The octant projection or octants projection, is a type of

map projection In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and longitud ...

proposed the first time, in 1508, by

Leonardo da Vinci Leonardo di ser Piero da Vinci (15 April 14522 May 1519) was an Italian polymath of the High Renaissance who was active as a painter, Drawing, draughtsman, engineer, scientist, theorist, sculptor, and architect. While his fame initially res ...

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 us ...

. Leonardo's authorship would be demonstrated by

Christopher Tyler Christopher William Tyler is a neuroscientist, creator of the autostereogram (" Magic Eye" pictures), and is the Head of the Brain Imaging Center at the Smith-Kettlewell Eye Research Institute He also holds a professorship at City University of ...

, who stated "For those projections dated later than 1508, his drawings should be effectively considered the original precursors..". In fact, there is a sketch of it on a page in the Codex Atlanticus manuscripts, made from the very hand of Leonardo, being Leonardo's sketch, the first known description of the ''octant projection''. The same page of the Codex contains sketches of eight other projections of the globe (those known in the late fifteenth century), being studied by Leonardo, ranging from the Ptolemy's conical planisphere projection to the one proposed by Rosselli,

Description

The octant projection it 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 polyhedral ...

. The projection is neither conformal nor equal-area, bound by circular arcs, with no meridians and no parallels, in which the spherical surface of the earth is divided into eight octants, each flattened into the shape of a

Reuleaux triangle A Reuleaux triangle is a curved triangle with constant width, the simplest and best known curve of constant width other than the circle. It is formed from the intersection of three circular disks, each having its center on the boundary of the ...

. 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 clover The four-leaf clover is a rare variation of the common three-leaf clover. According to traditional sayings, such clovers bring good luck, though it is not clear when or how this idea began. One early mention of "Fower-leafed or purple grasse" is ...

s side by side, 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 a circle of latitude, about in circumference, that divides Earth into the Northern and Southern hemispheres. It is an imaginary line located at 0 degrees latitude, halfway between the North and South poles. The term can als ...

, the remaining two (those that converge to the center of the pseudo clover), are part of the two

meridian Meridian or a meridian line (from Latin ''meridies'' via Old French ''meridiane'', meaning “midday”) may refer to Science * Meridian (astronomy), imaginary circle in a plane perpendicular to the planes of the celestial equator and horizon * ...

s that with the equator dissect the globe in the eight octants.

Similar projections

Projections also based on the

were published by: *1549 –

Oronce Finé Oronce Finé (or Fine; Latin: ''Orontius Finnaeus'' or ''Finaeus''; it, Oronzio Fineo; 20 December 1494 – 8 August 1555) was a French mathematician, cartographer, editor and book illustrator. Life Born in Briançon, the son and grandson of p ...

*1556 – Le Testu *1580 –

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

. *1616 – Nicolaas Geelkercken *1894 – Fiorini *1909 –

Bernard J. S. Cahill Bernard Joseph Stanislaus Cahill (London, January 30, 1866 - Alameda County, October 4, 1944), American cartographer and architect, was the inventor of the octahedral "Butterfly Map" (published in 1909 and patented in 1913). An early proponent of ...

*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, projections or projective 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, graphic ...

, 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 Henry Harrisse (May 28, 1829 – May 13, 1910) was a writer, lawyer, art critic, and American historian who authored books on the discovery of America and geographic representations of the New World. Biography Henry Harrisse was born Hen ...

(1892), or

Eugène Müntz Eugène Müntz (11 June 1845 in Soultz-sous-Forêts, Bas-Rhin – 30 October 1902 in Paris) was an Alsatian- French art historian. From 1873 to 1876 he was a member of the École française de Rome.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 us ...

). 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), Christoher 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