If '1' is the unit in real (1D) space, '1' and 'i' are the units in complex (2D) space, then surely one more unit ('j' ?) will be needed in 'whatchamaycallit' (3D) space ?
Also consider that if multiplication by 1 in real space is an identity operation (keeping things unchanged) and multiplication by i in complex space is a counterclockwise planar rotation by 90 degrees, what will multiplication by 'j' in 3D space mean ? Mind that now there are two addtional (basic) planes yz and zx to rotate in ?
2006-09-28 05:02:53 · 5 answers · asked by Problem Child 2 in Science & Mathematics ➔ Mathematics
excellent question,
the thing is, that no there is no system of numbers that have 3 dimensions.
the next system are the quaternions, but those are 4 dimensional, actually they are the analogue of the complex numbers in the following way:
the quaternions are to the complex numbers
what the complex numbers are to the real numbers,
in fact, we can think of the quaternions as two copies of C.
the next system of numbers would be the octonions, but these are also in dimension 8.
and that is it...
no more systems of numbers!!!!
amazing! isn't it?
2006-09-28 05:12:09 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Real and Complex number arises out of sqrt(-1). From our elementary algebra we know that there are only two possible roots for any quadratic equation and so there can only be two number system, real and complex.
In general, real numbers forms a subset of complex numbers.
Since there is no other possibility of representing numbers, complex representation is the saturation of definition of numbers.
2006-09-29 02:44:18 · answer #2 · answered by Anonymous · 2⤊ 0⤋
Quarternions
2006-09-28 05:17:10 · answer #3 · answered by ag_iitkgp 7 · 0⤊ 1⤋
Spherical vectors.
2006-09-28 05:07:20 · answer #4 · answered by Anonymous · 0⤊ 1⤋
round numbers and square roots
2006-09-28 05:06:48 · answer #5 · answered by Murphster 1 · 0⤊ 1⤋