A lune is either of two figures, both shaped roughly like a crescent Moon. The word "lune" derives from luna, the Latin word for Moon. This article is about Earths moon. ... Latin was the language originally spoken in the region around Rome called Latium. ...

In plane geometry, the crescent shape formed from two intersecting circles is called a lune.

Image File history File links Crescent. ... Image File history File links Crescent. ...

Plane geometry

In plane geometry, a lune is a convex area bounded by two intersecting circles. In the special case when the circles have the same radius, the figure is called a lens. Formally, a lune is the relative complement of one circle in another (where they intersect but neither is a subset of the other).^[1] In mathematics, plane geometry may mean: geometry of the Euclidean plane; or sometimes geometry of a projective plane, most commonly the real projective plane but possibly the complex projective plane, Fano plane or others; or geometry of the hyperbolic plane or two-dimensional spherical geometry. ... Look up convex in Wiktionary, the free dictionary. ... In set theory and other branches of mathematics, two kinds of complements are defined, the relative complement and the absolute complement. ...

Spherical geometry

A spherical lune. The two great circles are shown as thin black lines, whereas the lune itself (shown in green) is outlined in thick black lines, corresponding to its defining half great circles. The great circles intersect at two polar opposite points, such as the North and South poles.

In spherical geometry, a lune is an area on a sphere bounded by two half great circles.^[2] Such circles are the largest possible circles on a sphere; each great circle divides the surface of the sphere into two equal halves. Two great circles always intersect at two polar opposite points. Common examples of great circles are lines of longitude (meridians), which meet at the North and South Poles. Thus, the area between two meridians of longitude is a lune. The area of a spherical lune is 2θ R², where R is the radius of the sphere and θ is the dihedral angle between the two half great circles. When this angle equals 2π — i.e., when the second half great circle has moved a full circle, and the lune inbetween covers the sphere — the area formula for the spherical lune gives 4πR², the surface area of the sphere. Spherical geometry is the geometry of the two-dimensional surface of a sphere. ... A great circle is a circle on the surface of a sphere that has the same diameter as the sphere, dividing the sphere into two equal hemispheres. ... A sphere is a symmetrical geometrical object. ... Longitude is the east-west geographic coordinate measurement most commonly utilized in cartography and global navigation. ... For other uses, see North Pole (disambiguation). ... For other uses, see South Pole (disambiguation). ... In Aerospace engineering, the dihedral is the angle that the two wings make with each other. ...

The crescent Moon is a spherical lune, as described in the text. Here, the blue and red portions may be taken equally as the lighted and dark portions of the Moon visible from Earth, or vice versa.

The lighted portion of the Moon is a spherical lune. The first of the two intersecting great circles is the boundary separating the lighted half of the Moon from the dark half. The second great circle is that which separates the half visible from the Earth from the invisible half. Seen face on, this lighted spherical lune produces the familiar crescent shape of the Moon seen from Earth, as illustrated in the Figure at the left. Image File history File links Gibbous-Crescent-half-ellipse-in-circle. ... Image File history File links Gibbous-Crescent-half-ellipse-in-circle. ... This article is about Earths moon. ... This article is about Earth as a planet. ... Example of orthographic drawing from a US Patent (1913), showing two views of the same object. ...

See also

• Arbelos
• Spherical geometry
• Gauss-Bonnet theorem

Arbelos. ... Spherical geometry is the geometry of the two-dimensional surface of a sphere. ... The Gauss-Bonnet theorem in differential geometry is an important statement about surfaces which connects their geometry (in the sense of curvature) to their topology (in the sense of the Euler characteristic). ...

References