Curves by Equation:

Archimedes Curves: These curves are built by implementing the mathematical figures as seen in Image 3 it shows the math code for Image 1 which is the calculations for a tapered thread pattern of Image 2. This curve was used to build the threads.

Logarithmic Curves: Logarithmic and golden curves are the hardest to create mathematically but have the best air or fluid flow. As in the Archimedes the math is also implemented in the cad programs. The example of Image 6 shows the math code and Image 5 shows the curve in which the outer surface for the pump input is constructed. The reason I designed it based upon the Logarithmic figures is that of nature where there is a progression of accuracy and speed flow as seen in plant growth, weather patterns such as hurricanes, tornadoes, and in the solar systems such as our own Milky Way.