Today’s Special Number: 7
Like all bloggers, I like to review my stats and see which threads are getting the most traffic. And this one — National Pi Day — is a doozy by my dismal standards. 35 comments!
So, thinking I’ve spotted a trend, and being the politician that I am, I offer: 7, my favorite Special Number. If math sells around here, I’m the next Paul Erdos baby.
But seriously, 7 has quite a bit to recommend it. For example, it’s pretty simple in binary notation (111), and its inverse (notice the it’s-its distinction there, kids?) is .142857, repeating ad nauseum.
And what’s so special about that, you might ask? Well, check this out …
If you add 142857 to 142857, you get 285714. The same digits, re-arranged. Add another 142857 to that, and you get 428571. The same digits, re-arranged again.
Add 142857 again, and you get 571428. Ditto. Same with 714285 and 857142. It’s always the digits 1-4-2-8-5-7, re-arranged in some way. Then add 142857 to 857142 and you get 999999, and that just happens to be the 7th time we added 142857.
Here’s another way to say the same thing:
1/7 = .142857142857142857142857142857142857142857142857142857
2/7 = .285714285714285714285714285714285714285714285714285714
3/7 = .428571428571428571428571428571428571428571428571428571
4/7 = .571428571428571428571428571428571428571428571428571428
5/7 = .714285714285714285714285714285714285714285714285714285
6/7 = .857142857142857142857142857142857142857142857142857142
Seven. Dig it. No other prime comes close.
This entry was posted on Friday, June 16th, 2006 at 10:14 pm. You can subscribe to comments on this post through its RSS feed.
on June 17, 2006 at 6:08 am Scott wrote:
Can we discuss the mystical nature (and literary selling power)of Phi next week, professor Mahugh?
on June 17, 2006 at 6:19 am Dave wrote:
Very cool post!
on June 17, 2006 at 7:53 am sam wrote:
Cool
on June 17, 2006 at 11:47 am Doug wrote:
Scott, you and Tom will be glad to know I have a post on Phi up on blocks in the garage, nearly ready for unleashing on the world. After I finish pounding out the dents, painting the hood, and lubing it up in all the rights spots, I’m going to post it right here.
on June 17, 2006 at 5:25 pm Tom wrote:
Oh, unleash, unleash! Of course, a poorly lubed post can fall apart. Okay, your call. But I’m eager to see what you have to say about Phi.
The seven stuff is cool - I still have a hard time figuring out whether the digits and the values they represent are relevantly connected enough to make these things magic (as it were), but it’s a very cool and unlikely set of occurrences.
on June 18, 2006 at 7:26 am Scott wrote:
….my brain hurts.
on July 1, 2006 at 8:57 am Suny wrote:
can u tel me how to find factorial for this
number?
285714!=factorial of 285714
on July 2, 2006 at 2:35 pm Doug wrote:
Well, Suny, you’d multiply 285714 by every one of the numbers less than it, one at a time. And the result would be a really huge number, with about 30,000 digits.
Or did you mean the factors of that number? Let’s see … OK, I’ve got it:
2 x 3 x 3 x 3 x 11 x 13 x 37 = 285714
How did I do that? Ha! That’s the subject of an upcoming post … maybe later today. Thanks for asking!