Four Square

Yesterday was one of my favourite kinds of days. It was just warm enough to walk around without a jacket and the sun was bright yet gentle. When the temperature is in that range, there is no fretting with your clothing layers; you're just comfortable. And when you are comfortable, it's so easy to look for the beauty in the world. Mother Nature isn't one to disappoint. Thanks, Mom, for the changing leaves and the views of the coast mountains.

I decided to enhance my already-awesome-day with three upgrades.

1. A mid-morning stroll in the harbour with my man.

2. A Cinnamon Kiss Latte. (Move on over "pumpkin spice." My heart belongs to someone else now. Someone who brings the real spice back to my caffeine romance.)

3. A read-through of the proof that every positive integer (definition: a regular old number; no fractions, no decimals) can be written as the sum of four integer squares (an integer times itself).

Pick your favourite number. In our house, where Micheal Jordan is heavily featured, this number is 23. Now try to write it as the sum of four squares.

23 = 9 + 9 + 4 + 1 = (3x3) + (3x3) + (2x2) + (1x1)

(Note: 0x0 counts as an integer square. Also, if you know how to use superscript on blogger, please let me know how.)

What is truly remarkable is that EVERY positive integer can be written this way. Even this one: 84863672095433749084578467379049368059659357463527546367548986937846572

It also means that if you have a number of Skittles, you can arrange them in exactly four square shapes. Since 0x0 counts as a square, this means that you can arrange them in at most four squares. These squares must be filled in, like this.

 

If you had 7845674986935860893457289 Skittles, no temptation to eat them, and nothing better to do, you could arrange them in at most four square shapes. It would be possible! Then, if you ate some, you could rearrange the remaining Skittles into at most four new square shapes. Outstanding!

Furthermore, if we had a super-charged gravity pump capable of towing stars, we could arrange all of the stars in the universe into, you guessed it, at most four square shapes. If we had two super-charged gravity pumps, we could divide the stars into two groups. You and I could have a race; the first to arrange their collection of stars into at most four square shapes using their gravity pump would be declared the winner.

I think it would be quite a long race.

Bye for now.

Enjoy the autumn weather! Thanks for stopping by.