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Intersection graph of convex polygons whose vertices lie on a common circle
graph theory, a polygon-circle graph is an intersection graph of a set of convex polygons all of whose vertices lie on a common circle. These graphs have
Polygon-circle_graph
Intersection graph of a chord diagram
In graph theory, a circle graph is the intersection graph of a chord diagram. That is, it is an undirected graph whose vertices can be associated with
Circle_graph
Graph representing intersections between given sets
circular arc graph is defined as the intersection graph of arcs on a circle. A polygon-circle graph is defined as the intersection of polygons with corners
Intersection_graph
Concept in geometry
involves viewing the circle as the limit of a sequence of regular polygons with an increasing number of sides. The area of a regular polygon is half its perimeter
Area_of_a_circle
Plane figure bounded by line segments
solid polygons, a polygon may refer only to a simple polygon or to a solid polygon. A polygonal chain may cross over itself, creating star polygons and
Polygon
On tangency patterns of circles
circles in the plane. A circle packing is a collection of circles whose union is connected and whose interiors are disjoint. The intersection graph of
Circle_packing_theorem
Graph of intervisible locations in computational geometry
of time series analysis. Visibility graphs may be used to find Euclidean shortest paths among a set of polygonal obstacles in the plane: the shortest
Visibility_graph
Simple curve of Euclidean geometry
quadrilateral, is any convex polygon within which a circle can be inscribed that is tangent to each side of the polygon. Every regular polygon and every triangle
Circle
Study of graphs defined by geometric means
the polygon. It is not known how to test efficiently whether an undirected graph can be represented as a visibility graph. A partial cube is a graph for
Geometric_graph_theory
Geometric graph with unit edge lengths
Generalizing the triangle graph, every cycle graph is a unit distance graph, realized by a regular polygon. Two finite unit distance graphs, connected at a single
Unit_distance_graph
Problem in geometry
these diagonals in Moser's circle problem do not appear in the polygon problem. Similar arguments to those for Moser's circle problem can be used to show
Moser's_circle_problem
Topics referred to by the same term
polygon Diameter (graph theory), the longest distance between two vertices of a graph Diameter (group theory), the maximum diameter of a Cayley graph
Diameter_(disambiguation)
Area of discrete mathematics
computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context
Graph_theory
Shape bounded by non-intersecting line segments
simple polygons, polygonalization of point sets, constructive solid geometry formulas for polygons, and visibility graphs of polygons. A simple polygon is
Simple_polygon
Graph that can be embedded in the plane
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect
Planar_graph
Index of articles associated with the same name
objects in a circle Cyclic permutation, a permutation with one nontrivial orbit Cyclic polygon, a polygon which can be given a circumscribed circle Cyclic shift
Cyclic_(mathematics)
Graph drawing with vertices on a circle
In graph drawing, a circular layout is a style of drawing that places the vertices of a graph on a circle, often evenly spaced so that they form the vertices
Circular_layout
redirect targets Polygon-circle graph – Intersection graph of convex polygons whose vertices lie on a common circle Splitting circle method – Root-finding
List_of_circle_topics
Equiangular and equilateral polygon
regular polygon also has an inscribed circle or incircle that is tangent to every side at the midpoint. Thus a regular polygon is a tangential polygon. A regular
Regular_polygon
The graphs of bounded clique-width The intersection graphs of scaled and translated copies of any compact convex shape in the plane The polygon-circle graphs
Chi-bounded
Cubic graph with 10 vertices and 15 edges
bridgeless graph has a cycle-continuous mapping to the Petersen graph. More unsolved problems in mathematics In the mathematical field of graph theory, the
Petersen_graph
Type of plane partition
diagrams can be used to find the largest empty circle amid a set of points, and in an enclosing polygon; e.g. to build a new supermarket as far as possible
Voronoi_diagram
Limiting case which is different from the rest of the class
or at least one angle is 180°. Thus a degenerate convex polygon of n sides looks like a polygon with fewer sides. In the case of triangles, this definition
Degeneracy_(mathematics)
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
Non-crossing graph with vertices on outer face
graphs of polygon triangulations. They are examples of 2-trees, of series–parallel graphs, and of chordal graphs. Every outerplanar graph is a circle
Outerplanar_graph
Size of a two-dimensional surface
same area (as in squaring the circle); by synecdoche, "area" sometimes is used to refer to the region, as in a "polygonal area". The area of a shape can
Area
