This article is to wish very happy birthdays to Hagit and Leonid Kerbel, the lovely couple who (several years ago) founded Musica Mundi School, where I have the pleasure of working as the Mathematics Teacher. It’s Leonid’s birthday tomorrow, just one week after Hagit’s birthday.
Leonid and Hagit are not the same age in years; they actually have a uniquely special age difference. Let’s say that they have an age difference of n years, and you can consider n to be a non-zero whole number.
Why is their n uniquely special!? That’s because, in any year (*from when Leonid was just a few years old, and onwards from then), if we multiply Hagit’s age on her birthday in any year by Leonid’s age on his birthday in that same year* and then add on the magical mystery number n, the result will always be a square number.
Hagit and Leonid’s special age difference n is the only non-zero whole number in the Universe for which this beautiful property always holds true.
I like the fact that n matches the number of letters in LOVE: n=4.
Keen Maths enthusiasts can enjoying proving, quite easily, that the product of Hagit’s and Leonid’s ages (on Leonid’s birthdays*) + 4 will always produce a square number.
Here in this article, we’ll just give three examples to illustrate the result:-
(1 x 5) + 4 = 9 = 3 squared
(19 x 23) + 4 = 441 = 21 squared
(43 x 47) + 4 = 2025 = 45 squared.
It’s time for a quick joke…!
Why did the student eat his Music homework!?
It’s because Leonid told him it was a piece of cake!
Assuming that you don’t have to go to hospital after that one (!!), I’d like to finish by wishing you all a very happy weekend now.
With kindest wishes as always,
Paul Motwani xxx
P.S. In a recent photo taken by my wife, everyone has just eaten some delicious cake and is feeling pretty good!