anchor.diff:  \end{align*}
   ++++  
   
  -=== Summary of Part 1
  +== Summary of Part 1
   
   In Part 1, we covered the definition of quaternion stem:[q=(x,y,z,w)], the vector form of quaternion stem:[q=(\vec{v},w)], unit quaternion stem:[q=(sin⁡\frac{θ}{2}\vec{v},cos⁡\frac{θ}{2})] and how it is used to represent a rotation.
   
  
positive.code: 
  We slightly touched quaternion multiplication, and we proved an important equation stem:[{q_1^{-1}}{q_2^{-1}}=({q_2}{q_1})^{-1}].
  
  === Appendix: Derive Quaternion Multiplication
  
  This part is not very important for understanding quaternion. It is a bit calculation heavy and is more for fun. Feel free to skip.
  
  
negative.code: 
  This representation means if we fully understand flip, which is easier to visualize, we can fully understand rotation and quaternions, since any quaternion can be broken down to flips.
  
  == Quaternion and Flip
  
  Now let’s recall the quaternion vector form stem:[q=(sin⁡\frac{θ}{2}\vec{v},cos⁡\frac{θ}{2})]. With the discussion of flips above, you can almost immediately see why we are using stem:[\frac{θ}{2}] here.
  
  