Segment in a circle or sphere from its center to its perimeter or surface
circumradius. The inradius of a regular polygon is also called the apothem. In graph theory, the radius of a graph is the minimum over all vertices u of
Radius
Branch of geometry that studies combinatorial properties and constructive methods
sets of basic geometric objects, such as points, lines, planes, circles, spheres, polygons, and so forth. The subject focuses on the combinatorial properties
Discrete_geometry
Shape with six sides
equiangular. Its internal angle is one-third of a circle, equal to 120°. The Schläfli symbol denotes this polygon as { 6 } {\displaystyle \{6\}} . However, the
Hexagon
Polygon with an infinite number of sides
apeiron 'infinite, boundless' and γωνία gonia 'angle') or infinite polygon is a polygon with an infinite number of sides. Apeirogons are the rank 2 case
Apeirogon
Multi-lobed plane curve
negative half-cycles can be coincident in the graph of a rose. In addition, roses are inscribed in the circle r = a. When the period T of the sinusoid is
Rose_(mathematics)
In geometry a line segment joining two nonconsecutive vertices of a polygon or polyhedron
convex polygon, all the diagonals are inside the polygon, but for re-entrant polygons, some diagonals are outside of the polygon. Any n-sided polygon (n ≥
Diagonal
Four-dimensional analog of the dodecahedron
characteristic of the 5-cell which circle through a set of central planes and form face polygons but not great polygons. The annotated chord table is a complete
120-cell
Geometric model of the planar projection of the physical universe
Such a drawing is called a plane graph or planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to
Euclidean_plane
Field of mathematics which studies incidence structures
near polygon. Any connected bipartite graph is a near polygon and any near polygon with precisely two points per line is a connected bipartite graph. Also
Incidence_geometry
Type of topological space
circle. This makes it a simple example of a topological graph. A rose with n petals can also be obtained by identifying n points on a single circle.
Rose_(topology)
Goswami, Partha P. (2013). "Unsolved problems in visibility graphs of points, segments, and polygons". ACM Computing Surveys. 46 (2): 22:1–22:29. arXiv:1012
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Archimedean solid with 32 faces
represented as the symmetric graph with 30 vertices and 60 edges, one of the Archimedean graphs. It is a symmetric quartic graph, meaning that each vertex
Icosidodecahedron
Five-pointed star polygon
five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon. Drawing a circle around the
Pentagram
Shape with four equal sides and angles
uniform positive curvature, and every convex quadrilateral (a polygon with four great-circle arc edges) has angles whose sum exceeds 360° by an amount called
Square
Type of chart
web charts, spider charts, spider graphs, spider web charts, star charts, star plots, cobweb charts, irregular polygons, polar charts, and Kiviat diagrams
Radar_chart
Largest distance between two points
Zalgaller 1988, p. 93. Foster, Jim; Szabo, Tamas (2007), "Diameter graphs of polygons and the proof of a conjecture of Graham", Journal of Combinatorial
Diameter_of_a_set
Graph formed by touching unit circles
In geometric graph theory, a penny graph is a contact graph of unit circles. It is formed from a collection of unit circles that do not cross each other
Penny_graph
Planar graph drawn by relaxing springs
In graph drawing and geometric graph theory, a Tutte embedding or barycentric embedding of a simple, 3-vertex-connected, planar graph is a crossing-free
Tutte_embedding
Formula for area of a grid polygon
of vertices, edges, and faces of any planar graph. The vertices are just the grid points of the polygon; there are V = i + b {\displaystyle V=i+b} of
Pick's_theorem
Graph representing faces of another graph
mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each
Dual_graph
Planar graphs have straight drawings
The Circle packing theorem states that every planar graph may be represented as the intersection graph of a collection of non-crossing circles in the
Fáry's_theorem
Measure of distance in physical space
perimeter of a polygon is the sum of the lengths of its sides. The circumference of a circular disk is the length of the boundary (a circle) of that disk
Length
Polygon with 2 sides and 2 vertices
space. It may also be viewed as a representation of a graph with two vertices, see "Generalized polygon". A regular digon has both angles equal and both sides
Digon
Graph representing tangency between geometric objects
planar graph is a contact graph of homothetic copies of any given smooth convex set. The contact graphs of unit circles are called penny graphs. Representations
Contact_graph
Property of objects which are scaled or mirrored versions of each other
congruent) Line segments Circles Parabolas Hyperbolas of a specific eccentricity Ellipses of a specific eccentricity Catenaries Graphs of the logarithm function
Similarity_(geometry)
their dependencies. Coin graph drawing algorithms for finite connected planar graphs (approximately computing the theoretical circle-packing given by the
