the egg project

The mathematics behind this topic is simple and is all about how circles meet. The surface of an egg is smooth. Mathematically we are constructing it out of fragments of circles of different radii, but where those circles meet we do not want an abrupt change of slope.
In the first diagram below, two circles touch at point C. This means that at C there is a radius of each circle lying in the same line - the radii CB and CA. If we now remove arcs from each circle as shown in the second diagram, we obtain a smooth curve through point C. This principle is used throughout the egg project.