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Planar graph used as counterexample
The nested triangles graph with two triangles is the graph of the triangular prism, and the nested triangles graph with three triangles is the graph of
Nested_triangles_graph
Type of planar graph
-outerplanar graphs have treewidth at most 3 k − 1 {\displaystyle 3k-1} . However, some bounded-treewidth planar graphs such as the nested triangles graph may
K-outerplanar_graph
Points usable to draw any planar graph
universal for outerplanar graphs. Planar graphs that can be partitioned into nested cycles, 2-outerplanar graphs and planar graphs of bounded pathwidth, have
Universal_point_set
Size of bounding box of graph drawing
drawings of planar graphs with n vertices, the optimal worst-case bound on the area of a drawing is Θ(n2). The nested triangles graph requires this much
Area_(graph_drawing)
Graph with tight clique-coloring relation
triangulated graphs, comparability graphs, proper interval graphs, proper circular-arc graphs, and nested interval graphs". Journal of Graph Theory. 6 (3):
Perfect_graph
Archimedean solid with 32 faces
identical vertices, with two triangles and two pentagons meeting at each, and 60 identical edges, each separating a triangle from a pentagon. As such, it
Icosidodecahedron
Intersection graph for intervals on the real number line
interval graphs that have an interval representation in which every two intervals are either disjoint or nested are the trivially perfect graphs. A graph has
Interval_graph
Intersection graph of unit intervals on the real line
of each other. An indifference graph is also the intersection graph of a set of unit intervals, or of properly nested intervals (intervals none of which
Indifference_graph
System of elements that are subordinated to each other
computers. An example of visually representing hierarchy is through nested clusters. Nested clusters represent hierarchical relationships using layers of information
Hierarchy
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
Graphical technique for data sets
plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables. The plot can be
Plot_(graphics)
Type of diagrammatic notation for propositional logic
An existential graph is a type of diagrammatic or visual notation for logical expressions, created by Charles Sanders Peirce, who wrote on graphical logic
Existential_graph
Any planar graph can be subdivided by removing a few vertices
solving NP-hard optimization problems on these graphs. Separator hierarchies may also be used in nested dissection, an efficient variant of Gaussian elimination
Planar_separator_theorem
Semantics (ARIES): transaction recovery Join algorithms Block nested loop Hash join Nested loop join Sort-Merge Join The Chase Clock synchronization Berkeley
List_of_algorithms
Concept in quantum computing
computing, a graph state is a special type of multi-qubit state that can be represented by a graph. Each qubit is represented by a vertex of the graph, and there
Graph_state
Spherical triangle that can be used to tile a sphere
called a triangle group. In the sphere there are three Möbius triangles plus one one-parameter family; in the plane there are three Möbius triangles, while
Schwarz_triangle
Non-orientable surface with one edge
formed from three equilateral triangles does not come from an abstract simplicial complex, because all three triangles share the same three vertices,
Möbius_strip
NP-hard problem in combinatorial optimization
bound, a better way of creating an Eulerian graph is needed. By the triangle inequality, the best Eulerian graph must have the same cost as the best travelling
Travelling_salesman_problem
Five-pointed star polygon
triangles: five acute and five obtuse isosceles triangles. In all of them, the ratio of the longer side to the shorter side is φ. The acute triangles
Pentagram
CAD data-exchange format by Siemens
scene graph representation of an assembly, nested sub-assemblies of parts with CAD specific node and attributes data. Facet information (triangles) is stored
JT_(visualization_format)
Argentine-born American mathematician
Dejter I. J.; Franek F.; Mendelsohn E.; Rosa Alexander "Triangles in 2-factorizations", Journal of Graph Theory, 26 (1997) 83-94. Dejter I. J.; Franek F.; Rosa
Italo_Jose_Dejter
Family of problems in computational geometry
polygon of our subdivision in triangles, and restrict our data structure to the case of subdivisions formed exclusively by triangles. Kirkpatrick gives a data