List_of_algorithms
Theorem in topology
Jordan polygon (Lemma 1), and every Jordan curve can be approximated arbitrarily well by a Jordan polygon (Lemma 2). A Jordan polygon is a polygonal chain
Jordan_curve_theorem
Shape with three equal sides
given circle is also equilateral. It is the only regular polygon aside from the square that can be inscribed inside any other regular polygon. Given
Equilateral_triangle
Any planar graph can be subdivided by removing a few vertices
In graph theory, the planar separator theorem is a form of isoperimetric inequality for planar graphs, that states that any planar graph can be split
Planar_separator_theorem
Shape with eleven sides
hendecagon (also undecagon or endecagon) or 11-gon is an eleven-sided polygon. (The name hendecagon, from Greek hendeka "eleven" and –gon "corner", is
Hendecagon
Segment from the center of a polygon to the midpoint of one of its sides
}{n}}} An apothem of a regular polygon will always be a radius of the inscribed circle. Therefore, for a regular polygon: r = t {\displaystyle r=t} It
Apothem
Conic solid with a polygonal base
versa. Their skeleton may be represented as the wheel graph, that is they can be depicted as a polygon in which its vertices connect a vertex in the center
Pyramid_(geometry)
Operation combining two oriented knots
is known as knot theory and has many relations to graph theory. A knot is an embedding of the circle (S1) into three-dimensional Euclidean space (R3),
Knot_(mathematics)
Polygon associated with a compact Riemann surface
In mathematics, a fundamental polygon can be defined for every compact Riemann surface of genus greater than 0. It encodes not only information about
Fundamental_polygon
Line tangent to a curve at two locations
up the visibility graph approach to solving the Euclidean shortest path problem: the shortest path among a collection of polygonal obstacles may only
Bitangent
Varying methods used to calculate pi
a Circle, created the first algorithm for the calculation of π based on the idea that the perimeter of any (convex) polygon inscribed in a circle is
Approximations_of_pi
Form of an object
Some common shapes include: Circle, Square, Triangle, Rectangle, Oval, Star (polygon), Rhombus, Semicircle. Regular polygons starting at pentagon follow
Shape
Puzzle computer game involving planar graphs
is presented with a circular layout of a planar graph, with all the vertices placed on a single circle and with many crossings. The goal for the player
Planarity
Graph-theoretic description of polyhedra
planar graph, and every 3-connected planar graph can be represented as the graph of a convex polyhedron. For this reason, the 3-connected planar graphs are
Steinitz's_theorem
Number of "holes" of a surface
fundamental polygon. Genus of orientable surfaces Planar graph: genus 0 Toroidal graph: genus 1 Double Toroidal graph: genus 2 Pretzel graph: genus 3 The
Genus_(mathematics)
Graph drawing with vertices in horizontal layers
Layered graph drawing or hierarchical graph drawing is a type of graph drawing in which the vertices of a directed graph are drawn in horizontal rows or
Layered_graph_drawing
constant a field in algebra with a subscript, a complete graph on that many vertices the area of a polygon kinetic energy Kaon Potassium Sectional curvature
Latin letters used in mathematics, science, and engineering
Latin_letters_used_in_mathematics,_science,_and_engineering
Browser-based graphing calculator
with supporting features including the plotting of points, lines, circles, and polygons. In May 2023, Desmos released a beta version of a second, more sophisticated
Desmos
Mathematical group that can be generated as the set of powers of a single element
corresponds to a single cycle graphed simply as an n-sided polygon with the elements at the vertices. A Cayley graph is a graph defined from a pair (G,S)
Cyclic_group
Plane curve defined by an implicit equation
of three methods, one of which is the implicit equation given above. The graph of a function is usually described by an equation y = f ( x ) {\displaystyle
Implicit_curve
general position (small perturbations of a regular polygon) for which the β-skeleton is a dense graph with a quadratic number of edges. In the same quadratic
Beta_skeleton
Solid with six equal square faces
drawing a graph with vertices connected with an edge in a plane. Such a graph is called the cubical graph, a special case of the hypercube graph. The cube
Cube
Sharpest angle between edges at a vertex
each vertex of G close to the polygon vertex with the same color. Using this construction, they showed that every graph with maximum degree d has a drawing
Angular resolution (graph drawing)
Angular_resolution_(graph_drawing)
Regular polytope dual to the hypercube in any number of dimensions
cross-polytopes as 2-dimensional graphs. Petrie polygon projections map the points into a regular 2n-gon or lower order regular polygons. A second projection takes
Cross-polytope
Graph formed by subdivision of triangles
planar 3-trees, the maximal planar chordal graphs, the uniquely 4-colorable planar graphs, and the graphs of stacked polytopes. They are named after Apollonius
Apollonian_network
