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Regular polygon that can be constructed with compass and straightedge
a constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with
Constructible_polygon
Plane figure bounded by line segments
polygon given by a sequence of line segments. This is called the point in polygon test. Boolean operations on polygons Complete graph Constructible polygon
Polygon
Equiangular and equilateral polygon
theorem. Equivalently, a regular n-gon is constructible if and only if the cosine of its common angle is a constructible number—that is, can be written in terms
Regular_polygon
Natural number
Fermat primes is equal to the number of sides of the largest regular constructible polygon with a straightedge and compass that has an odd number of sides
32_(number)
Concave polygon Constructible polygon Convex polygon Cyclic polygon Equiangular polygon Equilateral polygon Penrose tile Polyform Regular polygon Simple
List of two-dimensional geometric shapes
List_of_two-dimensional_geometric_shapes
Polygon with 1 million edges
power of two. Thus the regular megagon is not a constructible polygon. Indeed, it is not even constructible with the use of an angle trisector, as the number
Megagon
Shape with five sides
regular pentagon is constructible with compass and straightedge, as 5 is a Fermat prime. A variety of methods are known for constructing a regular pentagon
Pentagon
Method of drawing geometric objects
is constructible if and only if it represents a constructible number, and an angle is constructible if and only if its cosine is a constructible number
Straightedge and compass construction
Straightedge_and_compass_construction
Natural number
and is most likely the last one. Therefore, a regular polygon with 65537 sides is constructible with compass and unmarked straightedge. Johann Gustav
65,537
Natural number
sides of a constructible polygon, but since constructibility is related to factorization, the list of odd numbers n for which an n-sided polygon is constructible
4,294,967,295
Polygon with 30 edges
thirty-sided polygon. The sum of any triacontagon's interior angles is 5040 degrees. The regular triacontagon is a constructible polygon, by an edge-bisection
Triacontagon
Polygon with 2 sides and 2 vertices
the regular digon is a constructible polygon. Some definitions of a polygon do not consider the digon to be a proper polygon because of its degeneracy
Digon
Number divisible only by 1 and itself
been verified as of 2017. A regular n {\displaystyle n} -gon is constructible using straightedge and compass if and only if the odd prime factors
Prime_number
Polygon with 1000 edges
of two. Thus the regular chiliagon is not a constructible polygon. Indeed, it is not even constructible with the use of an angle trisector, as the number
Chiliagon
Number constructible via compass and straightedge
coordinate system, a point is constructible if and only if its Cartesian coordinates are both constructible numbers. Constructible numbers and points have also
Constructible_number
Polygon with 17 edges
seventeen-sided polygon. A regular heptadecagon is represented by the Schläfli symbol {17}. As 17 is a Fermat prime, the regular heptadecagon is a constructible polygon
Heptadecagon
Polygon with 65537 sides
and all angles equal) is of interest for being a constructible polygon: that is, it can be constructed using a compass and an unmarked straightedge. This
65537-gon
Polygon with 24 edges
the Petrie polygon for many higher-dimensional polytopes, seen as orthogonal projections in Coxeter planes, including: Constructible Polygon John H. Conway
Icositetragon
Polygon with 12 edges
In geometry, a dodecagon, or 12-gon, is any twelve-sided polygon. A regular dodecagon is a figure with sides of the same length and internal angles of
Dodecagon
Polygon with 10000 edges
power of two. Thus the regular myriagon is not a constructible polygon. Indeed, it is not even constructible with the use of an angle trisector, as the number
Myriagon
Object modeling method
graphics, polygonal modeling is an approach for modeling objects by representing or approximating their surfaces using polygon meshes. Polygonal modeling
Polygonal_modeling
Shape with three equal sides
equality if and only if the triangle is equilateral. A regular polygon is constructible by compass and straightedge if and only if the odd prime factors
Equilateral_triangle
Natural number
property, it is possible to construct with compass and straightedge a regular polygon with 65535 sides (see, constructible polygon). 65535 occurs frequently
