Dual Quaternions
I give proofs and outline the theory for dual quaternions so we can use them for complex motion of Xenaʻs powers.
Metallic Means
I give the proof of the formula for the nth metallic mean which is used for Xenaʻs power.
Exponential Quaternion
I give the proof of the polar form for quaternions which lets us switch grids when we analyze them.
Tidal Theorem
I give the proof of the Tidal Theorem for the linear sum of numbers up to any number.