is a Pi k than a 5k. And we have two different solutions here. Lon' solution: he starts by converting miles into feet. One mile is 5280 feet. And then he says, well, 5 kilometers or a 5k is about 3.1 miles. And so Pi k would be 3.14 miles. So he just figures out this difference here is 0.04 miles. So he decided that if Pi k must be about 0.04 miles longer than a 5k, but 0.04 miles in feet, if we take that same, 5280 feet per mile is 211 feet. Next, we'll look at Teresa solution. Here we have Teresa solution. So Teresa has converted directly between meters and feet. She knows that 5k, 5 kilometers means 5000 meters. And she knows that that's about 16,404 feet. And that's going to turn out to be a better approximation for how many feet are in 56k. So now, which compares that to a Pi k, she took 3.14 miles for the Pi k, multiplies that by the same 5280 feet per mile and get 16,579 feet. Now if you look at the difference between her Pi k approximation and her 5k approximation in feet, you get a 175 feet. That's going to turn out to be a more accurate answer because she had a more accurate estimation for how many feet are in a meter. But we can get more accurate still, because pi doesn't stop at 3.14. Pi is better approximated as 3.14159. We are going to stop there even though we could go on further and further and get better and better approximations. But if we use 3.14159 miles, then we're going to end up getting 16,587.6 feet in a Pi k. And when we subtract how many feet are in a 5k, we're going to end up getting 183.4 feet. So if you're running a Pi k instead of a 5k, be prepared to those extra 183 feet. [Steven Mackay] And there you have it. The correct answer lies somewhere in the middle. So let's get ready for Pi Day and let's make it a great day. Go Hokies!