In this issue, we examine the reference plane used to measure that angle which we refer to as longitude. We do so as we so often see lines of constant longitude drawn on the maps we use every day. To do so introduces all sorts of ambiguity into the terminology used to define the concept of longitude. In all cases where a flat plane intersects a sphere , the shape formed by the points of intersection is a circle. In the case where the plane also includes the center of the sphere, the result is called a great circle as it is the largest circle which can be constructed by intersecting a sphere with a plane.
All great circles have the same radius which is equal to the radius of the sphere.
The term small circle applies to any circle formed by the intersection of a plane and a sphere which is not a great circle. The intersection of a sphere with any plane which does not also pass through the center of the sphere produces a small circle, i.e. a circle whose radius is less than that of the sphere. A great circle produced by a plane which not only contains the center of the sphere but also the entirety of the axis of rotation is said to produce two semi-circles known as meridians of longitude. The poles define the break points between the two semi circles. A meridian of longitude is often, perhaps incorrectly, referred to as a line of longitude.