Relationship between two lines that meet at a right angle
and y 2 ( x ) = m 2 x + b 2 {\displaystyle y_{2}(x)=m_{2}x+b_{2}} , the graphs of the functions will be perpendicular if m 1 m 2 = − 1. {\displaystyle
Perpendicular
Distance along a curve
curves that might not necessarily be smooth as a limit of lengths of polygonal chains. The curves for which this limit exists are called rectifiable
Arc_length
Construct in computational geometry
straight-line graphs in time O ( n log n ) {\displaystyle O(n\log n)} are known. The constrained Delaunay triangulation of a simple polygon can be constructed
Constrained Delaunay triangulation
Constrained_Delaunay_triangulation
Number, approximately 3.14
a circle, and successively doubling the number of sides until he reached a 96-sided regular polygon. By calculating the perimeters of these polygons, he
Pi
Branch of computer science
shortest path. Polygon triangulation: Given a polygon, partition its interior into triangles Mesh generation Boolean operations on polygons The computational
Computational_geometry
Database of data representing objects in geometric space
pairs, and geo_shape fields, which support points, lines, circles, polygons, multi-polygons, etc. GeoMesa is a cloud-based spatio-temporal database built
Spatial_database
2D shape constructed by joining together identical basic polygons
(that is, all one piece; see connected graph, connected space). Configurations of disconnected basic polygons do not qualify as polyforms. The mirror
Polyform
Straight path on a curved surface or a Riemannian manifold
great circle (see also great-circle distance). The term has since been generalized to more abstract mathematical spaces; for example, in graph theory
Geodesic
Subdivision of the plane by lines
hyperbolic lines. The intersection graph of the lines in a hyperbolic arrangement can be an arbitrary circle graph. The corresponding concept to hyperbolic
Arrangement_of_lines
Canadian computer scientist (1944–2019)
(mechanical) reconfiguration, the art gallery problem, polygon triangulation, the largest empty circle problem, unimodality (unimodal function), and others
Godfried_Toussaint
numerical analysis. Boolean operations on polygons Convex hull Hyperplane arrangement Polygon decomposition Polygon triangulation Minimal convex decomposition
List of combinatorial computational geometry topics
List_of_combinatorial_computational_geometry_topics
Operation that cuts polytope vertices, creating a new facet in place of each vertex
graph represents Coxeter group I2(n), with each node representing a mirror, and the edge representing the angle π/n between the mirrors, and a circle
Truncation_(geometry)
Shortest network connecting points
geometric graphs including the relative neighborhood graph and Delaunay triangulation. By constructing the Delaunay triangulation and then applying a graph minimum
Euclidean minimum spanning tree
Euclidean_minimum_spanning_tree
Type of plane curve
Examples of convex curves include the convex polygons, the boundaries of convex sets, and the graphs of convex functions. Important subclasses of convex
Convex_curve
Spiral with constant distance from itself
large outer circle, making more subdivisions of both its circumference and radius, increasing the number of concentric circles (see Polygonal Spiral). Approximating
Archimedean_spiral
Triangulation method
diagram contains vertices of degree four or greater and its dual graph contains polygonal faces with four or more sides. The various triangulations of these
Delaunay_triangulation
Natural number
graphs with n edges)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A002816 (Number of polygons that
177_(number)
Notation for a polyhedron's vertex figure
this in the star polygon notation of sides p/q such that p<2q, where p is the number of sides and q the number of turns around a circle. For example, "3/2"
Vertex_configuration
Solid with eight equal triangular faces
octahedron give rise to a graph, a discrete structure drawn in a plane. The name is octahedral graph. The octahedral graph is an example of a four-connected
Regular_octahedron
Unsolved problem about inscribing a square in a Jordan curve
general case remains open. Let C {\displaystyle C} be a Jordan curve. A polygon P {\displaystyle P} is inscribed in C {\displaystyle C} if all vertices
Inscribed_square_problem
Four-dimensional analog of the octahedron
squares are Clifford parallel polygons. Note that only the vertices of the great squares (the points on the great circle) are √2 apart; points on the edges
16-cell
Way to divide polygon into smaller parts
mathematics, a finite subdivision rule is a recursive way of dividing a polygon or other two-dimensional shape into smaller and smaller pieces. Subdivision
Finite_subdivision_rule
NP-hard problem in combinatorial optimization
in the original graph. For points in the Euclidean plane, the optimal solution to the travelling salesman problem forms a simple polygon through all of
Travelling_salesman_problem
Sphere tangent to every edge of a polyhedron
every face must have an inscribed circle (that is, it must be a tangential polygon), and all of these inscribed circles must belong to a single sphere.
