However, if we draw a triangle ABC using three great circles then we find that a congruent triangle XYZ forms on the opposite side of the sphere.
Find the great circle which is the locus of points at the intersection of the sphere and the plane.
The buttons down the left-hand side allow you to rotate the sphere, move an element, insert a new point, insert a new great circle (called a 'line'), insert a new geodesic (called a 'segment'), or insert a new circle.
A "straight line" in an elliptic plane is an arc of great circle on the sphere.
Since only one hemisphere is displayed, each "point" is represented by one point except those "points" such as D, E, and F on the blue bounding great circle which appear twice.
A completed "straight line" in the elliptic plane is a great circle on the sphere.
In this instance of the method, great circles originating from vertex B of T are projected onto straight lines originating from vertex B' of T' (Figure 15).
To understand these limits, the intersection I of a spherical cap defined by angular length s, and, originating from the center of that cap, an infinitely tight spherical lune defined by two great circles with angle [tau] are constructed (Figure 18a).
To measure distortion angle [lambda], many very small segments of great circles are constructed that intersect the edges of T perpendicularly.
The correct determination, for example, of the circumferences of great circles at aphelion and perihelion seem to be beyond practical determination.
Let the radius of curvature of a great circle at closest approach be pCn(rc).
It is now clear that the fundamental element of distance in the gravitational field is the circumference of a great circle, centred at the heart of an extended spherical body and passing through a spacetime event external thereto.
The one projection that sends all great circles to straight lines, the central azimuthal or gmomonic projection, does not preserve relative distances along those lines.
Thus if we replace the great circle arcs with chords of those arcs, we get exactly the edges and vertices of the convex hull of the vertex set.
Triangle edges are reconstructed (as great circle arcs) by linking vertices.