Morning Mathematical Monsters & Maniacs!
(Today’s post is sponsored by the letter “M”)
Over the past 600+ episodes, The Simpsons has taken us on an amazing mathematical journey involving fractions, probability, Fermat’s last theorem, and hundreds of other aspects from the wonderful world off mathematics.
And what better way to start your week, then by discussing math Monday morning?
So let’s get started this week by continuing our discussion from last week about Perfect numbers and move on to Narcissistic numbers.
In the finale of Season 17, Marge and Homer Turn a Couple Play (Season 17, Episode 22), the Springfield Isotopes’s star first baseman Buck “Home Run King” Mitchell is having marital problems with his pop star wife Tabitha Vixx (voiced by This Is Us star Mandy Moore). So when he sees Homer and Marge kissing on the Jumbotron, he asks them for advice. But when Homer is later caught giving a neck massage to Tabitha, both couples break up again – and it is hard for Homer and Marge to give advice when they are not talking to each other themselves.
Towards the end of the episode, Tabitha appears on the Jumbotron asking the stadium crowd to guess the evening’s attendance. At first glance, it appears as though the three numbers are just random numbers. However, as we saw the last two weeks and will see today, these three numbers are more than just random numbers.
The third number on the Jumbotron is 8,208.
8,208 is a narcissistic number, which is a number that is the sum of its own digits each raised to the power of the number of digits.
8,208 is the 16th narcissistic number in the base 10 decimal system. The first ten are the ten single digit numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), as anything raised to the power 1 is itself. So all one-digit numbers are narcissistic numbers. The following 6 narcissistic numbers are:
153 = 13 + 53 + 33
370 = 33 + 73 + 03
371 = 33 + 73 + 13
407 = 43 + 03 + 73
1,634 = 14 + 64 + 34 + 44
8,208 = 84 + 24 + 04 + 84
In 1985, mathematician D. Winters proved there are only 88 narcissistic numbers in the base 10 decimal system. The 88th and largest narcissistic number has 39 digits and is 115,132,219,018,763,992,565,095,597,973,971,522,401.
115,132,219,018,763,992,565,095,597,973,971,522,401 = 139 + 139 + 539 + 139 + 339 + 239 + 239 + 139 + 939 + 039 + 139 + 839 + 739 + 639 + 339 + 939 + 939 + 239 + 539 + 639 + 539 + 039 + 939 + 539 + 539 + 939 + 739 + 939 + 739 + 339 + 939 + 739 + 139 + 539 + 239 + 239 + 439 + 039 + 139
Now that we know the secret behind the third number on the Jumbotron, one has to wonder why did the writers of the episode select these three numbers and why did I start this series of post with these three numbers? It could be argued the both Tabitha and I are perfect, in our prime, and narcissistic. 🙂
Be sure to come back next week when we talk about a different concept of math.
Do you remember this episode? Did you catch the number 8,208 on the Jumbotron? Did you recognize the number 8,208 as a narcissistic number? Are you familiar with Narcissistic numbers? Sound off in the comments below. You know we love hearing from you.