science

Octant projection

Octant projection is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Octant projection rather than just read about it. In short: The octant projection or octants projection, is a type of map projection proposed the first time, in 1508, by Leonardo da Vinci in his Codex Atlanticus. 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…

Key takeaways

Octant projection belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Octant projection to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Octant projection from memory before moving on to harder problems.

Reference excerpt

The octant projection or octants projection, is a type of map projection proposed the first time, in 1508, by Leonardo da Vinci in his Codex Atlanticus. 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's conical planisphere projection and Roselli's pseudocylindric projection.

Description

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

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, 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, 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 Codex Atlanticus 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 (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), 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 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

See also World map List of map projections List of works by Leonardo da Vinci Leonardo's world map Rhumbline network Waterman butterfly projection Waterman polyhedron Bernard J. S. Cahill

References

External links

Proyecciones-cartograficas

Illustrations

Worked examples

Example 1 — a first encounter with Octant projection

Start with the simplest possible case. Write down what Octant projection claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Octant projection before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Octant projection ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Octant projection

In research: Octant projection appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Octant projection in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Octant projection is common in secondary-school and first-year university syllabi. It links to neighbouring topics Map projections, Works attributed to Leonardo da Vinci, so understanding it makes those chapters shorter.
In everyday life: Look for Octant projection outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Octant projection in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Octant projection means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Octant projection out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Octant projection in simple terms?

Why does Octant projection matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Octant projection?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Octant projection.