Point_location
Feature to efficiently execute queries efficiently in DBMS softwares
relational database management systems and other databases such as NoSQL and graph databases. The query optimizer attempts to determine the most efficient
Query_optimization
Invariant in graph theory
In the mathematical field of graph theory, the queue number of a graph is a graph invariant defined analogously to stack number (book thickness) using
Queue_number
Tiling of the hyperbolic plane
right triangles. It is one of several Escher prints based on the half-plane model of the hyperbolic plane. The print itself replaces each triangle by a
Binary_tiling
Point set triangulation minimizing total length
subdivided into triangles that meet edge-to-edge and vertex-to-vertex, in such a way as to minimize the sum of the perimeters of the triangles. The problem
Minimum-weight_triangulation
Upper bound on intersecting set families
The theorem may also be formulated in terms of graph theory: the independence number of the Kneser graph K G n , r {\displaystyle KG_{n,r}} for n ≥ 2 r
Erdős–Ko–Rado_theorem
Representation of a graph as a path graph "thickened" by some amount
In graph theory, a path decomposition of a graph G is, informally, a representation of G as a "thickened" path graph, and the pathwidth of G is a number
Pathwidth
finding as many triangles as possible among the vertices of a convex polygon, such that no two triangles that share a vertex have nested angles at that
Tripod_packing
Uniform 4-polytope
have two other uncolored triangles across the opposite diagonal. Transparent Schlegel diagram seen as one tetrahedron nested inside another, with 4 triangular
Tetrahedral_prism
filtration (sometimes shortened to "Rips filtration") is the collection of nested Vietoris–Rips complexes on a metric space created by taking the sequence
Vietoris–Rips_filtration
instruments, such as "drums", "saxophone", and "triangle" will show their respective sounds in the Knowledge Graph. "juneteenth( see it )" will show a button
List_of_Google_Easter_eggs
Shape with four equal sides and angles
permute the eight isosceles triangles between the half-edges and the square's center (which stays in place); any of these triangles can be taken as the fundamental
Square
Social structure made up of a set of social actors
field which emerged from social psychology, sociology, statistics, and graph theory. Georg Simmel authored early structural theories in sociology emphasizing
Social_network
Fractal composed of tangent circles
one in each of these six curved triangles, tangent to its three sides. These in turn create 18 more curved triangles, and the construction continues by
Apollonian_gasket
Trigonometric values in terms of square roots and fractions
Repeated application of the half-angle formulas leads to nested radicals, specifically nested square roots of 2 of the form 2 ± ⋯ {\displaystyle {\sqrt
Exact_trigonometric_values
Replacing subterm in a formula with another term
a rewriting system whose objects are terms, which are expressions with nested sub-expressions. For example, the system shown under § Logic above is a
Rewriting
Four-dimensional analog of the icosahedron
triangular in a special way, but one in which golden triangles rather than equilateral triangles meet at the center. Only a few uniform polytopes have
600-cell
Doughnut-shaped surface of revolution
together two congruent geodesic triangles in the hyperbolic plane along their (identical) boundaries, where each triangle has angles of π/2, π/3, and 0
Torus
Four-dimensional analog of the octahedron
8 tetrahedra, 12 triangles, and 6 edges meeting at every vertex. Its edge figure is a square. There are 4 tetrahedra and 4 triangles meeting at every
16-cell
Inverse functions of sin, cos, tan, etc.
S2CID 123395287 S. M. Abrarov and B. M. Quine (2018), "A formula for pi involving nested radicals", The Ramanujan Journal, 46 (3): 657–665, arXiv:1610.07713, doi:10
Inverse trigonometric functions
Inverse_trigonometric_functions
Number whose square is a given number
of Pythagoras' theorem by similar triangles, triangle AHC is similar to triangle CHB (as indeed both are to triangle ACB, though we don't need that, but
Square_root
Two-dimensional cellular automaton
while tracking the fates of various small starting configurations using graph paper, blackboards, and physical game boards, such as those used in Go.
