In spherical geometry, a spherical lune (or biangle) is an area on a sphere bounded by two half great circles which meet at antipodal points. [1] It is an example of a digon, {2} θ, with dihedral angle θ. [2] The word "lune" derives from luna, the Latin word for Moon.

Jan 6, 2024 · The region on a sphere bordered by two half circles that intersect at antipodal points is known as a spherical lune. It is defined as the curved surface area of the wedge. The term antipodal refers to that point on the surface of sphere which is diametrically opposed to it.

6 days ago · A sliver of the surface of a sphere of radius r cut out by two planes through the azimuthal axis with dihedral angle theta. The surface area of the lune is S=2r^2theta, which is just the area of the sphere times theta/(2pi). The volume of the associated spherical wedge has volume V=2/3r^3theta.

Spherical Lune is the curve surface of the wedge, it is a surface formed by revolving a semi-circular arc about its diameter by less than 360°. The formula for spherical wedge and Lune can be found by ratio and proportion, meaning, spherical wedge is similar to the sphere and spherical Lune is similar to spherical surface.

Spherical lune is the area on a sphere surrounded by two half circles that meet at antipodal points.When we say antipodal, we mean it is the point on the surface of a sphere which is diametrically opposite to it. If we draw a line from one point to …

In analyzing two great circles that lie in a sphere, the two planes that the great circles lie in divide the sphere into four parts. These regions are known as lunes, which comes from the Latin word “luna,” meaning moon. So, a lune in spherical geometry is a two-sided polygon lying on a sphere.

More precisely, a spherical lune is the region between two elliptic line segments connecting two antipodal points. Recall that antipodal points are identified, so the Klein lune only has a single vertex!

To get started, let S be the sphere of radius 1 centered at the origin O in three dimensional space. Using xyz coordinates, we can place O at (0; 0; 0), which means x = y = z = 0, then S is given by x2 + y2 + z2 = 1. Points will now be understood as points on S. A line is now a great circle.

In geometry, a spherical wedge or ungula is a portion of a ball bounded by two plane semidisks and a spherical lune (termed the wedge's base). The angle between the radii lying within the bounding semidisks is the dihedral α.

A lune is a two-sided polygon lying on a sphere. To find the area of a lune, one must know the lunar angle and the formula 2R 2 (lunar angle), where R represents the radius of the sphere. If the lunar angle is not given, find p(pi)/q, where p represents the union of the lunes and q is the number of equal lunes drawn in a hemisphere.