65,535
Geometric construction used in Ancient Greek mathematics
constructed with neusis. (If a regular p-gon is constructible, then ζ p = e 2 π i p {\displaystyle \zeta _{p}=e^{\frac {2\pi i}{p}}} is constructible
Neusis_construction
Polygon with 257 sides
and all angles equal) is of interest for being a constructible polygon: that is, it can be constructed using a compass and an unmarked straightedge. This
257-gon
Shape with four equal sides and angles
construction means that squares are constructible polygons. A regular n {\displaystyle n} -gon is constructible exactly when the odd prime factors of
Square
Positive integer of the form (2^(2^n))+1
current top 100 generalized Fermat primes. Constructible polygon: which regular polygons are constructible partially depends on Fermat primes. Double
Fermat_number
Polygon shape with eight sides
(oktágōnon) 'eight angles') is an eight-sided polygon or 8-gon. A regular octagon has Schläfli symbol {8} and can also be constructed as a quasiregular truncated square
Octagon
Shape with six sides
meaning "six", and γωνία, gonía, meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting)
Hexagon
Topics referred to by the same term
can be constructed with compass and straightedge Constructible number, a complex number associated to a constructible point Constructible polygon, a regular
Constructibility
Polygon with 20 edges
twenty-sided polygon. The sum of any icosagon's interior angles is 3240 degrees. The regular icosagon has Schläfli symbol {20}, and can also be constructed as a
Icosagon
Polygon with 16 edges
triacontadigon, {32}. As 16 = 24 (a power of two), a regular hexadecagon is constructible using compass and straightedge: this was already known to ancient Greek
Hexadecagon
Shape with ten sides
(from the Greek δέκα déka and γωνία gonía, "ten angles") is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is
Decagon
Construction of an angle equal to one third a given angle
2^{t}3^{u}+1} (i.e. Pierpont primes greater than 3). Bisection Constructible number Constructible polygon Morley's trisector theorem Trisectrix Dudley, Underwood
Angle_trisection
sometimes encountered as well. Polygons are primarily named by prefixes from Ancient Greek numbers. To construct the name of a polygon with more than 20 and fewer
List_of_polygons
Circle associated with a quadratic equation
circles have been used to develop ruler-and-compass constructions of regular polygons. Given a quadratic equation in the form x2 − sx + p = 0 the circle associated
Carlyle_circle
Regular non-convex polygon
In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not
Star_polygon
Mathematical connection between field theory and group theory
regular polygons that are constructible (this characterization was previously given by Gauss but without the proof that the list of constructible polygons was
Galois_theory
Polygon with 15 edges
× 5, a product of distinct Fermat primes, a regular pentadecagon is constructible using compass and straightedge: The following constructions of regular
Pentadecagon
Polygon with 23 sides
23-gon is a 23-sided polygon. The icositrigon has the distinction of being the smallest regular polygon that is not neusis constructible. A regular icositrigon
Icositrigon
Measure of angles
scaling CORDIC, algorithms for trigonometric functions Constructible polygon, including all polygons with 2n sides "Binary angular measurement". Archived
Binary_angular_measurement
11-cell 57-cell Convex polygon Concave polygon Constructible polygon Cyclic polygon Equiangular polygon Equilateral polygon Regular polygon Penrose tile Polyform
List_of_mathematical_shapes
Polygon with 13 edges
prime, the regular tridecagon cannot be constructed using a compass and straightedge. However, it is constructible using neusis, or angle trisection. The
Tridecagon
Set of polygons to define the surface of a 3D model
convex polygons (n-gons). A polygonal mesh may also be more generally composed of concave polygons, or even polygons with holes. The study of polygon meshes
Polygon_mesh
Polygon with 18 edges
× 32, a regular octadecagon cannot be constructed using a compass and straightedge. However, it is constructible using neusis, or an angle trisection with
Octadecagon
Shape bounded by non-intersecting line segments
These polygons include as special cases the convex polygons, star-shaped polygons, and monotone polygons. The sum of external angles of a simple polygon is
Simple_polygon
Shape with seven sides
