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May 7th, 2017, 06:18 AM   #1
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Dimensions, and numbers beyond real numbers

I am not that advanced in math, so the question I am asking might seem really elementary. But while I was watching this video, ,
I noticed a pattern that

1 dimensional objects need only 1 type of number to move(real numbers)
2 dimensional objects need only 2 types of numbers to move(real and complex)
3 dimensional objects need only 4 types of numbers to move(real,i,j,k)

and the pattern is for any n-th dimension, the number of points needed is
2^n-1

How true is this equation? And I would be really interested to know more about this concept.
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May 7th, 2017, 07:20 AM   #2
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What do you mean move?
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May 7th, 2017, 10:40 AM   #3
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Quote:
Originally Posted by studiot View Post
What do you mean move?
I might not be using the correct terms but I meant rotating n-dimensional object
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May 7th, 2017, 10:55 AM   #4
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So why do you think you need 4 types of number to rotate a 3D object?
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May 7th, 2017, 11:47 AM   #5
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Quote:
Originally Posted by Elektron View Post
I might not be using the correct terms but I meant rotating n-dimensional object
In one dimension objects cannot be rotated.

In two dimensions a single angle, $\theta$, is all that is needed.

In three dimensions two angles are necessary

I'm going to guess that this continues into higher dimensions and that you need $n-1$ angles to rotate an $n$ dimensional object.

Basically you've got the product of $n-1$ rotation matrices each having it's own parameter.

Where the quaternions come in is if you want to translate and rotate a three dimensional object using a single matrix.
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