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the largest empty rectangle problem, maximal empty rectangle problem or maximum empty rectangle problem, is the problem of finding a rectangle of maximal
Largest_empty_rectangle
Smallest rectangle which encloses some planar set of points
Geographic information system Geospatial metadata Largest empty rectangle, also known as maximal empty rectangle Minimum bounding box R-tree Shapefile Spatial
Minimum_bounding_rectangle
Bounding sphere Farthest-first traversal Largest empty rectangle G. T. Toussaint, "Computing largest empty circles with location constraints," International
Largest_empty_sphere
bounding circle Largest empty rectangle (Maximum empty rectangle) Largest empty sphere 2-D case: Maximum empty circle (largest empty circle) Collision
List of combinatorial computational geometry topics
List_of_combinatorial_computational_geometry_topics
Polygon in which all angles are right
of this type are rectangles, and the term axis-aligned rectangle is preferred, although orthogonal rectangle and rectilinear rectangle are in use as well
Rectilinear_polygon
Distance estimation problems in computational geometry
Smallest enclosing rectangle: unlike the bounding box problem mentioned above, the rectangle may be of any orientation Largest empty rectangle Geometric spanner
Proximity_problems
International standard for paper sizes, including A4
sometimes called "A4 rectangles" or "silver rectangles". In other contexts, the term "silver rectangle" can also refer to a rectangle in the proportion 1:(1 + √2)
International standard paper sizes
International_standard_paper_sizes
Algorithm for computing greatest common divisors
the rectangle can be divided into segments of length c, which divides the rectangle into a grid of squares of side length c. The GCD g is the largest value
Euclidean_algorithm
Problem in computer science
returned value is that of the largest element (i.e., the value closest to 0), or negative infinity if the input was empty. For correctness, an exception
Maximum_subarray_problem
Number
boxes, or other symbols. 0 (zero, /ˈziː.roʊ/) is a number representing an empty quantity. Adding (or subtracting) 0 to any number leaves that number unchanged;
0
Illusion technique
to make performers apparently materialise from nowhere or disappear into empty space. Pepper would sometimes greet an audience by suddenly materialising
Pepper's_ghost
Four-sided polygon
rhombus and a rectangle (i.e., four equal sides and four equal angles). Oblong: longer than wide, or wider than long (i.e., a rectangle that is not a
Quadrilateral
R-tree variant and index for multidimensional objects
should group "similar" data rectangles together, to minimize the area and perimeter of the resulting minimum bounding rectangles (MBRs). Packed Hilbert R-trees
Hilbert_R-tree
Cube that fits through hole in smaller cube
ask for the largest square that lies within a unit cube. More generally, Jerrard & Wetzel (2004) show how to find the largest rectangle of a given aspect
Prince_Rupert's_cube
Concept in computational geometry
intersects at least one rectangle (hence m ≤ n). Each rectangle is intersected by exactly one line. Since the height of all rectangles is H, it is not possible
Maximum_disjoint_set
Figurate number
producing a rectangle with dimensions n × ( n + 1 ) {\displaystyle n\times (n+1)} , which is also the number of objects in the rectangle. Clearly, the
Triangular_number
Office skyscraper in Manhattan, New York
consists of two long hallways on the northern and southern sides of the rectangle, as well as a shorter hallway on the eastern side and another long hallway
Empire_State_Building
Natural number between 89 and 91
90 degrees is called a right angle. In normal space, the interior angles of a rectangle measure 90 degrees each, while in a right triangle, the angle opposing
90_(number)
Portable folding leisure chair
third rectangle to maintain it upright. A rectangular piece of canvas, of the type used in hammocks, was attached to two of the wooden rectangles to provide
Deckchair
District in Greater London, England
to the UK average and has left the area empty and isolated. Belgrave Square, one of the grandest and largest 19th-century squares, is the centrepiece
Belgravia
All numbers between two given numbers
{\displaystyle n} finite intervals. For n = 2 {\displaystyle n=2} this is a rectangle; for n = 3 {\displaystyle n=3} this is a rectangular cuboid (also called
Interval_(mathematics)
Set of edges without common vertices
that matching. Finding a largest matching in a bipartite graph can be treated as a network flow problem. Finding a largest matching in a general graph
Matching_(graph_theory)