Conway's_Game_of_Life
Branching diagram of evolutionary relationships between organisms
encoded in a number of different formats, all of which must represent the nested structure of a tree. They may or may not encode branch lengths and other
Phylogenetic_tree
Special n-gon that has the largest area among all diameter-one n-gons
10 {\displaystyle S_{10}} , it cannot be expressed in closed form using nested radicals. Graham conjectured that the optimal solution for the general case
Biggest_little_polygon
Model to describe distributed systems
class of discrete event dynamic system. A Petri net is a directed bipartite graph that has two types of elements: places and transitions. Place elements are
Petri_net
Laboratory tool
rubber stopper to insert glass tubing. Cork borers usually come in a set of nested sizes along with a solid pin for pushing the removed cork (or rubber) out
Cork_borer
UI test highlights 'Most viewed' video portions in playback progress bar graph". 9to5Google. Archived from the original on January 1, 2022. Retrieved January
History_of_YouTube
Numbers obtained by adding the two previous ones
side of each of these triangles is the sum of the three sides of the preceding triangle. The Fibonacci cube is an undirected graph with a Fibonacci number
Fibonacci_sequence
Curve where spinning and moving lines cross
equivalence between the quadratrix, the image of the Lambert W function, and the graph of the function y = x cot x {\displaystyle y=x\cot x} . The discovery
Quadratrix_of_Hippias
2013 Android mobile operating system
getting rid of the Wi-Fi upstream and downstream traffic indicators (triangles pointing up and down), though they can still be seen in the quick control
Android_KitKat
Infinitely detailed mathematical structure
displaying short descriptions of redirect targets Matryoshka doll – Russian nested wooden toy created in 1890 Menger Sponge – Three-dimensional fractalPages
Fractal
Smallest convex set containing a given set
depth form a nested family of convex sets, with the convex hull outermost, and the bagplot also displays another polygon from this nested family, the contour
Convex_hull
U-570, which was surrendered in September 1941, and recommissioned as HMS Graph Ned Kelly (1970) – British-Australian biographical bushranger film about
List of 1970s films based on actual events
List_of_1970s_films_based_on_actual_events
Apparent curve that separates earth from sky
above, the top of the lighthouse will be visible to a lookout in a crow's nest at the top of a mast of the boat if D B L < 3.57 ( h B + h L ) , {\displaystyle
Horizon
Methods of calculating definite integrals
astronomers calculated Jupiter's position from the area under a time-velocity graph". Science. 351 (6272): 482–484. Bibcode:2016Sci...351..482O. doi:10.1126/science
Numerical_integration
Series of large language models developed by Google AI
Browsing SageTV Santa Tracker Schemer Scholar Search AI Overviews Knowledge Graph SafeSearch Searchwiki Sheets Shoploop Shopping Sidewiki Sites Slides Snapseed
T5_(language_model)
General-purpose programming language
extensions, notably from the High Performance Fortran specification: FORALL and nested WHERE constructs to aid vectorization User-defined PURE and ELEMENTAL procedures
Fortran
Programming language
C (and also unlike most other languages in the C family), Pascal allows nested procedure definitions to any depth, and allows most kinds of definitions
Pascal_(programming_language)
Me. Retrieved January 5, 2014. "Google to Acquire Nest". Retrieved January 13, 2014. Google Buys Nest Labs for B, IEEE Spectrum, 2014.01.14 "Alphabet Investor
List of mergers and acquisitions by Alphabet
List_of_mergers_and_acquisitions_by_Alphabet
Four-dimensional analog of the dodecahedron
4-polytopes, two irregular 4-polytopes occur naturally in the sequence of nested 4-polytopes: the 96-point snub 24-cell and the 480-point diminished 120-cell
120-cell
Graphical set representation involving overlapping shapes
Euler and Venn diagrams Euler diagram of types of triangles, using the definition that isosceles triangles have at least (rather than exactly) 2 equal sides
