Asymmetric lower northern shaft

The adjustment to the dynamic geometry that is required to straighten out the plot in the lower northern shaft so that it matches the hexagonal rod is entirely logical and is based on how the lower shafts have already been created. There are two methods that have been used:

1. The lower southern shaft was formed by creating a tangent line from the static base end point of the secondary ellipse
2. The lower northern shaft was created by forming a tangent line from the projection of the dynamic southern end of the secondary ellipse's base end point.

If you look at the projection of the base end of the secondary ellipse you can see that the result of combining these two methods of formation. When the ellipse's rotation is a positive angle, method one is used, and when the rotation angle is negative, method two is used, and consequently the hexagonal rod can be correctly plotted.

If you zoom in on the lower section of the pyramid and look at the secondary ellipse and the moving end of the equator line you can see the asymmetric nature of the geometry that is now forming the tangent line in more detail and if you zoom in on the intersect area you can see that the intersect point, when plotted over time, draws the hexagonal rod. The blue section is the bent part of the rod, and the yellow section is the straight part of the rod which runs parallel to the shaft and is positioned on the shaft's floor.

Because the geometric plot of the rod is orthogonal to the axis of the rod that runs down its length, and the straight part of the rod is parallel to the floor of the shaft, then the mathematics plot that is on the screen must be a picture of the rod 'sitting upright' in the shaft, a position from which it will require rotating in 3D to fit into the shaft which bends to the west (into the screen).

Before rotating this geometric plot of the rod in 3D there are some points that need looking at on the next two pages to ensure that the plot is being drawn correctly.