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My precalc teacher was rambling a few days ago about functions. She said that the two dimensional functions that we are doing now also exist in the third and fourth dimension. She said that some answers (she cited imaginary numbers) are only right at certain points in time.
If it's true, that's pretty deep... If not, it was a wasted few minutes even thinking about it.
I can grasp the third dimension, that's easy to visualize... but some answers being right at certain points of time, and the same answers wrong at others? Seems a bit strange.
Yeah, its pretty weird stuff but its true. I have a graphing calculator program on my computer and it shows some 4-D functions. Basically they are like 3-D functions which are easy to visualize except they move. So you might have a cube that gets bigger and then gets smaller. I have to idea how it works though. Or another example is the screensavers on windows called 3D flowerbox.
We took a week in precalc learning about the fourth dimension. It was a nightmare. Really cool, though...you should definitely check out a book called "flatland"...it's about moving between the different dimensions, real quick read.
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