Euler_diagram
Digital application and media distribution service by Google
Google removed the shopping bag from the Google Play icon, with only the triangle and associated colors remaining. In March 2018, Google experimented by
Google_Play
2017 American documentary by Greg Kohs
Browsing SageTV Santa Tracker Schemer Scholar Search AI Overviews Knowledge Graph SafeSearch Searchwiki Sheets Shoploop Shopping Sidewiki Sites Slides Snapseed
AlphaGo_(film)
Theoretical milestones of child development
from the original on 22 August 2009. "When Do Babies Start Rolling Over?". Nested Bean. Retrieved 12 January 2023. Jim McMorran; Damian Crowther; Stew McMorran;
Child_development_stages
Type of formal logic
+ N T := K + T S4 := T + 4 S5 := T + 5 D := K + D. K through S5 form a nested hierarchy of systems, making up the core of normal modal logic. But specific
Modal_logic
City in California, United States
Marshall, San Diego Bay is "the surface expression of a north-south-trending, nested graben". The Rose Canyon and Point Loma fault zones are part of the San
San_Diego
polygons in 2D or 3D Triangle mesh — consists of triangles in 2D or 3D Triangulation (geometry) — subdivision of given region in triangles, or higher-dimensional
List of numerical analysis topics
List_of_numerical_analysis_topics
Count of permutations by cycles
K=k_{1}+\cdots +k_{p}.} The sum is a sum over all partitions of p. Another exact nested sum expansion for these Stirling numbers is computed by elementary symmetric
Stirling numbers of the first kind
Stirling_numbers_of_the_first_kind
Canadian academic and University president
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Shirley_M._Tilghman
2010 smartphone developed by Google and Samsung
Technologies, supports OpenGL ES 1.1/2.0 and is capable of up to 20 million triangles per second. The Nexus S has 512 MB of RAM (Mobile DDR) (128MB is assigned
Nexus_S
Monetary System, 1946–1985 (1986) online Rozman, Gilbert, ed. Asia's Alliance Triangle: US-Japan-South Korea Relations at a Tumultuous Time (Palgrave Macmillan
Japan–United_States_relations
Polarization pattern of the daytime sky
The geometry for the sky polarization can be represented by a celestial triangle based on the Sun, zenith, and observed pointing (or the point of scattering)
Rayleigh_sky_model
Classification system for symmetry groups in geometry
Coxeter group can be represented by Coxeter notation [(3,3,(3),3,3)], with nested/overlapping parentheses showing two adjacent [(3,3,3)] loops, and is also
Coxeter_notation
2014 Android mobile operating system
completely changed from a left arrow, a house, and two squares, to a left triangle, a circle and a square. Lollipop also contains significant new platform
Android_Lollipop
Use of functions that call themselves
support nested functions, the auxiliary function can be nested inside the wrapper function and use a shared scope. In the absence of nested functions
Recursion_(computer_science)
Most populous city in Pennsylvania, US
point is 82 °F (28 °C) which occurred on July 15, 1995. See or edit raw graph data. Philadelphia County received an ozone grade of F and a 24-hour particle
Philadelphia
Mathematical theorem in real analysis
result) so that each K i {\displaystyle K_{i}} is nonempty. This yields a nested sequence of sets ∅ ≠ K N + 1 ⊂ K N ⊂ ⋯ ⊂ K 1 ⊂ E {\displaystyle \emptyset
Steinhaus_theorem
Number, approximately 3.14
However, like every number, π can be represented by an infinite series of nested fractions, called a simple continued fraction: π = 3 + 1 7 + 1 15 + 1 1
Pi
Stratification of a genetic population based on allele frequencies
at all; and there may be hierarchical structure where subpopulations are nested. Clusters may be admixed themselves, and may not have a useful interpretation
Population structure (genetics)
Population_structure_(genetics)
Varying methods used to calculate pi
Plato's repeated discussion of special right triangles that are either isosceles or halves of equilateral triangles. Accurate to four digits: 1 + e − γ = 3
