The octant projection or octants projection, is a type of

map projection In cartography, a map projection is any of a broad set of Transformation (function) , transformations employed to represent the curved two-dimensional Surface (mathematics), surface of a globe on a Plane (mathematics), plane. In a map projection, ...

proposed the first time, in 1508, by

Leonardo da Vinci Leonardo di ser Piero da Vinci (15 April 1452 - 2 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, draughtsman, engineer, scientist, theorist, sculptor, and architect. While his fame initially rested o ...

in his

Codex Atlanticus The Codex Atlanticus (Atlantic Codex) is a 12-volume, bound set of drawings and writings (in Italian) by Leonardo da Vinci, the largest single set. Its name indicates the large paper used to preserve original Leonardo notebook pages, which was u ...

. Leonardo's authorship would be demonstrated by Christopher Tyler, who stated "For those projections dated later than 1508, his drawings should be effectively considered the original precursors." The same page of the Codex contains sketches of eight other projections of the globe (those known in the late fifteenth century) studied by Leonardo, including

Ptolemy Claudius Ptolemy (; , ; ; – 160s/170s AD) was a Greco-Roman mathematician, astronomer, astrologer, geographer, and music theorist who wrote about a dozen scientific treatises, three of which were important to later Byzantine science, Byzant ...

's conical planisphere projection and Roselli's pseudocylindric projection.

Description

The octant projection is the first known

polyhedral map projection A polyhedral map projection is a map projection based on a spherical polyhedron. Typically, the polyhedron is overlaid on the globe, and each face of the polyhedron is transformed to a polygon or other shape in the plane. The best-known polyhedra ...

. 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 equator is the circle of latitude that divides Earth into the Northern Hemisphere, Northern and Southern Hemisphere, Southern Hemispheres of Earth, hemispheres. It is an imaginary line located at 0 degrees latitude, about in circumferen ...

, 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

Projections also based on the Reuleaux triangle were published by: *1549 – Oronce Finé *1556 – Le Testu *1580 –

John Dee John Dee (13 July 1527 – 1608 or 1609) was an English mathematician, astronomer, teacher, astrologer, occultist, and alchemist. He was the court astronomer for, and advisor to, Elizabeth I, and spent much of his time on alchemy, divination, ...

*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, who decided to treat separately Leonardo's projection authorship (1508) from Leonardo's map authorship (1514), the other authors before him treat together the authorship of both map and

projection Projection or projections may refer to: Physics * Projection (physics), the action/process of light, heat, or sound reflecting from a surface to another in a different direction * The display of images by a projector Optics, graphics, and carto ...

, for they speak about "the eighth of a supposed globe represented in a plane" or about "globe sections" (Harrisse) or others about " gores", which are in fact a projection of the globe. So, bearing in mind the fact that Tyler was the first scholar to mention the sketch of this projection in

in 2017, the authorship of the map it is not universally accepted, with some authors being completely against any minimal contribution from Leonardo, such as Henry Harrisse (1892), or

Eugène Müntz Eugène Müntz (11 June 1845 – 30 October 1902) was a French art historian who specialized in the Italian Renaissance art. LIfe and career Eugène Müntz was born on 11 June 1845 in Soultz-sous-Forêts, Bas-Rhin. His brother was Achille Münt ...

(1899 – citing Harrisse authority from 1892, although none of them talks about the projection's sketch in

). Other scholars accept explicitly both (map and

: "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), Snyder in his book ''Flattening the Earth'' (1993), Christopher Tyler in his paper (2014) "Leonardo da Vinci's World Map", José Luis Espejo in his book (2012) ''Los mensajes ocultos de Leonardo Da Vinci'', 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

) 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

References

External links