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Neusis construction, the Glossary

In geometry, the neusis (νεῦσις;; plural: label) is a geometric construction method that was used in antiquity by Greek mathematicians.^[1]

51 relations: Angle trisection, Archimedes, Constructible polygon, Decagon, Dodecagon, Doubling the cube, Ellipse, Equilateral triangle, Euclid, Euclid's Elements, Field (mathematics), Geometry, Greek mathematics, Hendecagon, Heptadecagon, Heptagon, Hexadecagon, Hexagon, Hieronymus Georg Zeuthen, Hippocrates of Chios, Hyperbola, Icosagon, Icositetragon, Icositrigon, Idealism, Isaac Newton, Line element, MIT Press, Nonagon, Octadecagon, Octagon, Oenopides, Pappus of Alexandria, Parabola, Pentadecagon, Pentagon, Pierpont prime, Plato, Prime power, Quadratrix, Quintic function, Regular number, Square, Steel square, Straightedge and compass construction, Tetradecagon, Thomas Heath (classicist), Tomahawk (geometry), Triacontagon, Tridecagon, ... Expand index (1 more) »

Angle trisection

Angle trisection is a classical problem of straightedge and compass construction of ancient Greek mathematics. Neusis construction and Angle trisection are Euclidean plane geometry.

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Archimedes

Archimedes of Syracuse was an Ancient Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily.

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Constructible polygon

In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. Neusis construction and constructible polygon are Euclidean plane geometry.

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Decagon

In geometry, a decagon (from the Greek δέκα déka and γωνία gonía, "ten angles") is a ten-sided polygon or 10-gon.

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Dodecagon

In geometry, a dodecagon, or 12-gon, is any twelve-sided polygon.

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Doubling the cube

Doubling the cube, also known as the Delian problem, is an ancient geometric problem. Neusis construction and Doubling the cube are Euclidean plane geometry.

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Ellipse

In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.

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Equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides have the same length.

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Euclid

Euclid (Εὐκλείδης; BC) was an ancient Greek mathematician active as a geometer and logician.

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Euclid's Elements

The Elements (Στοιχεῖα) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid 300 BC.

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Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers.

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Geometry

Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures.

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Greek mathematics refers to mathematics texts and ideas stemming from the Archaic through the Hellenistic and Roman periods, mostly from the 5th century BC to the 6th century AD, around the shores of the Mediterranean.

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Hendecagon

In geometry, a hendecagon (also undecagon or endecagon) or 11-gon is an eleven-sided polygon.

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Heptadecagon

In geometry, a heptadecagon, septadecagon or 17-gon is a seventeen-sided polygon. Neusis construction and heptadecagon are Euclidean plane geometry.

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Heptagon

In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon.

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Hexadecagon

In mathematics, a hexadecagon (sometimes called a hexakaidecagon or 16-gon) is a sixteen-sided polygon.

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Hexagon

In geometry, a hexagon (from Greek ἕξ, hex, meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon.

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Hieronymus Georg Zeuthen

Hieronymus Georg Zeuthen (15 February 1839 – 6 January 1920) was a Danish mathematician.

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Hippocrates of Chios

Hippocrates of Chios (Ἱπποκράτης ὁ Χῖος; c. 470 – c. 410 BC) was an ancient Greek mathematician, geometer, and astronomer.

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Hyperbola

In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.

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Icosagon

In geometry, an icosagon or 20-gon is a twenty-sided polygon.

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Icositetragon

In geometry, an icositetragon (or icosikaitetragon) or 24-gon is a twenty-four-sided polygon.

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Icositrigon

In geometry, an icositrigon (or icosikaitrigon) or 23-gon is a 23-sided polygon.

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Idealism

Idealism in philosophy, also known as philosophical idealism or metaphysical idealism, is the set of metaphysical perspectives asserting that, most fundamentally, reality is equivalent to mind, spirit, or consciousness; that reality is entirely a mental construct; or that ideas are the highest type of reality or have the greatest claim to being considered "real".

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Isaac Newton

Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author who was described in his time as a natural philosopher.

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Line element

In geometry, the line element or length element can be informally thought of as a line segment associated with an infinitesimal displacement vector in a metric space.

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MIT Press

The MIT Press is a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts.

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Nonagon

In geometry, a nonagon or enneagon is a nine-sided polygon or 9-gon.

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Octadecagon

In geometry, an octadecagon (or octakaidecagon) or 18-gon is an eighteen-sided polygon.

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Octagon

In geometry, an octagon is an eight-sided polygon or 8-gon.

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Oenopides

Oenopides of Chios (Οἰνοπίδης ὁ Χῖος; born c. 490 BCE) was an ancient Greek geometer, astronomer and mathematician, who lived around 450 BCE.

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Pappus of Alexandria

Pappus of Alexandria (Πάππος ὁ Ἀλεξανδρεύς; AD) was a Greek mathematician of late antiquity known for his Synagoge (Συναγωγή) or Collection, and for Pappus's hexagon theorem in projective geometry.

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Parabola

In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.

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Pentadecagon

In geometry, a pentadecagon or pentakaidecagon or 15-gon is a fifteen-sided polygon.

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Pentagon

In geometry, a pentagon is any five-sided polygon or 5-gon.

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Pierpont prime

In number theory, a Pierpont prime is a prime number of the form 2^u\cdot 3^v + 1\, for some nonnegative integers and.

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Plato

Plato (Greek: Πλάτων), born Aristocles (Ἀριστοκλῆς; – 348 BC), was an ancient Greek philosopher of the Classical period who is considered a foundational thinker in Western philosophy and an innovator of the written dialogue and dialectic forms.

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Prime power

In mathematics, a prime power is a positive integer which is a positive integer power of a single prime number.

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Quadratrix

In geometry, a quadratrix is a curve having ordinates which are a measure of the area (or quadrature) of another curve.

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Quintic function

In mathematics, a quintic function is a function of the form where,,,, and are members of a field, typically the rational numbers, the real numbers or the complex numbers, and is nonzero.

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Regular number

Regular numbers are numbers that evenly divide powers of 60 (or, equivalently, powers of 30).

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Square

In Euclidean geometry, a square is a regular quadrilateral, which means that it has four sides of equal length and four equal angles (90-degree angles, π/2 radian angles, or right angles).

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Steel square

The steel square is a tool used in carpentry.

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Straightedge and compass construction

In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an idealized ruler and a pair of compasses.

See Neusis construction and Straightedge and compass construction

References

[1] https://en.wikipedia.org/wiki/Neusis_construction

Also known as Neuseis, Neusis.

, Trisectrix.

Neusis construction, the Glossary

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References