Approximations_of_pi
Kind of fair item allocation
showed that: The problem is weakly NP-hard even when the wanted bundles are nested. The problem is APX-hard even for very sparse instances. There is a log-factor
Envy-free_pricing
Capital city of Australia
May 2013. Retrieved 2 June 2009. "Climate: Canberra – Climate graph, Temperature graph, Climate table". Climate-Data.org. Archived from the original on
Canberra
Stack-based method for clustering
find pairs of clusters to merge by following paths in the nearest neighbor graph of the clusters. Every such path will eventually terminate at a pair of
Nearest-neighbor chain algorithm
Nearest-neighbor_chain_algorithm
Species of bacterium
Christopher H.; Wei, Cong (18 November 2025). "Genome degradation results in nested symbiosis and endosymbiont replacement in cicadas". Nature Communications
Karelsulcia_muelleri
Arithmetic operation, inverse of nth power
its application leads to the inequality in the first step above. A non-nested radical expression is said to be in simplified form if no factor of the
Nth_root
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List_of_Stadia_games
Protests over private buses using public stops
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San Francisco tech bus protests
San_Francisco_tech_bus_protests
Google Android apps list
by Google Jump Inspector Motion Stills MyTracks (merged with Google Fit) Nest (merged with the Google Home app) Notable Women One Today by Google Pixel
List of Android apps by Google
List_of_Android_apps_by_Google
– professor of computer science, inventor of many algorithms related to graph theory, winner of the 1986 Turing Award, recipient of the 1982 Nevanlinna
List of Princeton University people
List_of_Princeton_University_people
Building in Manhattan, New York
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St._John's_Terminal
Generalization of a polytope in real space
called a Shephard group) acts transitively on the flags, that is, on the nested sequences of a point contained in a line contained in a plane and so on
Complex_polytope
NESTED TRIANGLES-GRAPH
NESTED TRIANGLES-GRAPH
Surname or Lastname
English
English : occupational name for a jester, Middle English gester.German : from the Germanic personal name Gastharo, composed of the elements gast ‘warrior’ + heri ‘army’.
Female
Welsh
Welsh pet form of Greek Hagne (English Agnes), NESTA means "chaste; holy."
Male
English
Short form of English Sylvester, VESTER means "from the forest."
Surname or Lastname
English
English : habitational name from any of various places called Newstead, in particular the one in Nottinghamshire, which is named from Old English nīwe ‘new’ + stede ‘monastic site’.
Female
Scandinavian
Scandinavian form of Persian Esther, ESTER means "star."
Male
English
English surname transferred to forename use, from the city name Leicester which was recorded in the 10th century as Ligora caester "Ligora's fort." Ligora is related to Liguria, a very old place name of obscure origin, dating back to pre-Roman times. There has been some speculation concerning a possible connection between Ligora/Liguria and Celtic Lug, LESTER means "oath."
Girl/Female
Biblical
They rested.
Female
English
Medieval Latin form of Persian Esther, HESTER means "star."
Female
French
French feminine form of Latin unisex Cælestis, CÉLESTE means "heavenly."
Surname or Lastname
English (Devon), Dutch, and German
English (Devon), Dutch, and German : occupational name for a baker, from Anglo-Norman French pestour, pistour, Middle Dutch pester, pister ‘baker’ (Old French pestor, pesteur, German Pistor, from Latin pistor).Jewish (Ashkenazic) : unexplained.
Surname or Lastname
English
English : occupational name for someone who looked after animals, Middle English bester, from beste ‘beast’ (see Best).German : habitational name for someone from a place called Beste.Slovenian (Gorenjska; also Bešter) : probably a derivative of Vester 3, a reduced form of the personal name Silvester. Replacement of initial V- with B- is quite common in Slovenian surnames.
