Fits Danze shower and tub & shower trims with the diverter on the tub spout. Fits all Danze shower and tub & shower trims with the diverter on the valve trim / handle trim. This item Danze D112000BT Shower Single Control Pressure Balance Mixing Valve with Screwdriver Stops.
This theorem involves Euler's polyhedral formula (sometimes called Euler's formula). Today we would state this result as: The number of vertices V, faces F, and edges E in a convex 3-dimensional polyhedron, satisfy V + F - E = 2.
Since you have a formula for calculating $F_x$ as a function of $\mathbf{v}$ and $t$, you can use the $x$-velocity at any given time step to calculate an approximation to the $x$-velocity at the next time step, and similarly for the other components. This is called the Euler method for numerical integration.