heptagon is not constructible with compass and straightedge but is constructible with a marked ruler and compass. It is the smallest regular polygon with this
Heptagon
Set of primitive shapes whose union equals a polygon
In geometry, a covering of a polygon is a set of primitive units (e.g. squares) whose union equals the polygon. A polygon covering problem is a problem
Polygon_covering
Polygon with 14 edges
× 7, a regular tetradecagon cannot be constructed using a compass and straightedge. However, it is constructible using neusis with use of the angle trisector
Tetradecagon
Polygonal region of all points visible from a given point in a plane
visible from p. The visibility polygon can also be defined for visibility from a segment, or a polygon. Visibility polygons are useful in robotics, video
Visibility_polygon
Universality of construction using just a straightedge and a single circle with center
Poncelet–Steiner theorem to non-Euclidean geometries. Apollonian circles Constructible polygon Drafting Geometric algebra Geometric invariant theory Geometrography
Poncelet–Steiner_theorem
Constant-width curve of equal-radius arcs
In geometry, a Reuleaux polygon is a curve of constant width made up of circular arcs of constant radius. These shapes are named after their prototypical
Reuleaux_polygon
Shape with nine sides
geometry, a nonagon (/ˈnɒnəɡɒn/) or enneagon (/ˈɛniəɡɒn/) is a nine-sided polygon or 9-gon. The name nonagon is a prefix hybrid formation, from Latin (nonus
Nonagon
Natural number
primes 3 and 17, a regular polygon with 51 sides is constructible with compass and straightedge, the angle π/51 is constructible, and the number cos π/51
51_(number)
Skew polygon derived from a polytope
the facets. The Petrie polygon of a regular polygon is the regular polygon itself; that of a regular polyhedron is a skew polygon such that every two consecutive
Petrie_polygon
Non-planar polygon with infinitely many sides
infinite skew polygons with vertices alternating between two parallel lines. Infinite helical polygons are 3-dimensional infinite skew polygons with vertices
Infinite_skew_polygon
Circle that passes through the vertices of a triangle
polygons are cyclic, but not every polygon is. The circumcircle of a triangle can be constructed using straightedge and compass by first constructing
Circumcircle
Polygon with equally angled vertices
a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths. For clarity, a planar equiangular polygon can be called
Equiangular_polygon
Prime number of the form 2^u × 3^v + 1
polygons which can be constructed with only compass and straightedge (constructible polygons) are the special case where n = 0 and ρ is a product of distinct
Pierpont_prime
Fictional character in the DC Universe
Justice League Action, voiced by John de Lancie. This version can generate polygonal force fields and is assisted by an army of robots and drones. Brainiac
Brainiac_(character)
Shape with eleven sides
a^{2}.} As 11 is not a Fermat prime, the regular hendecagon is not constructible with compass and straightedge. Because 11 is not a Pierpont prime, construction
Hendecagon
Tool for solving polynomial equations
In mathematics, the Newton polygon is a tool for understanding the behaviour of polynomials over local fields, or more generally, over ultrametric fields
Newton_polygon
2014 video game
(May 28, 2014). "The Sims 4's Build Mode lets you click, drag and construct". Polygon. Archived from the original on August 30, 2021. Retrieved August
The_Sims_4
Formula for area of a grid polygon
In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points
Pick's_theorem
rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form
List_of_types_of_numbers
Convex polyhedron with regular faces
polygons, no two in the same plane; those polygons are called the faces. A Johnson solid is a convex polyhedron whose faces are all regular polygons,
Johnson_solid
Polygon visible from one of its points
polygon is a polygonal region in the euclidean plane which is a star domain, that is, a polygon that contains a point from which the entire polygon boundary
Star-shaped_polygon
Points on a common circle
cocyclic) if they lie on a common circle. A polygon whose vertices are concyclic is called a cyclic polygon, and the circle is called its circumscribing
Concyclic_points
Polygon with many longest diagonals
diameters) and include every vertex of the polygon. Reinhardt polygons may be constructed from certain Reuleaux polygons, curves of constant width made up of
Reinhardt_polygon
Problem of constructing equal-area shapes