Male
Hebrew
(כֶּשֶׂד) Hebrew name KESED means "increase." In the bible, this is the name of the 4th son of Nahor. Chesed is the Anglicized form.
Biblical
They rested
Male
Greek
(ÎÎστωÏ) Greek name NESTOR means "homecoming." In mythology, this is the name of a son of Nileas (Latin Neleus) and king of Pylos.
Surname or Lastname
English and French
English and French : variant spelling of Best.German : topographic name for someone who lived by the Beste river, a tributary of the Trave, or a habitational name from any of various villages called Besten, said by Bahlow to be named with a Middle Low German word for poor soil.
Male
Scottish
Medieval Scottish form of Latin Crescentius, KESTER means "to spring up, grow, thrive."
Surname or Lastname
English
English : probably a variant of Easton.The Esten family has been associated with Scituate, MA, and Providence, RI, since the 17th century.
Male
English
Low German pet form of Latin Silvester, FESTER means "from the forest."
Surname or Lastname
English
English : variant of Eastes, still pronounced today as two syllables, as it was in medieval times.This name was brought to New England by Matthew (1645–1723) and Richard (born 1647) Estes, sons of Robert and Dorothy Estes of Dover, England. Probably unconnected is the founder of the VA and TN family of this name, Benjamin Estes (born 1736 in VA; died 1811 in TN).
Girl/Female
Greek
Poor, pure, or chaste. St. Agnes was a 3rd century Christian martyr whose January 21st feast day...
NESTED TRIANGLES-GRAPH
NESTED TRIANGLES-GRAPH
Girl/Female
Latin American Greek English French
Horn.
Boy/Male
Tamil
Kshrinag | கà¯à®·à¯à®°à¯€à®¨à®¾à®•
Shiva
Girl/Female
Indian, Sindhi
Joy; Happiness
Boy/Male
Indian
Prism, Manifesto, Law, Defended or protected by God or liked or victorious
Boy/Male
Hindu, Indian
Making Alive
Male
Chinese
old, to grow.
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Telugu
Consciousness
Boy/Male
Tamil
One who is victorious
Male
Czechoslovakian
, free.
Boy/Male
Hindu
Trustworthy friend, Pride, Ever smiling, Devine smile
NESTED TRIANGLES-GRAPH
NESTED TRIANGLES-GRAPH
NESTED TRIANGLES-GRAPH
NESTED TRIANGLES-GRAPH
NESTED TRIANGLES-GRAPH
imp. & p. p.
of Nestle
v. t.
To set or adorn, as with studs or bosses; to set thickly; to stud; as, to bestud with stars.
a.
Marked with a band or circle; as, a belted stalk.
v. t.
To divide into triangles; specifically, to survey by means of a series of triangles properly laid down and measured.
a.
Having (such) meat; -- used chiefly in composition; as, thick-meated.
a.
Having three angles; triangular.
n.
A small constellation near the South Pole, containing three bright stars.
n.
A draughtsman's square in the form of a right-angled triangle.
imp. & p. p.
of Bestead
a.
Having (such) a chest; -- in composition; as, broad-chested; narrow-chested.
a.
Inclosed in a cyst. See Cysted.
a.
Having hard or strong hands; as, a hard-fisted laborer.
a.
Close-fisted; covetous; niggardly.
a.
Furnished with a mast or masts; -- chiefly in composition; as, a three-masted schooner.
a.
Encircled by, or secured with, a belt; as, a belted plaid; girt with a belt, as an honorary distinction; as, a belted knight; a belted earl.
a.
Not in a state of contingency or suspension; fixed; as, vested rights; vested interests.
n.
An instrument of percussion, usually made of a rod of steel, bent into the form of a triangle, open at one angle, and sounded by being struck with a small metallic rod.
v. t.
To cause to fester or rankle.