Newton's Cube 4 Circular Projective Geometry

Continued from page 3

See figure "Projection Lines 1"

I departed from actually investigating the ellipse and measuring the angles created by tangents. I decided to consider the behaviour of arcs and tangents both inside an ellipse and inside an enclosing square to see if they was any advantage to using them:

See figure “Projection Lines for an ellipse”

We can consider the arc AB fixed and revolve point P around the ellipse but the arc length will increase (for example AC to BD in figure 2). If we keep the arc AC fixed instead and rotate C or P we can see that a this is better but still the locus is not a square.

See figure “Projection Lines for an ellipse 2”

By including the condition the triangle (such as DAB) must be isoceles a blue square outline does eem apprximated. I have not chcked this in practise finding a different solution.

See figure “Projection Lines for an ellipse 3”

Continued on page 5