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Constructible polygon

Index Constructible polygon

In mathematics, a constructible polygon is a regular polygon that can be constructed with compass and straightedge. [1]

92 relations: Abelian group, Algebraic number, Almagest, American Mathematical Monthly, Analytic geometry, Ancient history, Bisection, Carl Friedrich Gauss, Carlyle circle, Compass-and-straightedge construction, Complex number, Composition series, Constructible number, Coprime integers, Cyclotomic field, Cyclotomic polynomial, Decagon, Dimension (vector space), Disquisitiones Arithmeticae, Dodecagon, Enneacontagon, Enneacontahexagon, Enneadecagon, Equilateral triangle, Euclid, Euclid's Elements, Euler's totient function, Fermat number, Field (mathematics), Friedrich Julius Richelot, Galois theory, Gaussian period, GeoGebra, Greek mathematics, Group theory, Hectogon, Hendecagon, Heptacontagon, Heptadecagon, Heptagon, Hexacontagon, Hexacontatetragon, Hexadecagon, Hexagon, Icosagon, Icositetragon, Johann Gustav Hermes, Kummer theory, List of polygons, Magnus Georg Paucker, ..., Modular arithmetic, Monogon, Necessity and sufficiency, Neusis construction, Nonagon, Number theory, Octacontagon, Octadecagon, Octagon, Pascal's triangle, Pentacontagon, Pentadecagon, Pentagon, Pierpont prime, Pierre Wantzel, Polygon, Prime number, Ptolemy, Quadratic equation, Quadratrix of Hippias, Rational number, Real number, Regular polygon, Sierpinski triangle, Square, Tetracontadigon, Tetracontagon, Tetracontaoctagon, Tetradecagon, The Mathematical Intelligencer, Totally real number field, Triacontadigon, Triacontagon, Triacontatetragon, Tridecagon, Trigonometric functions, Trigonometric number, Vector space, Zero of a function, 120-gon, 257-gon, 65537-gon. Expand index (42 more) »

Abelian group

In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written.

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Algebraic number

An algebraic number is any complex number (including real numbers) that is a root of a non-zero polynomial (that is, a value which causes the polynomial to equal 0) in one variable with rational coefficients (or equivalently – by clearing denominators – with integer coefficients).

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Almagest

The Almagest is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy. One of the most influential scientific texts of all time, its geocentric model was accepted for more than 1200 years from its origin in Hellenistic Alexandria, in the medieval Byzantine and Islamic worlds, and in Western Europe through the Middle Ages and early Renaissance until Copernicus.

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American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

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Analytic geometry

In classical mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system.

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Ancient history

Ancient history is the aggregate of past events, "History" from the beginning of recorded human history and extending as far as the Early Middle Ages or the post-classical history.

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Bisection

In geometry, bisection is the division of something into two equal or congruent parts, usually by a line, which is then called a bisector.

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Carl Friedrich Gauss

Johann Carl Friedrich Gauss (Gauß; Carolus Fridericus Gauss; 30 April 177723 February 1855) was a German mathematician and physicist who made significant contributions to many fields, including algebra, analysis, astronomy, differential geometry, electrostatics, geodesy, geophysics, magnetic fields, matrix theory, mechanics, number theory, optics and statistics.

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Carlyle circle

In mathematics, a Carlyle circle (named for Thomas Carlyle) is a certain circle in a coordinate plane associated with a quadratic equation.

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Compass-and-straightedge construction

Compass-and-straightedge construction, also known as ruler-and-compass construction or classical construction, is the construction of lengths, angles, and other geometric figures using only an idealized ruler and compass.

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Composition series

In abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces.

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Constructible number

In geometry and algebra, a real number is constructible if and only if, given a line segment of unit length, a line segment of length || can be constructed with compass and straightedge in a finite number of steps.

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Coprime integers

In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.

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Cyclotomic field

In number theory, a cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to, the field of rational numbers.