infinitely many pairs of constructible circles and constructible regular quadrilaterals of equal area, which, however, are constructed simultaneously. There
Squaring_the_circle
2D shape constructed by joining together identical basic polygons
compound constructed by joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex plane-filling polygon, such
Polyform
Polyhedron with 14 faces
topologically distinct forms of a tetradecahedron, with many constructible entirely with regular polygon faces. A tetradecahedron is sometimes called a tetrakaidecahedron
Tetradecahedron
In geometry, a convex polyhedron whose faces are regular polygons is known as a Johnson solid, or sometimes as a Johnson–Zalgaller solid. Some authors
List_of_Johnson_solids
Star polygon
In geometry, an octagram is an eight-angled star polygon. The name octagram combine a Greek numeral prefix, octa-, with the Greek suffix -gram. The -gram
Octagram
Type of plane partition
Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons, after Alfred H. Thiessen. Voronoi diagrams have practical and theoretical
Voronoi_diagram
Archimedean solid with 62 faces
of thirteen convex isogonal nonprismatic solids constructed of two or more types of regular polygon faces. It has a total of 62 faces: 20 regular triangular
Rhombicosidodecahedron
Type of figurate number
In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon. These are one type of 2-dimensional figurate
Polygonal_number
Family of cubic graphs formed from regular and star polygons
regular polygon to the corresponding vertices of a star polygon. They include the Petersen graph and generalize one of the ways of constructing the Petersen
Generalized_Petersen_graph
Property of a planar simple closed curve
In mathematics, an orientation of a curve (including polygonal curves) is the choice of one of the two possible senses for travelling on the curve, as
Curve_orientation
Polytope or tiling whose vertices are identical
In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries
Isogonal_figure
1955 mathematics book by Constance Reid
their close connection to constructible polygons. The heptagon, with seven sides, is the smallest polygon that is not constructible, because it is not a product
From_Zero_to_Infinity
Diagram showing applied forces and moments on a physical body
the applied forces are arranged as the edges of a polygon of forces or force polygon (see § Polygon of forces). A body is said to be "free" when it is
Free_body_diagram
11-pointed star polygon
In geometry, a hendecagram (also endecagram or endekagram) is a star polygon that has eleven vertices. The name hendecagram combines a Greek numeral prefix
Hendecagram
Smallest convex polygon containing a given polygon
geometry, the convex hull of a simple polygon is the polygon of minimum perimeter that contains a given simple polygon. It is a special case of the more general
Convex hull of a simple polygon
Convex_hull_of_a_simple_polygon
Solid with 2 parallel n-gonal bases connected by n parallelograms
In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy (rigidly moved without rotation) of
Prism_(geometry)
Polygon constructed from another
(vertex-transitive) polygon is an isotoxal (edge-transitive) polygon. For example, the (isogonal) rectangle and (isotoxal) rhombus are duals. In a cyclic polygon, longer
Dual_polygon
The Polygon (or simply Polygon) is an area in the city of Southampton, England. The area is located north of the Western Esplanade, Commercial Road and
The_Polygon,_Southampton
1992 book by Underwood Dudley
theorems, Goldbach's conjecture, magic squares, divisibility rules, constructible polygons, twin primes, set theory, statistics, and the Van der Pol oscillator
Mathematical_Cranks
Polygon with one edge and one vertex
Most definitions of a polygon in Euclidean geometry do not admit the monogon. In spherical geometry, a monogon can be constructed as a vertex on a great
Monogon
Generalised concept of incidence structure of polygons
In mathematics, a generalized polygon is an incidence structure introduced by Jacques Tits in 1959. Generalized n-gons encompass as special cases projective
Generalized_polygon
Natural number
can be constructed by compass and straightedge alone, which makes the heptagon the first regular polygon that cannot be directly constructed with these
7
Cyclic polygon all of whose sides are tangent to an incircle
In geometry, a bicentric polygon is a tangential polygon (a polygon all of whose sides are tangent to an inner incircle) which is also cyclic — that is
