The student and its teacher

This picture reminded me of those times you admired your teacher/lecturer for being able to know all these amazing things, while you on the other end didn't have a clue what was going on. The image of the wizard is really fitting, perhaps some genuises are wizards...? Or family of wizards? I wonder...

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Vectors

I like vectors. It is a very good method to visualize the 3-dimentional world of maths. In algebra we learn all about its properties, the dot- and cross product, matrices etc. But where will I ever use vectors? Physics is one field in which it is commonly used to describe such thing as motion, forces, direction, etc.

Say for example that you have two forces acting on an object on the same point, but now you want to know what the resulting force will be, i.e. where will this object go and with what force or speed. Of course there are ways to calculate this, but why not make it fun? A very easy way to do this is to use vectors, where the length of the vectors will represent the magnitude of the force and the direction of the vectors, the direction of the force. Then you use a bit of geometry to create a rectangle from these vectors, the diagonal of the rectangle will then be the answer you are looking for. Clever isn’t it? This resulting vector is sometimes called the sum of the forces. There are many other applications for vectors, and although it isn’t always necessary to use them, it can make it easier by visualising the problem.

A vector space is a space where the elements are vectors. These spaces have nice properties and are used in many applications. It has a lot of theory behind it and was used in some cases to develop some very deep mathematics. Ever heard of a Hilbert space? It is just a complete vector space of which the norm is defined. Norms are defined differently depending on the space. I will discuss this some other time.

So for now, imagine you are a vector in your space (world) and think about what your direction is (where are you heading?) and what is your length (how great a impact have you made in this world?).

The emperor calls

Due to recent comments on my blog (of which I have almost forgotten… I’m ashamed to say) I have decided that I owe it to everyone out there to keep this blog going. I’m considering the idea of it being the emperor of mathematics that is telling me to keep writing, that being the number 0 of course. Nobody messes with 0. If you get it crossed with you it will reduce you to nothing…
Well on a lighter note, I am still studying mathematics, having completed my degree and now studying towards a post-graduate honours degree. I still love it and am going to share with you, whoever you may be, whatever mathematics there is multiplying in my mind.

Time flies...

Wow!
Such a long time and no writing. That's not good.
I still love mathematics. I guess I've been so busy with it, that I haven't had time to get to this blog.

But I'll definitely make more time for it.
I'm now entering my final year of studying, then I'll get my degree!
After that I'm not sure yet, but maths stays on my mind...
I also plan on moving, but we'll see.

Happy festive season!

Living in two dimensions

Living in two dimensions would surely give rise to a monotonous and dull world. It would be flat, without texture (literally) and uninteresting. Maybe then we would all just be normal shapes, depending on species and size. Possibly there would still be colours, although it would have to be dull, because there is no room for shadows or splashes of light in two dimensions.

Every shape would move differently and the bigger the shape, the more careful it would have to move since it could easily get stuck between obstacles, which are made more complex because of the flatness that causes the shapes not to be able to see over anything. But then again, will they see? Or merely sense? Seeing would be a waste, they will only see lines and possibly colours, no depth.

Movement would be confined to the compass directions, no going up or down. There would be no wind, no rainbows, no rain, no water, no fire.

There would really be nothing to do, or would there? Trading three dimensions for two seems not to be a fair trade at all. Does it even make sense to think this way?