Decomposition of an integer as a sum of positive integers
Equivalently, these are the partitions whose Young diagram fits inside an M × N rectangle. There is a recurrence relation p ( N , M ; n ) = p ( N , M − 1 ; n )
Integer_partition
Algebraic structure of set algebra
{\displaystyle \mathbb {R} ^{n}} is generated by half-infinite rectangles and by finite rectangles. For example, B ( R n ) = σ ( { ( − ∞ , b 1 ] × ⋯ × ( − ∞
Σ-algebra
Operations research problem of packing items into the largest number of bins
either X U Y or Z are empty. Phase 2: If X U Y is empty, fill bins with items from Z by the simple next-fit rule. If Z is empty, pack the items remaining
Bin_covering_problem
Municipality and town in Meta Department, Colombia
articulating axis is the Meta River. The Municipality is an irregular rectangle circumscribed by the Meta River to the north, the Manacacias River and
Puerto_Gaitán
Divergent sum of positive unit fractions
integral. Specifically, consider the arrangement of rectangles shown in the figure to the right. Each rectangle is 1 unit wide and 1 n {\displaystyle {\tfrac
Harmonic_series_(mathematics)
people living to the ages of 90–100. In 2100 the graph is shaped as a rectangle with people of all ages and genders remaining steady. It narrows slightly
Demographics_of_Sweden
Megamall with attractions in Hennepin County, Minnesota, U.S.
arranged along three levels of pedestrian walkways on the sides of the rectangle, with a fourth level on the south and east sides. Four anchor department
Mall_of_America
Result in combinatorics and graph theory
{\displaystyle r\times n} Latin rectangle can always be extended to an ( r + 1 ) × n {\displaystyle (r+1)\times n} Latin rectangle when r < n {\displaystyle
Hall's_marriage_theorem
On the unique representation of integers as sums of non-consecutive Fibonacci numbers
+ 34 −43 = F−2 + F−7 + F−10 = (−1) + 13 + (−55) 0 is represented by the empty sum. 0 = F−1 + F−2 , for example, so the uniqueness of the representation
Zeckendorf's_theorem
Province of Thailand
modern-day Phanat Nikhom District. The city was in the shape of an irregular rectangle and was surrounded by a moat. Mueang Phra Rot was established from the
Chonburi_province
Sequence of operations for a task
description: If a set of numbers is empty, then there is no highest number. Assume the first number in the set is the largest. For each remaining number in
Algorithm
Data type that allows for values that are one of multiple different data types
sealed interface Shape permits Circle, Rectangle {} record Circle(double radius) implements Shape {} record Rectangle(double width, double height) implements
Union_type
City in Tennessee, United States
the Tennessee River at Kingston. This series of bends creates a half-rectangle formation—surrounded by water on the northeast, east, and southwest—in
Oak_Ridge,_Tennessee
Palace in Gatchina, Leningrad Oblast, Russia
three main parts are distinguished. The central body is an elongated rectangle, the corners of which are adjoined by two five-sided pentahedron towers
Great_Gatchina_Palace
Monastery in Armenia
the roofing, near the main lighting apertures. The transition from the rectangle of their base to the octagon of the top is decorated with tre- and quatrefoils
Haghartsin_Monastery
Ancient capital of China
104 BC in Shanglin Park. It was a rectangle 20×30 li with a tower 46 m high. Epang Palace (阿房宮, Ēpáng Gōng) Two of the largest ethnic groups in Chang'an were
Chang'an
Sliding block puzzle
identically shaped rectangles. Frank E. Moss filed U.S. patent 668,386 in 1900 for a sliding puzzle of six squares and four rectangles, which is one of
Klotski
have erupted in the Holocene epoch; these include Eldgjá, source of the largest lava eruption in human history. Some of the various eruptions of lava,
Volcanism_of_Iceland
Business and educational center in New York City
MetroTech Center was formed in 1992 by making a 16-acre (65,000 m2) rectangle of downtown Brooklyn into a superblock (bounded by Jay Street, Johnson
Brooklyn_Commons
2D geometric minimization problem
of axis-aligned rectangles and a strip of bounded width and infinite height, determine an overlapping-free packing of the rectangles into the strip, minimizing
Strip_packing_problem
Recursive integer sequence
diagram is a 2-by-n rectangle. In other words, it is the number of ways the numbers 1, 2, ..., 2n can be arranged in a 2-by-n rectangle so that each row
Catalan_number
rectangles (or dominoes) such that each pair of touching rectangles shares exactly one edge, of length 1, and the adjacency graph of the rectangles is
1000_(number)
Unrelated vertices in graphs
other independent set. A maximum independent set is an independent set of largest possible size for a given graph G {\displaystyle G} . This size is called
