The Pi-Memorization ‘Controversy’ !?
That’s right. There appears to be a controversy of sorts around – of all things! – who has memorized the most digits in the decimal expansion of pi !
If you go by the official Guinness Book of World Records, the record is over 70,000 digits, set in March of this year!! It took over 10 hours to recite the digits! For more details see GuinnessPi.
On the other hand, a Japanese man named Akira Haraguchi appears to have bettered this number TWICE (at least) and has witnesses to verify most of his attempts. He has recited digits to over 50,000 places on four separate occasions, and his record is over 100,000 digits (taking 16 hours)! It is not clear why Guinness will not recognize his attempts. For more details, including the Guinness ‘controversy’, see HaraguchiPi.
I’ve only recently learned of these discrepancies, and I hope to discover more soon. Either way, it is clear that such memorization efforts are mind-boggling!! (I once memorized pi to 50 places in my grad school days – now I can’t even keep track of my cell phone!)
So – Why isn’t 1 a Prime Number??
(Inspired by last week’s FoxTrot2 Cartoon!)
Two common mistakes when it comes to primes: 1 is NOT considered a prime, and 2 is prime (the only even prime)!! The fact that 1 is not a prime is often confusing, right? After all, it is technically a number that is ‘divisible only by 1 and itself’ – which is how most people remember and word the definition of prime. So, why isn’t it considered a prime?
Actually, this is not one of those things that ‘came down off the mountain with Moses’. No high authority decreed that 1 shouldn’t be prime – indeed, there was a time (centuries back) when 1 was considered a prime! So, it’s one of those things that has developed into a convention over time, for a variety of reasons, mathematically. One hears lots of ‘explanations’ for this, but for me, there are two main reasons. To see these two reasons, visit 1NotPrime.
Classic Unsolved/Unknown Problems in Mathematics
There are obviously many unsolved problems in mathematics. And as you might guess, many of them are so esoteric that only a handful of mathematicians know of them (or even care! :-))
But there are a few classic unsolved/unknown problems that are easy for any of us to at least understand the statement. Some of these are interesting, because they seem like they should be ‘solvable’, especially when apparently ‘harder’ questions of a similar nature are known! It’s one of the kinds of mysteries that make mathematics so beautiful to some folks.
Here are three of those types of mysterious unknown problems. Perhaps you can solve them and make us both famous! 🙂 See Unsolved Problems.
Non-Prime Numbers – Fascinating Fact
One of last week’s Brain Teasers asked if you could find five consecutive numbers, none of which is prime*. (We call such numbers [other than 1] composite.) This isn’t too hard, if you look: The first such string occurs at 24, 25, 26, 27, and 28. Another starts at 32, and another at 48, . . .
If you’re curious about these things, you might wonder: Could you find 6 straight composites? How about 10? 20? Or, as a middle schooler might ask, ‘Can you find a million?? What would be the largest string you could find? For the fascinating answer to these questions, and an even-more-surprising result, see Consecutive Composites.
* Recall: A prime is a number [other than 1] which is divisible only by itself and 1. Examples: 2,3,5, . . . 41, 43, . . . 101, 103, . . . ad infinitum.
The Absent-Minded Professor!
It seems that we all love ‘absent-minded’ stories! Is it my imagination or do folks seem to link these stories with MATH professors? Well in this case, it would certainly be justified.
Norbert Weiner was a 20th century Professor of Mathematics at MIT (and he was actually born in Columbia, MO!) All sorts of ‘absent-minded’ type stories are told of him!! Three of my favorites stretch the limits of believability, but all seem to have gained some credibility – though one never knows for sure, I suppose. To see all three stories, visit Absent-Minded Professor.