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Cyclotomic polynomial

In mathematics, more specifically in algebra, the nth cyclotomic polynomial, for any positive integer n, is the unique irreducible polynomial with integer coefficients that is a divisor of x^n-1 and is not a divisor of x^k-1 for any.

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Decagon

In geometry, a decagon is a ten-sided polygon or 10-gon.

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Dimension (vector space)

In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.

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Disquisitiones Arithmeticae

The Disquisitiones Arithmeticae (Latin for "Arithmetical Investigations") is a textbook of number theory written in Latin by Carl Friedrich Gauss in 1798 when Gauss was 21 and first published in 1801 when he was 24.

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Dodecagon

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

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Enneacontagon

In geometry, an enneacontagon or enenecontagon or 90-gon (from Ancient Greek ἑννενήκοντα, ninety) is a ninety-sided polygon.

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Enneacontahexagon

In geometry, an enneacontahexagon (or enneacontakaihexagon) or 96-gon is a ninety-six-sided polygon.

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Enneadecagon

In geometry an enneadecagon or 19-gon is a nineteen-sided polygon.

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Equilateral triangle

In geometry, an equilateral triangle is a triangle in which all three sides are equal.

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Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

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Euclid's Elements

The Elements (Στοιχεῖα Stoicheia) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC.

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Euler's totient function

In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to.

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Fermat number

In mathematics a Fermat number, named after Pierre de Fermat who first studied them, is a positive integer of the form where n is a nonnegative integer.

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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 when they are applied to rational and real numbers.

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Friedrich Julius Richelot

Friedrich Julius Richelot (6 November 1808 – 31 March 1875) was a German mathematician, born in Königsberg.

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Galois theory

In the field of algebra within mathematics, Galois theory, provides a connection between field theory and group theory.

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Gaussian period

In mathematics, in the area of number theory, a Gaussian period is a certain kind of sum of roots of unity.

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GeoGebra

GeoGebra is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level.

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Greek mathematics

Greek mathematics refers to mathematics texts and advances written in Greek, developed from the 7th century BC to the 4th century AD around the shores of the Eastern Mediterranean.

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Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

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Hectogon

In geometry, a hectogon or hecatontagon or 100-gon is a hundred-sided polygon.

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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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Heptacontagon

In geometry, a heptacontagon (or hebdomecontagon from Ancient Greek ἑβδομήκοντα, seventy) or 70-gon is a seventy-sided polygon.

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Heptadecagon

In geometry, a heptadecagon or 17-gon is a seventeen-sided polygon.

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Heptagon

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

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Hexacontagon

In geometry, a hexacontagon or hexecontagon or 60-gon is a sixty-sided polygon.

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Hexacontatetragon

In geometry, a hexacontatetragon (or hexacontakaitetragon) or 64-gon is a sixty-four-sided polygon.

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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, "six" and γωνία, gonía, "corner, angle") is a six-sided polygon or 6-gon.

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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 tetracosagon) or 24-gon is a twenty-four-sided polygon.

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Johann Gustav Hermes

Johann Gustav Hermes (20 June 1846 – 8 June 1912) was a German mathematician.

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Kummer theory

In abstract algebra and number theory, Kummer theory provides a description of certain types of field extensions involving the adjunction of nth roots of elements of the base field.

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List of polygons

In geometry, a polygon is traditionally a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain.

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Magnus Georg Paucker

Magnus Georg von Paucker (Магнус-Георг Андреевич Паукер; Magnus-Georg Andreyevich Pauker, in Simuna – in Jelgava) was the first Demidov Prize winner in 1832 for his work Handbuch der Metrologie Rußlands und seiner deutschen Provinzen.

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Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

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Monogon

In geometry a monogon is a polygon with one edge and one vertex.

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Necessity and sufficiency

In logic, necessity and sufficiency are terms used to describe an implicational relationship between statements.