Independent set (graph theory)
Independent_set_(graph_theory)
sections: a main slender 80-meter tower on a plan resembling two connected rectangles, flanked by lower one- and two-story blocks linked by a connecting passage
Architecture_of_Katowice
Device producing a high-temperature explosion
(8.7 in) thermobaric rockets. A full salvo from the TOS-1 will cover a rectangle 200 by 400 m (220 by 440 yd). The Iskander-M theatre ballistic missile
Thermobaric_weapon
1346 English victory during the Hundred Years' War
French defences there were completely inadequate. The treasury was all but empty. On 29 July, Philip proclaimed the arrière-ban for northern France, ordering
Battle_of_Crécy
German bolt-action rifle
of five shots inside an 8 cm × 12 cm (3.1 in × 4.7 in) wide and high rectangle at a distance of 100 m (109.4 yd) during the factory zeroing (Anschießen)
Karabiner_98k
Neighborhood in Denver, Colorado, United States of America
corner of Park Hill. Hartman platted the land in squares as opposed to rectangles, which created a group of streets with slight variation from other sections
Park_Hill,_Denver
Combinatorial and geometric result used in measure theory of Euclidean spaces
that the collection of balls is not empty; that is, n > 0. Let B j 1 {\displaystyle B_{j_{1}}} be the ball of largest radius. Inductively, assume that B
Vitali_covering_lemma
Number divisible only by 1 and itself
{\displaystyle n} are any number of copies of 2 or 3 together with a (possibly empty) set of distinct Pierpont primes, primes of the form 2 a 3 b + 1 {\displaystyle
Prime_number
Places where bricks are made
was a series of downdraught kilns, connected in a circle or in a long rectangle. Each kiln had an access channel to the next so as soon as the one kiln
Brickfield
Symbols for constants, special functions
ψ_n(z), ψ^((n))(z), or F_n(z-1)... Crilly, Tony (1994). "A Supergolden Rectangle". The Mathematical Gazette. 78 (483): 320–325. doi:10.2307/3620208. JSTOR 3620208
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
Municipality in Andalusia, Spain
stable population growth. The flag of Morón de la Frontera is a blue rectangle that contains the municipal coat of arms in the center. It is unknown
Morón_de_la_Frontera
German automotive brand, subsidiary of Stellantis
ring was used in a yellow rectangle, with the Opel writing below. The whole logo was again delimited by a black rectangle. The basic form and proportions
Opel
Nazi extermination camp in Poland (1942–1943)
by Deutsche Reichsbahn to Treblinka. The information in the rows with an empty last column comes from Dam im imię na wieki, page 114. The first major trial
Treblinka_extermination_camp
National park in Argentina
not border on Chile. Los Alerces National Park is shaped like a rough rectangle, extending approximately 65 kilometres (40 mi) north to south along the
Los_Alerces_National_Park
Modernist architectural style
the following: Square or rectangular footprint Simple cubic "extruded rectangle" form Windows running in broken horizontal rows forming a grid All facade
International_Style
Skyscraper in Frankfurt, Germany
several meters. In the resulting niches on each side, two elongated rounded rectangles are located, housing the lifts and emergency staircases. The theme of
Silberturm
Four-dimensional analog of the dodecahedron
so each great polygon is either a rectangle or a compound of a rectangle, with the two chords as the rectangle's edges. Each of the 15 complementary
120-cell
1993 film by Steven Spielberg
by Chip Kidd for the book's cover, put it into a circle, and added a rectangle with the title to create a badge-like structure. A jungle silhouette was
Jurassic_Park
national states. At the beginning of the 21st century, the Kurds remain the largest of the groups without their own statehood. The Treaty of Sèvres between
Secession_in_Turkey
Construction project in New York City (1931–1974)
1932 revision to the plan, the proposed plaza's shape was changed to a rectangle, and the fountain was moved to the western side of the plaza. The sculptor
Construction of Rockefeller Center
Construction_of_Rockefeller_Center
University campus in Raleigh, North Carolina, US
and field events and soccer games. It will consist of an oval (rounded rectangle) running track with a soccer field situated in the center. Dail Stadium
Main Campus of North Carolina State University
Main_Campus_of_North_Carolina_State_University
Ancient human settlement
shape of a T, made up of a 13 x 5.6 metre rectangle with a peristyle of 5 x 12 columns and another rectangle of 6.78 x 7.25 metres. Across the east–west
Selinunte
East Slavic ethnic group
