How much calculus do you know? (the more the merrier!)
Looking at those pictures you should have enough data for the low pass and high pass filters. But, what worries me is what you chose for the time constants. What you need to do is plot the voltage across the resistor vs. the voltage of the...
Quaternions are also used by 3d programmers a lot for "camera" classes. Many people now argue that these things are useless because vector algebra and calculus can do the exact same thing. It is my understanding that this is a precurser to that branch of mathematics.
Of course tachyons exist. Don't you remember when data discovered the cloaked romulan vesels???
Of course then there's this amusing limerick i've heard.
edit: found the author :D
IIRC, silicon is much quicker to fabricate.
There are semiconductor technologies that put germanium islands in silicon and all kinds of other weird things.
Actually that c comes from Permittivity and permeability of free space... electromagnetism stuff. It is also not casual that e is every where as well. If anything you're describing things in a very mathematical sense.
Maybe you're not getting it. A 2-d space can be made up of x^2 + x^3.
A dimension is a purely mathematical concept.... Even in physics.
Now to really get your noodle. You can transform a set of vectors to another set of vectors. A NullSpace is the set of all vectors that get mapped to 0 vector.
First of all, each dimension doesn't have to be perpendicular. What defines a dimension is that the basis vectors can't be a linear combination of each other.
If you are really interrested try reading some linear algebra. that will give you a good idea of what is a space, subspace...