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Neusis construction

The neusis is a geometric construction method that was used in antiquity by Greek mathematicians.

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Nonagon

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

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Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

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Octacontagon

In geometry, an octacontagon (or ogdoëcontagon or 80-gon from Ancient Greek ὁγδοήκοντα, eighty) is an eighty-sided polygon.

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Octadecagon

An octadecagon (or octakaidecagon) or 18-gon is an eighteen-sided polygon.

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Octagon

In geometry, an octagon (from the Greek ὀκτάγωνον oktágōnon, "eight angles") is an eight-sided polygon or 8-gon.

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Pascal's triangle

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.

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Pentacontagon

In geometry, a pentacontagon or pentecontagon or 50-gon is a fifty-sided polygon.

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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 (from the Greek πέντε pente and γωνία gonia, meaning five and angle) is any five-sided polygon or 5-gon.

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Pierpont prime

A Pierpont prime is a prime number of the form for some nonnegative integers and.

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Pierre Wantzel

Pierre Laurent Wantzel (5 June 1814 in Paris – 21 May 1848 in Paris) was a French mathematician who proved that several ancient geometric problems were impossible to solve using only compass and straightedge.

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Polygon

In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed polygonal chain or circuit.

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Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

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Ptolemy

Claudius Ptolemy (Κλαύδιος Πτολεμαῖος, Klaúdios Ptolemaîos; Claudius Ptolemaeus) was a Greco-Roman mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology.

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Quadratic equation

In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to.

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Quadratrix of Hippias

The quadratrix or trisectrix of Hippias (also quadratrix of Dinostratus) is a curve, which is created by a uniform motion.

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Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Regular polygon

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

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Sierpinski triangle

The Sierpinski triangle (also with the original orthography Sierpiński), also called the Sierpinski gasket or the Sierpinski Sieve, is a fractal and attractive fixed set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles.

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Square

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

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Tetracontadigon

In geometry, a tetracontadigon (or tetracontakaidigon) or 42-gon is a forty-two-sided polygon.

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Tetracontagon

In geometry, a tetracontagon or tessaracontagon is a forty-sided polygon or 40-gon.

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Tetracontaoctagon

In geometry, a tetracontaoctagon (or tetracontakaioctagon) or 48-gon is a forty-eight sided polygon.

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Tetradecagon

In geometry, a tetradecagon or tetrakaidecagon or 14-gon is a fourteen-sided polygon.

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The Mathematical Intelligencer

The Mathematical Intelligencer is a mathematical journal published by Springer Verlag that aims at a conversational and scholarly tone, rather than the technical and specialist tone more common among academic journals.

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Totally real number field

In number theory, a number field K is called totally real if for each embedding of K into the complex numbers the image lies inside the real numbers.

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Triacontadigon

In geometry, a triacontadigon (or triacontakaidigon) or 32-gon is a thirty-two-sided polygon.

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Triacontagon

In geometry, a triacontagon or 30-gon is a thirty-sided polygon.

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Triacontatetragon

In geometry, a triacontatetragon or triacontakaitetragon is a thirty-four-sided polygon or 34-gon.

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Tridecagon

In geometry, a tridecagon or triskaidecagon or 13-gon is a thirteen-sided polygon.

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Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

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Trigonometric number

In mathematics, a trigonometric number is an irrational number produced by taking the sine or cosine of a rational multiple of a full circle, or equivalently, the sine or cosine of an angle which in radians is a rational multiple of π, or the sine or cosine of a rational number of degrees.

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Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

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Zero of a function

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).

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120-gon

In geometry, a 120-gon is a polygon with 120 sides.

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257-gon

In geometry, a 257-gon (diacosipentacontaheptagon, diacosipentecontaheptagon) is a polygon with 257 sides.

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65537-gon

In geometry, a 65537-gon is a polygon with 65537 sides.

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Redirects here:

Constructable polygon, Gauss-Wantzel theorem, Gauss–Wantzel theorem.

References

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

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