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September 2nd, 2017, 03:42 AM   #1
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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 03:48 AM.
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September 2nd, 2017, 03:42 AM   #2
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the Page:
https://en.wikipedia.org/wiki/Quaternion
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September 2nd, 2017, 04:00 AM   #3
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$i$, $j$ 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.
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September 2nd, 2017, 04:26 AM   #4
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cool

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September 2nd, 2017, 04:28 AM   #5
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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 04:47 AM.
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September 2nd, 2017, 05:05 AM   #6
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Your English is quite good, and better than that of some people who have English as their main language.
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September 2nd, 2017, 05:25 AM   #7
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Google "Quaternion". In particular look at https://en.wikipedia.org/wiki/Quater...atial_rotation.
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