coat of arms. The national flag of Ukraine is a blue and yellow bicolour rectangle, with the colour fields of the same form and equal size and the colours
Ukrainians
Pan-European news television channel
and blue lower case word "news" below. October 1998 – June 2008: blue rectangle enclosing white camel case word "EuroNews". June 2008 – May 2016: white
Euronews
Problem in combinatorial optimization
problem, there is a set of rectangles with different values, and a rectangular knapsack. The goal is to pack the largest possible value into the knapsack
Knapsack_problem
Property of a mathematical space
Moreover, the boundary of a discrete set of points is the empty set, and therefore the empty set can be taken to have dimension −1. Similarly, for the
Dimension
Memorial in Berlin, Germany
subterranean documentation area mars the steady measure of the order of rectangles. Admittedly, all objections against this pedagogical extra fall silent
Memorial to the Murdered Jews of Europe
Memorial_to_the_Murdered_Jews_of_Europe
United States historic place
80 km) west of downtown Pawtucket, on 8 acres (3.2 ha) in the shape of a rectangle with one corner cut off. It is bounded by Conant, Pine, and Weeden Streets
Jenckes_Spinning_Company
Numbers obtained by adding the two previous ones
and (n + 1)-th Fibonacci numbers. To see this, begin with a Fibonacci rectangle of size F n × F n + 1 {\displaystyle F_{n}\times F_{n+1}} and decompose
Fibonacci_sequence
artwork titled "Democracy Dies in Darkness," the motto of the Post, of a rectangle covered in gray paint strokes. Michele Norris resigned two days later
News media endorsements in the 2024 United States presidential election
News_media_endorsements_in_the_2024_United_States_presidential_election
TV test pattern, used to be widely used in European (PAL) countries
negative R-Y signal; Vertical bars – positive and negative R-Y signal; Two rectangles – G-Y signal. To the right of the circle: Vertical bar – line alternating
Philips_circle_pattern
Art from the period of the imperial Cholas (c. 850 CE – 1250 CE) in South India
square at the base and 186 feet high. The temple, which forms a large rectangle 340 feet long and 110 feet wide occupies the middle of an immense walled
Chola_art_and_architecture
tournaments have featured the other games in the series, with the two largest and most popular Smash Bros. scenes revolving around Melee and Super Smash
Super_Smash_Bros._in_esports
Type of two-dimensional barcode
of rectangular codes. For squares, the minimum size is 9 × 9 modules; rectangles have a minimum of 19 × 5 modules. iQR codes add error correction level
QR_code
Used to count, measure, and label
0.001 m. If the sides of a rectangle are measured as 1.23 m and 4.56 m, then multiplication gives an area for the rectangle between 5.614591 m2 and 5.603011
Number
Device that converts other energy to electrical energy
Faraday himself built an early alternator. His machine was a "rotating rectangle", whose operation was heteropolar: each active conductor passed successively
Electric_generator
Dam in Nevada and Arizona, US
crumble. Instead, the ground where the dam would rise was marked with rectangles, and concrete blocks in columns were poured, some as large as 50 ft square
Hoover_Dam
the cylinder, and it was flattened with a wooden spatula into a flat rectangle. The French used a variation of this plan, called "Plateau" or "Cive"
French Gothic stained glass windows
French_Gothic_stained_glass_windows
Japanese television game show
composed of either four-sided or six-sided rooms is laid out in a 4x3 rectangle (5x4 when playing with three guards). Contestants navigate the maze while
Takeshi's_Castle
Complex of buildings in New York City
lifetime. The first logo, used from 1973 to 1993, consisted of two open rectangles, one of which was upside down. When the complex reopened after the 1993
World Trade Center (1973–2001)
World_Trade_Center_(1973–2001)
Commercial building in Manhattan, New York
back of 342 Bowery. The extension changed the shape of the lot from a rectangle to one resembling the letter L. This shape is shown in a 2024 interactive
57_Great_Jones_Street
Indian mathematician and astronomer (598–668)
smaller and smaller pieces. To obtain a recurrence one has to know that a rectangle proportional to the original eventually recurs, a fact that was rigorously
Brahmagupta
Defunct American nuclear production site
from the hazardous rectangle No main highway, railway, or employee village closer than 10 miles (16 km) from the hazardous rectangle Ground that could
Hanford_Site
many people. Among all human activities, fossil fuel combustion is the largest contributor to the ongoing buildup of carbon in the Earth's biosphere.
