by Simon
6. September 2010 17:46
More hardcore, actual mathematics will be coming soon. But that requires me to actually have MathJax (the natively installed mathtype software that I've installed on the server) to be up and running and functioning within the blogging software. And then I have to go back and convert all the image based math equations into MathJax typeset. In the mean time - at my last study group, we began talking about symbology. In our last class, we learned that the overbar not only means a repeating decimal, but also means the conjugate of something. Which got me thinking about the below. I don't suggest you try this on your math teacher until I've actually taken over the Mathematical world and imposed my own definitions upon it, but still - take a think about how things you wouldn't normally think of doing can be applied in different ways.
When we see the following equation:
We immediately think - oh! That's a perfect square! Or, at least, maths teachers would desperately hope that's what we think of. And so we factor it:
(x+5) \\ (x+5)^2 $)
Now say we see the following equation.
Again, maths teachers would hope we jump up and shout "that's a difference of squares!" And so, we factor it.
(x-5) $)
But there's no shortcut! But, hang on.
^{\bar 2} $)
Look! It's an overbar! And an overbar, in this context, could be defined (by me, of course) to mean "take this expression, and multiply it by its conjugate."
So, if we accept the definition of Mathematics by Simon (MbS for short) what would this multiply out to?
^{\bar 2} $)
A cursory glance of the internet tells me that no-one uses the bar over the exponent to mean something else, but if you know better, please tell me!
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