Monday Maths 16

I have more pictures for you today :)

My boyfriend really liked this one. I think it's mostly because he actually got it, but I think it's funny too. I've been doing a lot about converging sequences in Analysis recently.

Why is 6 scared of 7...?

I told you that Fibonacci pops up in nature all the time! Even in the shape of storms.

I realise that I really ought to write an actual blog post sometime soon. I have an idea for one, but it's finding the time/energy/words to write it that is slowing me down. Soon!

The Dominoes and the Chessboard

On Monday, I posted a puzzle regarding a chessboard and some dominoes. As promised, I am now going to give the answer (so that my boyfriend's family will stop arguing about it!)

So, is it possible to place 32 dominoes, each covering two squares, on a chessboard with two diagonally opposite corners cut out?

The answer is: No. It is not possible.

But how do you prove it? Most of the modules in my degree this term are all about proving things, and it can get very confusing. Especially Analysis. But there is a simple way to think about this puzzle.

As the two corners cut out of the chessboard are diagonally opposite each other, they must be the same colour. This means that we have 30 of one colour (in the picture above it is black) and 32 of the other colour (obviously, in this case white). As the dominoes only cover two squares, no matter how you place them, they are going to cover one of each colour. So if we pair off the colours, we can match 30 black to 30 white, but then we are left with 2 of the same colour left over. We know that a single domino cannot cover two squares of the same colour, so the puzzle is therefore impossible.

Hopefully I explained that clearly so you aren't left feeling as confused as before!

Monday Maths Madness 13

Back to pictures this week. My boyfriend keeps sending me links to pictures on 9gag.com that are maths related, so I have enough to do a post about them!

This is a bit what I feel like in my lectures at the moment! Especially Analysis. You think it's simple, but when you actually come to write it down, there are no words to explain it.

The square root of a negative number is called an imaginary number. Anything else is a real number. Squaring an imaginary number makes it real. Shit just got real.

This is my personal favourite. I'm doing a lot about planes in Intro to Geometry at the moment. So far there have been no snakes though... Just triangles.