C = circle made by intersection of the xy-plane and unit sphere S

C_{O} = (0,0,0) = origin = center of circle C

r = = radius of circle C

(r,0,0) = intersection of positive x-axis with unit sphere S = S_{N} (north pole)

(-r,0,0) = intersection of negative x-axis with unit sphere S

(0,r,0) = intersection of positive y-axis with unit sphere S

(0,-r,0) = intersection of negative y-axis with unit sphere S

z = length from origin to center of unit sphere

S = unit sphere

S_{O } = (0,0, s_{z} ) = center of unit sphere S, where -1 < s_{z} < 1

S_{N} = (r,0,0) = north pole of unit sphere S

S_{C} = (0,0,1-z) = projection of line segment between S_{O} and C_{O} to the surface of sphere S

N = cone having circle C as its base and sphere center S_{O} as its apex

P = (r cos, r sin,0) = tangent point on circle C where planes , , and intersect

h = arc length of circle C from P to S_{N}

h = (from analyzing a chord in circle C)

h = (from analyzing isosceles triangle ∆S_{N}S_{O}P, which has two sides of length 1)

= plane containing point S_{O} and also the equator of sphere S

= plane containing point S_{O} and also the tangent (in the xy-plane) to circle C at point S_{N}

= plane containing point S_{O} and also the tangent (in the xy-plane) to circle C at point P

= plane containing point S_{O} and point P and point S_{N}

= plane containing point S_{O} and point P and plane is perpendicular to plane

a = great circle arc λ

b = great circle arc υ

c = great circle arc ∠S_{C}S_{O}P

D = midpoint of side a

= ∠

= arc length in degrees from (r,0,0) to point P = ∠S_{N}C_{O}P = dihedral ∠S_{N}-S_{O}C_{O}-P

= ∠PS_{O}S_{N}

= angle between the axis of cone N and the cardinal axis of sphere S = ∠S_{N}S_{O}C_{O}.