Midsphere
POLYGON CIRCLE-GRAPH
POLYGON CIRCLE-GRAPH
Girl/Female
Greek Latin
A witch.
Male
Greek
Greek myth name of one of the horses of the noon-day sun, PHLEGON means "the burning/blazing one."
Girl/Female
Latin
Circle of light.
Girl/Female
Latin
Circle of light.
Biblical
zealous; burning
Girl/Female
Biblical
Zealous, burning.
Male
English
Medieval English variant spelling of Roman Latin Julian, JOLYON means "descended from Jupiter (Jove)."
Girl/Female
Bengali, Indian
Circle; Normal
Female
English
English name derived from the vocabulary word, from Latin miraculum, MIRACLE means "marvel, wonder."
Boy/Male
English
From the bird hill.
Girl/Female
Latin
Circle of light.
Female
Slovene
Feminine form of Slovene Ciril, CIRILA means "lord."
Girl/Female
Japanese
Ball; circle.
Boy/Male
French Israeli
The circle.
Male
Slovene
Slovene form of Greek Kyrillos, CIRIL means "lord."
Boy/Male
English
Birch.
Female
Yiddish
(מִירל) Yiddish form of Hebrew Miryam, MIRELE means "obstinacy, rebelliousness" or "their rebellion."Â
Female
French
French form of Latin Carola, CAROLE means "man."
Boy/Male
Christian, Hindu, Indian
Bright Circle
Male
Celtic
, sea circle.
POLYGON CIRCLE-GRAPH
POLYGON CIRCLE-GRAPH
Girl/Female
Tamil
Nidhyana | நிதà¯à®¯à®¾à®¨à®¾
Intuition
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit
To End Evil or Bad; Lord Ganesha
Girl/Female
Muslim
Messenger
Girl/Female
African, American, Christian, Danish, French, German, Greek, Gujarati, Hebrew, Hindu, Indian, Kannada, Latin, Malayalam, Parsi, Swahili
Moon; Fame; News; Ethiopian; One who is Famous; Welcoming; Hospitable; Power of Zeus; Belonging to Zeus; Guest; Stranger; Woman; Beautiful Ornament
Boy/Male
Hindu
Girl/Female
French Persian
Jasmine.
Girl/Female
Hindu, Indian, Telugu
The Sea
Boy/Male
Arabic, Hindu, Indian, Muslim
Divided
Girl/Female
Tamil
Kundana | கà¯à®¨à¯à®¤à®¨à®¾
Boy/Male
Biblical
Sickness, a company of dancers, a harp.
POLYGON CIRCLE-GRAPH
POLYGON CIRCLE-GRAPH
POLYGON CIRCLE-GRAPH
POLYGON CIRCLE-GRAPH
POLYGON CIRCLE-GRAPH
n.
A little circle; esp., an ornament for the person, having the form of a circle; that which encircles, as a ring, a bracelet, or a headband.
imp. & p. p.
of Circle
n.
One entire round in a circle or a spire; as, a cycle or set of leaves.
n.
Alt. of Corcule
n.
One of the individual zooids forming the compound organism of a polyzoan.
pl.
of Polyzoon
v. t.
See Encircle.
v. i.
To move circularly; to form a circle; to circulate.
n.
A circlet.
n.
A miracle play.
n.
Any plant of the genus Polygonum.
n.
An instrument of observation, the graduated limb of which consists of an entire circle.
n.
A polyzoon.
a.
Containing, or made up, of, several languages; as, a polyglot lexicon, Bible.
a.
Having the form of a circle; round.
n.
Any species of Polyzoa; one of the Polyzoa.
n.
An amphitheatrical circle for sports; a circus.
n.
A circle; a circus; a circular erection or arrangement of objects.
v. t.
To form a circle about; to inclose within a circle or ring; to surround; as, to encircle one in the arms; the army encircled the city.
n.
To encompass, as by a circle; to surround; to inclose; to encircle.