<story><title>Quaternions: the Strange Numbers That Birthed Modern Algebra</title><url>https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/</url></story><parent_chain></parent_chain><comment><author>TipVFL</author><text>Quaternions recently made me look pretty smart.&lt;p&gt;I was consulting at a company that&amp;#x27;s developing a VR real estate app, and the first thing I did was check to see whether they were calculating their rotations with quaternions.&lt;p&gt;It was easy to do, I just looked straight up and then turned my head to the right. My view rotated to the left, and I almost vomited. I immediately ripped the headset off and said, &amp;quot;You&amp;#x27;re using euler angles to calculate rotations, you need to use quaternions.&amp;quot;&lt;p&gt;I felt pretty good about finding the biggest flaw in their system in 3 seconds.</text></comment>
<story><title>Quaternions: the Strange Numbers That Birthed Modern Algebra</title><url>https://www.quantamagazine.org/the-strange-numbers-that-birthed-modern-algebra-20180906/</url></story><parent_chain></parent_chain><comment><author>calebh</author><text>I&amp;#x27;ve found that the easiest way to understand quaternions is by visualizing them as scaled &amp;quot;look&amp;quot; or &amp;quot;orientation&amp;quot; vectors.&lt;p&gt;For example, if an airplane is oriented in the direction (x,y,z) at a rotation θ around that axis, then its rotation in quaternion form is cos(θ&amp;#x2F;2)+x sin(θ&amp;#x2F;2) i + y sin(θ&amp;#x2F;2) j + z sin(θ&amp;#x2F;2) k&lt;p&gt;Notice that the multiplications involving x, y, and z are just scaling the vector.&lt;p&gt;The other important thing to realize is that sin(θ&amp;#x2F;2) is greater than or equal to zero in the interval [0, 2*pi]. So a quaternion is just a look vector where the magnitude of the vector is determined by the rotation around the look vector axis.&lt;p&gt;See this page for a useful picture: &lt;a href=&quot;http:&amp;#x2F;&amp;#x2F;www.chrobotics.com&amp;#x2F;library&amp;#x2F;understanding-quaternions&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;www.chrobotics.com&amp;#x2F;library&amp;#x2F;understanding-quaternions&lt;/a&gt;</text></comment>