Bicentric_polygon
Natural number
with n = 3, and therefore a Fermat prime. Thus, a regular polygon with 257 sides is constructible with compass and unmarked straightedge. It is currently
257_(number)
Mathematical term in geometry
In geometry, a generalized polygon can be called a polygram, and named specifically by its number of sides. All polygons are polygrams, but they can also
Polygram_(geometry)
Flat-sided three-dimensional shape
ἕδρον (-hedron) 'base, seat') is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron"
Polyhedron
Polygonal stone columns
in which the vertical joints form polygonal columns and give the impression of having been artificially constructed. Bugarama in Rusizi, Rwanda[citation
List of places with columnar jointed volcanics
List_of_places_with_columnar_jointed_volcanics
Property of objects which are scaled or mirrored versions of each other
similar. Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure. Two congruent shapes
Similarity_(geometry)
Smallest convex set containing a given set
complexity of the problem. The convex hull of a simple polygon in the plane can be constructed in linear time. Dynamic convex hull data structures can
Convex_hull
Theorem in Euclidean geometry
cyclic polygon, the sum of inradii of triangles is constant. Conversely, if the sum of inradii is independent of the triangulation, then the polygon is cyclic
Japanese theorem for cyclic polygons
Japanese_theorem_for_cyclic_polygons
Special n-gon that has the largest area among all diameter-one n-gons
In geometry, the biggest little polygon for a number n {\displaystyle n} is the n {\displaystyle n} -sided polygon that has diameter one (that is, every
Biggest_little_polygon
CONSTRUCTIBLE POLYGON
CONSTRUCTIBLE POLYGON
CONSTRUCTIBLE POLYGON
CONSTRUCTIBLE POLYGON
Boy/Male
Hindu, Indian, Tamil
Bodyguard
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
A Friend
Girl/Female
Greek
Lover of man.
Girl/Female
Indian
Queen of the apes.
Girl/Female
Indian, Marathi
Name of Goddess
Girl/Female
Hindu
Hanuman Lakshmi
Boy/Male
African, Arabic, Muslim, Sindhi, Swahili
Friday
Girl/Female
Indian, Punjabi, Sikh
Pass through
Boy/Male
Arabic
Benevolence; Charity
Girl/Female
French
Loves God.
CONSTRUCTIBLE POLYGON
CONSTRUCTIBLE POLYGON
CONSTRUCTIBLE POLYGON
CONSTRUCTIBLE POLYGON
CONSTRUCTIBLE POLYGON
n.
Capability of being contracted; quality of being contractible; as, the contractibility and dilatability of air.
a.
Derived from, or depending on, construction or interpretation; not directly expressed, but inferred.
a.
Capable of contraction.
a.
Of or pertaining to a natural order of apetalous plants (Polygonaceae), of which the knotweeds (species of Polygonum) are the type, and which includes also the docks (Rumex), the buckwheat, rhubarb, sea grape (Coccoloba), and several other genera.
n.
The act or process, by which living tissues or cells take up and convert into their own proper substance the nutritive material brought to them by the blood, or by which they transform their cell protoplasm into simpler substances, which are fitted either for excretion or for some special purpose, as in the manufacture of the digestive ferments. Hence, metabolism may be either constructive (anabolism), or destructive (katabolism).
a.
Building up; constructive; -- opposed to destructive.
n.
The constructive metabolism of the body, as distinguished from katabolism.
a.
Capable of being instructed; teachable; docible.
adv.
In a constructive manner; by construction or inference.
a.
Capable of being extended, whether in length or breadth; susceptible of enlargement; extensible; extendible; -- the opposite of contractible or compressible.
n.
One of a series of substances formed, in secreting cells, by constructive or anabolic processes, in the production of protoplasm; -- opposed to katastate.
a.
Capable of expansion; that may be dilated; -- opposed to contractible; as, the lungs are dilatable by the force of air; air is dilatable by heat.
a.
Constructive.
n.
The doctrine of polygons; an extension of some of the principles of trigonometry to the case of polygons.
a.
Having ability to construct or form; employed in construction; as, to exhibit constructive power.
a.
Pertaining to anabolism; an anabolic changes, or processes, more or less constructive in their nature.
n.
Any plant of the genus Polygonum.
a.
Polygonal.
a.
Pertaining to a master builder, or to architecture; evincing skill in designing or construction; constructive.
a.
According to interpretation; constructive.