Definition of the Eccentricity - Circle Projection

The "Circle Projection" definition of the ellipse can be described as follows: “An Ellipse is mathematically identical to a circle viewed at an angle”. This is demonstrated in Figure 1 below where the the circle is first rotated on the x axis (front view), and then rotated on the y axis (side view).

Based on this definition of the ellipse, the eccentricity can be described by how much the circle is rotated in the 'z' direction. More specifically, the eccentricity is the ratio of the value 'z' (depth) over the value 'a' (semi-major axis).

1. If the circle is rotated 90 degrees on the x axis then the front view becomes a line.
• The eccentricity in this case, or ratio of z to a, becomes 1.
2. If the circle is rotated 0 degrees on the x axis then the front view becomes a circle.
   • The eccentricity in this case, or ratio of z to a, becomes 0.
     

Figure 1- Front view and Side view