Health and environmental impact of the petroleum industry
Health_and_environmental_impact_of_the_petroleum_industry
on-screen graphic on British television, namely a small white outline rectangle that was broadcast on the screen throughout ITV's broadcast of the documentary
Digital on-screen graphics by country
Digital_on-screen_graphics_by_country
Area of the West Midlands, England
ISBN 978-0-7190-7770-8. The notion of the Black Country, that is to say, a rectangle of territory bounded by Walsall to the north and Smethwick, Halesowen
Black_Country
Ancient Roman villa complex near Licenza, Italy
17th century which still exists. The later villa's overall plan is a rectangle of about 43 x 113 m in which a garden area of 43 x 85 m with surrounding
Horace's_Villa
q are relatively prime), and since the total number of points in the rectangle WYXA is ( p − 1 2 ) ( q − 1 2 ) , {\displaystyle \left({\frac
Proofs of quadratic reciprocity
Proofs_of_quadratic_reciprocity
Decade of the Gregorian calendar (2000–2009)
here by Kanye West in 2007 Bandanas, large hoop earrings and wireframe rectangle sunglasses were fashion trends in the early-2000s, as modeled here by
2000s
World War II British heavy bomber aircraft
the aircraft from above and to the side. The mid-upper gunner sat on a rectangle of canvas that was slung beneath the turret and would stay in position
Avro_Lancaster
Mathematical theorem
the Riemann mapping theorem states that if U {\displaystyle U} is a non-empty simply connected open subset of the complex number plane C {\displaystyle
Riemann_mapping_theorem
Gaussian elimination: The Chinese solved a system of linear equations. The rectangle of coefficients was reduced to triangular and then diagonal form, in a
List_of_Chinese_inventions
(180 cm) wide by 3.5 feet (110 cm) tall, with a 24-by-18-inch (61 by 46 cm) rectangle marked on the glass immediately above the basket. backcourt 1. The half
Glossary_of_basketball_terms
Hill in Pembrokeshire, Wales
and outside the embankments are terraced enclosures, hut circles and rectangles. Approximately 25 hut circles are at the north east end of the site. On
Mynydd_Carningli
UNESCO World Heritage Site in Tamil Nadu, India
plan is based on a square and circle, or stacked squares (producing a rectangle). The reliefs, sculptures and architecture incorporate Shaivism, Vaishnavism
Group of Monuments at Mahabalipuram
Group_of_Monuments_at_Mahabalipuram
Annual auto race held in Speedway, Indiana, US
Motor Speedway, a 2.5-mile (4 km) oval circuit. The track is a rounded rectangle, with four distinct turns of identical dimensions, connected by four straightaways
Indianapolis_500
LARGEST EMPTY-RECTANGLE
LARGEST EMPTY-RECTANGLE
Girl/Female
Biblical
Den, making empty, watching.
Surname or Lastname
English
English : variant of Taggart.Possibly an altered spelling of French Target, a nickname for someone who carried a square buckler, Old French targe.
Boy/Male
Arabic
Empty.
