## Missed A Mile

I’m honestly annoyed with myself. It’s only a little annoyed, though. I didn’t notice when I made my 5,280th tweet on @Nebusj. It’s one of those numbers — the count of feet in a mile — that fascinated the young me. It seemed to come from nowhere — why not 5,300? Why not 5,250? Heck, why not 5,000? — and the most I heard about why it was that was that 5,280 was equal to eight furlongs. What’s a furlong, I might wonder? 5,280 divided by eight is 660, which doesn’t clear things up much.

Yes, yes, I know *now* why it’s 5,280. It was me at age seven that couldn’t sort out why *this* rather than *that*.

But what a number. It had that compelling mix of precision and mystery. And so divisible! When you’ve learned how to do division and think it’s fun, a number like 5,280 with so many divisors is a joy. There’s 48 of them, all told. All the numbers you see on a times table except for 7 and 9 go into it. It’s practically teasing the mathematically-inclined kid to find all these factors. 5,279 and 5,281 are mere primes; 5,278 and 5,282 aren’t nearly so divisor-rich as 5,280. Even 1,760, which I knew well as the number of yards in a mile, isn’t so interesting. And compared to piddling little numbers like 12 or 144 — well!

5,280 is not why I’m a mathematician. I credit a Berenstain Bears book that clearly illustrated what mathematicians do is “add up sums in an observatory on the moon”. But 5,280 is one of those sparkling lights that attracted me to the subject. I imagine having something like this, accessible but mysterious, is key to getting someone hooked on a field. And while I agree the metric system is best for most applications, it’s also true 1,000 isn’t so interesting a number to stare at. You can find plenty of factors of it, but they’ll all follow too-easy patterns. You won’t see a surprising number like 55 or 352 or 1,056 or 1,320 among them.

So, I’m sorry to miss an interesting number like that for my 5,280th tweet. I hope I remember to make some fuss for my 5,280th blog post.

## Ken Dowell 4:02 pm

onTuesday, 23 June, 2015 Permalink |You had me going to my Twitter page to see if I also missed the one milestone. But alas I’m only around 2700. Since that’s about 5 years worth I might need a reminder around five years from now to look out for 5280.

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## Joseph Nebus 3:25 am

onThursday, 25 June, 2015 Permalink |It’s a shame there’s no setting warnings about how many tweets you’ve made, or alarms to make sure the significant ones are credited so. Maybe if I ever make my silly little Twitter app …

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## dianafesmire 4:42 pm

onTuesday, 23 June, 2015 Permalink |I was also thinking about 5280 this week while I was at the horse races with friends. We were trying to figure out how long the races were. They were listed in the program in number of furlongs. I had no idea that 5280 had so many factors and the numbers on both sides of it are prime – Wow! I think I will pose the idea to my sixth graders of finding all the factors the first few weeks of school this year while we are in our Prime Time unit. Thanks for the math! Got my morning off to a great start!

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## Joseph Nebus 3:29 am

onThursday, 25 June, 2015 Permalink |I’m delighted you enjoyed, and glad I could give a fun puzzle to play with. It’s not exactly coincidence that 5,280 should have so many factors. The length of “a mile” can be a pretty arbitrary thing — see how much variation there is in the length of “miles” across different unit systems — so why not pick a unit that can be divided lots of ways as need be?

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## sheldonk2014 5:58 pm

onTuesday, 23 June, 2015 Permalink |I know I get excited in a low level way,like when I get a bag if new socks but a number you got this one Joseph

Sheldon

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## Joseph Nebus 3:30 am

onThursday, 25 June, 2015 Permalink |Well, now … how many socks? Six — a perfect number — or maybe twelve — an abundant number — perhaps?

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## 528 and Level 6 | Find the Factors 2:31 am

onTuesday, 30 June, 2015 Permalink |[…] feet is one tenth of a mile. Joseph Nebus has written a fascinating post on WHY a mile is 5280 feet. Factoring that number is part of the […]

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## scifihammy 11:15 am

onSaturday, 4 July, 2015 Permalink |As a kid, I was also fascinated by this number of feet in a mile :)

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## Joseph Nebus 6:54 pm

onSaturday, 4 July, 2015 Permalink |I’m glad to know I’m not alone in that. I suspected it, of course, since who can’t look at 5,280 and wonder, but it never gets mentioned out loud.

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## scifihammy 7:05 am

onSunday, 5 July, 2015 Permalink |haha For sure I kept quiet about it – as I had enough trouble fitting in as a kid, being small and skinny with glasses, without piping up how interesting 5280 was!! :)

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## Joseph Nebus 6:36 pm

onSunday, 5 July, 2015 Permalink |Ah well. 5280 just has so much over however many tablespoons are in a quarter-cup or whatever other stuff I actually get asked.

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