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May 7th, 2017, 07:18 AM  #1 
Newbie Joined: Dec 2016 From: New York Posts: 4 Thanks: 0  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 nth dimension, the number of points needed is 2^n1 How true is this equation? And I would be really interested to know more about this concept. 
May 7th, 2017, 08:20 AM  #2 
Senior Member Joined: Jun 2015 From: England Posts: 740 Thanks: 208 
What do you mean move?

May 7th, 2017, 11:40 AM  #3 
Newbie Joined: Dec 2016 From: New York Posts: 4 Thanks: 0  
May 7th, 2017, 11:55 AM  #4 
Senior Member Joined: Jun 2015 From: England Posts: 740 Thanks: 208 
So why do you think you need 4 types of number to rotate a 3D object?

May 7th, 2017, 12:47 PM  #5  
Senior Member Joined: Sep 2015 From: USA Posts: 1,763 Thanks: 905  Quote:
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 $n1$ angles to rotate an $n$ dimensional object. Basically you've got the product of $n1$ 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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complex, dimensions, math, numbers, real 
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