Super Safi’s Monday Morning Math Mayhem 18 – Pronic Numbers

Morning Mathematical Monsters & Maniacs!

(Today’s post is sponsored by the letter “M”)

Hi, I’m Super Safi and you may remember me from such stats and strategy posts as Kwik-E-Mart Farming and the advanced losing-to-win Superheroes battle strategy.

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?

With our summer Bracket Battle hiatus to determine the Most Desired Episode Content concluded, we resume Monday Morning Math Mayhem anew. And we resume right where the Bracket Battle and Math Mayhem left off.

The winner of this summers Bracket Battle for Most Desired Episode Content was Alone Again, Natura-Diddily (Season 11, Episode 14). And notable content from the episode included racecar driver Clay Babcock and his number 42 racecar.

Before the Bracket Battle, Math Mayhem was discussing Bat Math and we discussed Jackie Robinson, who’s number 42 was the first uniform number retired across baseball, ensuring no baseball player will wear 42 (except on Jackie Robinson day when all personel wear 42).

Jackie Robinson

So today, to resume where we left off with Bat Math and in honour of the Bracket Battle winner, we will be looking at one of the properties of the number 42.

Pronic Numbers

A pronic number is a number which is the product of two consecutive integers:

Pronic number   =   n   x   (n + 1)

42 is the seventh pronic number, and the product of 6 times 7. Examples of the first few pronic numbers include 0, 2, 6, 12, 20, 30, 42, …

0   x   1   =   0

1   x   2   =   2

2   x   3   =   6

3   x   4   =   12

4   x   5   =   20

5   x   6   =   30

6   x   7   =   42

Pronic numbers date back to famous Greek philosopher and early mathematician Aristotle, who document pronic numbers in one of his notable works Metaphysics.

Aristotle

Another property of pronic numbers is that you can also get the product of    n   x   (n + 1)   by adding the first   n   even numbers:

0   x   1   =   0   =   0

1   x   2   =   2   =   2

2   x   3   =   6   =   2   +   4

3   x   4   =   12   =   2   +   4   +   6

4   x   5   =   20   =   2   +   4   +   6   +   8

5   x   6   =   30   =   2   +   4   +   6   +   8   +   10

6   x   7   =   42   =   2   +   4   +   6   +   8   +   10   +   12

One last cool property of pronic numbers is that if you append the number 25 to the end of a pronic number, the result is a square number:

0:   025   =   5²

2:   225   =   15²

6:   625   =   25²

12:   1225   =   35²

20:   2025   =   45²

30:   3025   =   55²

42:   4225   =   65²

Were you familiar with pronic numbers? Did you remember 42 was a pronic number? Did you notice Clay Babcock’s car number was 42? Were you familiar with the other properties of pronic numbers? Sound off in the comments below. You know we love hearing from you.