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September 2nd, 2017, 02:42 AM  #1 
Senior Member Joined: Nov 2011 Posts: 197 Thanks: 2  formula. please help!!!!
In a page of Wikipedia, there is a formula I don't understand. My English is bad English. Please tell me in simple words what the meaning is of: ijk = −1 In the formula, what is i, j and k... Thank your forward. If you could, help me to design this message in better English after you help me in the question. Last edited by skipjack; September 2nd, 2017 at 02:48 AM. 
September 2nd, 2017, 02:42 AM  #2 
Senior Member Joined: Nov 2011 Posts: 197 Thanks: 2 
the Page: https://en.wikipedia.org/wiki/Quaternion 
September 2nd, 2017, 03:00 AM  #3 
Senior Member Joined: Aug 2017 From: United Kingdom Posts: 197 Thanks: 59 Math Focus: Algebraic Number Theory, Arithmetic Geometry 
$i$, $j$ and $k$ are just symbols for which the following is true: $i^2 = j^2 = k^2 = ijk = 1$ From this, you can deduce that $ij = ji = k$, $jk = kj = i$ and $ki = ik = j$ These guys appear in various situations. One of the five groups (up to isomorphism) of order 8 is the group $Q_8 = \{\pm 1, \pm i, \pm j, \pm k \}$. There is also the ring $H = \{a + bi + cj + dk \,  \, a, b, c, d \in \mathbb{R} \}$ of quaternions, with addition and multiplication as you'd expect. In some sense, the ring structure of this set is at the heart of why every integer can be written as a sum of four squares. 
September 2nd, 2017, 03:26 AM  #4 
Senior Member Joined: Nov 2011 Posts: 197 Thanks: 2  cool 
September 2nd, 2017, 03:28 AM  #5 
Senior Member Joined: Nov 2011 Posts: 197 Thanks: 2  other thing
How can I design the message in Real English. If somebody help I will be happy. other question: what is mean of "quaternion units."?! I need little explainsion, or example or something else. Last edited by shaharhada; September 2nd, 2017 at 03:47 AM. 
September 2nd, 2017, 04:05 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 19,054 Thanks: 1618 
Your English is quite good, and better than that of some people who have English as their main language.

September 2nd, 2017, 04:25 AM  #7 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,191 Thanks: 871 
Google "Quaternion". In particular look at https://en.wikipedia.org/wiki/Quater...atial_rotation.


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