Boy/Male
American, Australian, Danish, French, Jamaican, Latin
Vain; Empty; Poor; Robbed; Hollow
Biblical
den; making empty; watching
Surname or Lastname
English and French
English and French : in medieval times this did not denote a rank in the army, but was an occupational name for a servant, Middle English, Old French sergent (Latin serviens, genitive servientis, present participle of servire ‘to serve’). The surname probably originated for the most part in this sense, but the word also developed various more specialized meanings, being used for example as a technical term for a tenant by military service below the rank of a knight, and as the name for any of certain administrative and legal officials in different localities, which may also have contributed to the development of the surname. The sense ‘non-commissioned officer’ did not arise until the 16th century.William Sargent (1624–1717) came to Gloucester, MA, from Devon, England before 1678. Many of his descendants distinguished themselves in the civil and military affairs of the colonies and some in literary or artistic paths, notably the portrait painter John Singer Sargent (1856–1925).
Boy/Male
British, English, Spanish
Strong Leader; Empty
Girl/Female
Biblical
Den, cave, making empty.
Girl/Female
Biblical
Void, empty.
Girl/Female
Biblical
Empty, temple of the head.
Boy/Male
English American German
Earnest.
Biblical
den; cave; making empty
Boy/Male
Hindu, Indian
Empty
Surname or Lastname
English
English : from Old French argent ‘silver’, hence probably a nickname for someone with silver-gray hair, or possibly an occupational nickname for a silversmith or moneyer.
Boy/Male
Arabic, Australian, German, Greek, Kurdish
Empty; Void
Male
English
Variant spelling of English Ernest, EARNEST means "battle (to the death), serious business."
Boy/Male
Biblical
Who is empty or exhausted.
Biblical
who is empty, exhausted;free, empty, exhausted;
Surname or Lastname
English (Suffolk, of Norman origin)
English (Suffolk, of Norman origin) : nickname for someone with silvery hair, a variant of Argent, with the French definite article l(e).French : metonymic occupational name for a silversmith, from French argent ‘silver’.
Male
Swedish
Variant spelling of Swedish Laris, LARES means "of Laurentum."
LARGEST EMPTY-RECTANGLE
LARGEST EMPTY-RECTANGLE
Girl/Female
Tamil
Star, The pupil of the eye, Meteor, Fragance
Female
Russian
Variant spelling of Russian Agnessa, AGNESSE means "chaste; holy."
Boy/Male
Hindu
Happy kingdom, Lord Shiva
Biblical
gracious; merciful; graceful; She that gives
Boy/Male
Hindu, Indian
Splendorous
Boy/Male
Buddhist, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
Lord Buddha
Girl/Female
Australian, Spanish
Consolation; Comfort
Boy/Male
Muslim/Islamic
Shining
Boy/Male
Australian, Swedish
He will Sing
Boy/Male
Muslim
One who rallies people
LARGEST EMPTY-RECTANGLE
LARGEST EMPTY-RECTANGLE
LARGEST EMPTY-RECTANGLE
LARGEST EMPTY-RECTANGLE
LARGEST EMPTY-RECTANGLE
pl.
of Empty
v. t.
To empty.
a.
Empty.
p. pr. & vb. n.
of Empty
superl.
Destitute of reality, or real existence; unsubstantial; as, empty dreams.
v. t.
To deprive of the contents; to exhaust; to make void or destitute; to make vacant; to pour out; to discharge; as, to empty a vessel; to empty a well or a cistern.
a.
Empty; frivolous.
n.
An empty box, crate, cask, etc.; -- used in commerce, esp. in transportation of freight; as, "special rates for empties."
superl.
Producing nothing; unfruitful; -- said of a plant or tree; as, an empty vine.
imp. & p. p.
of Empty
superl.
Destitute of, or lacking, sense, knowledge, or courtesy; as, empty brains; an empty coxcomb.
a.
Alt. of Largesse
superl.
Containing nothing; not holding or having anything within; void of contents or appropriate contents; not filled; -- said of an inclosure, as a box, room, house, etc.; as, an empty chest, room, purse, or pitcher; an empty stomach; empty shackles.
a.
Empty.
v. t.
To empty.
v. i.
To become empty.
v. t.
To use in earnest.
superl.
Destitute of effect, sincerity, or sense; -- said of language; as, empty words, or threats.
v. t.
To empty.
compar.
of Empty.