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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 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.
 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
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Quote:
 Originally Posted by studiot What do you mean move?
I might not be using the correct terms but I meant rotating n-dimensional object

 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
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Quote:
 Originally Posted by Elektron 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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