Octant projection

The octant projection is the first known polyhedral map projection. It is neither conformal nor equal-area. In it, the spherical surface of the earth is divided into eight octants, each flattened into the shape of a Reuleaux triangle bound by circular arcs. If transferred to an elastic support, it would be possible to cover with them the surface of a model of the earth's globe. The eight triangles are oriented in a similar way as per two four-leaf clovers side by side (fleurons), being the earth poles in the center of each clove. One of the sides of the eight triangles, (the one opposite to the center of the pseudo clover), is one fourth of the equator, the remaining two (those that converge to the center of the pseudo clover), are part of the two meridians that with the equator dissect the globe in the eight octants. ==Similar projections==

with sketches of eight other projections of the globe being studied by Leonardo Projections also based on the Reuleaux triangle were published by: • 1549 – Oronce Finé • 1556 – Le Testu • 1580 – John Dee • 1616 – Nicolaas Geelkercken • 1894 – Fiorini • 1909 – Bernard J. S. Cahill • 1916 – Anthiaume • 1938 – Uhden • 1955 – Keuning • 1975 – Cahill–Keyes ==History of authorship research==

Although Leonardo's first description of the octant projection has been proved by Tyler, or Eugène Müntz (1899 – citing Harrisse authority from 1892, although none of them talks about the projection's sketch in Codex Atlanticus). Other scholars accept explicitly both (map and projection: "the eight of a supposed globe represented in a plane"), completely as a Leonardo's work, describing the projection as the first of this type, among them, R. H. Major (1865) in his work Memoir on a mappemonde by Leonardo da Vinci, being the earliest map hitherto known containing the name of America, Grothe, the Enciclopedia universal ilustrada europeo-americana (1934), or David Bower in his work (2012) "The unusual projection for one of John Dee's maps of 1580". Others also accept explicitly both (map and projection) as authentic, although leaving in the air Leonardo's direct hand, giving the authorship of the work to one of his disciples as Nordenskjold states in his book Facsimile-Atlas (1889) confirmed by Dutton (1995) and many others: "on account of the remarkable projection..not by Leonardo himself, but by some ignorant clerk", or Keunig (1955) being more precise: "by one of his followers at his direction". == Octant projection layouts ==

's octant projection in eight octants with Reuleaux triangle's shape 's shape ==See also==