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General Science
General Science
complex numbers and a question on 3 Dimensional numbers
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complex numbers and a question on 3 Dimensional numbers
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Spacetectonics
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complex numbers and a question on 3 Dimensional numbers
«
on:
13/12/2012 08:31:41 »
Hi All,
Could some one please explain this to me ?
Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part,
now the question is ,how we could extend Complex numbers into "3 dimensional" plane?
Cheers
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imatfaal
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Re: complex numbers and a question on 3 Dimensional numbers
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Reply #1 on:
13/12/2012 10:31:26 »
Hello and welcome
Yes we can! And there are methods for extending into 3, 4, and even more dimensions.
The first extension are called
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. This is the same man who came up with Hamiltonian mechanics - which is vital to the mathematics of quantum mechanics and field theory.
Whilst complex numbers rest on the idea that
Quarternions use the following foundation
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Spacetectonics
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Re: complex numbers and a question on 3 Dimensional numbers
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Reply #2 on:
13/12/2012 13:35:51 »
Thanks Imatfaal,
That makes more sense to me now!
Cheers
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evan_au
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Re: complex numbers and a question on 3 Dimensional numbers
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Reply #3 on:
14/12/2012 12:05:39 »
Quaternions can be used to represent a point of an object in 3-dimensional space as ai+bj+ck+d (you only really need to store a, b and c).
A 3-dimensional object can be represented as a list of such points
Movement, rotation and scaling of objects can be represented as multiplying the coordinates of each point by another quaternion.
This could be used in 3D computer graphics, computer games, etc
However, quaternions are a special case; it only works for certain numbers of dimensions (4), but not 3 or 5. It is possible to generalise them further (eg
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(some nice graphics in the 90s from 12:30 to 14:00)
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Last Edit: 14/12/2012 20:13:59 by evan_au
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Re: complex numbers and a question on 3 Dimensional numbers
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Reply #3 on:
14/12/2012 12:05:39 »
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