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Circle Packing In A Square
Circle packing in a square is a packing problem in recreational mathematics, where the aim is to pack unit circles into the smallest possible square. Equivalently, the problem is to arrange points in a unit square aiming to get the greatest minimal separation, , between points. To convert between these two formulations of the problem, the square side for unit circles will be . Solutions Solutions (not necessarily optimal) have been computed for every . Solutions up to are shown below. The obvious square packing is optimal for 1, 4, 9, 16, 25, and 36 circles (the six smallest square number In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals and can be written as . The usu ...s), but ceases to be optimal for larger squares from 49 onwards. Circle packing in a rectangle Dense packings of circles in non-square recta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Packing Problem
Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to either pack a single container as densely as possible or pack all objects using as few containers as possible. Many of these problems can be related to real-life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap. In a bin packing problem, you are given: * A ''container'', usually a two- or three-dimensional convex region, possibly of infinite size. Multiple containers may be given depending on the problem. * A set of ''objects'', some or all of which must be packed into one or more containers. The set may contain different objects with their sizes specified, or a single object of a fixed dimension that can be used repeatedly. Usually the packi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
10 Circles In A Square
1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. The fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number multiplied by 1 equals the same number. Most if not all properties of 1 can be deduced from this. In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number. 1 is by convention not considered a prime number; this was not universally accepted until the mid-20th century. Additionally, 1 is the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
19 Circles In A Square
Nineteen or 19 may refer to: * 19 (number), the natural number following 18 and preceding 20 * one of the years 19 BC, AD 19, 1919, 2019 Films * ''19'' (film), a 2001 Japanese film * ''Nineteen'' (film), a 1987 science fiction film Music * 19 (band), a Japanese pop music duo Albums * ''19'' (Adele album), 2008 * ''19'', a 2003 album by Alsou * ''19'', a 2006 album by Evan Yo * ''19'', a 2018 album by MHD * ''19'', one half of the double album ''63/19'' by Kool A.D. * ''Number Nineteen'', a 1971 album by American jazz pianist Mal Waldron * ''XIX'' (EP), a 2019 EP by 1the9 Songs * "19" (song), a 1985 song by British musician Paul Hardcastle. * "Nineteen", a song by Bad4Good from the 1992 album ''Refugee'' * "Nineteen", a song by Karma to Burn from the 2001 album ''Almost Heathen''. * "Nineteen" (song), a 2007 song by American singer Billy Ray Cyrus. * "Nineteen", a song by Tegan and Sara from the 2007 album '' The Con''. * "XIX" (song), a 2014 song by Slipknot. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
18 Circles In A Square
Eighteen or 18 may refer to: * 18 (number), the natural number following 17 and preceding 19 * one of the years 18 BC, AD 18, 1918, 2018 Film, television and entertainment * ''18'' (film), a 1993 Taiwanese experimental film based on the short story ''God's Dice'' * ''Eighteen'' (film), a 2005 Canadian dramatic feature film * 18 (British Board of Film Classification), a film rating in the United Kingdom, also used in Ireland by the Irish Film Classification Office * 18 (''Dragon Ball''), a character in the ''Dragon Ball'' franchise * "Eighteen", a 2006 episode of the animated television series ''12 oz. Mouse'' Music Albums * ''18'' (Moby album), 2002 * ''18'' (Nana Kitade album), 2005 * '' 18...'', 2009 debut album by G.E.M. Songs * "18" (5 Seconds of Summer song), from their 2014 eponymous debut album * "18" (One Direction song), from their 2014 studio album ''Four'' * "18", by Anarbor from their 2013 studio album '' Burnout'' * "I'm Eighteen", by Alice Cooper commonly r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
17 Circles In A Square
Seventeen or 17 may refer to: *17 (number), the natural number following 16 and preceding 18 * one of the years 17 BC, AD 17, 1917, 2017 Literature Magazines * ''Seventeen'' (American magazine), an American magazine * ''Seventeen'' (Japanese magazine), a Japanese magazine Novels * ''Seventeen'' (Tarkington novel), a 1916 novel by Booth Tarkington *''Seventeen'' (''Sebuntiin''), a 1961 novel by Kenzaburō Ōe * ''Seventeen'' (Serafin novel), a 2004 novel by Shan Serafin Stage and screen Film * ''Seventeen'' (1916 film), an American silent comedy film *''Number Seventeen'', a 1932 film directed by Alfred Hitchcock * ''Seventeen'' (1940 film), an American comedy film *''Eric Soya's '17''' (Danish: ''Sytten''), a 1965 Danish comedy film * ''Seventeen'' (1985 film), a documentary film * ''17 Again'' (film), a 2009 film whose working title was ''17'' * ''Seventeen'' (2019 film), a Spanish drama film Television * ''Seventeen'' (TV drama), a 1994 UK dramatic short starring Christien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
16 Circles In A Square
Sixteen or 16 may refer to: *16 (number), the natural number following 15 and preceding 17 *one of the years 16 BC, AD 16, 1916, 2016 Films * ''Pathinaaru'' or ''Sixteen'', a 2010 Tamil film * ''Sixteen'' (1943 film), a 1943 Argentine film directed by Carlos Hugo Christensen * ''Sixteen'' (2013 Indian film), a 2013 Hindi film * ''Sixteen'' (2013 British film), a 2013 British film by director Rob Brown Music *The Sixteen, an English choir *16 (band), a sludge metal band *Sixteen (Polish band), a Polish band Albums * ''16'' (Robin album), a 2014 album by Robin * 16 (Madhouse album), a 1987 album by Madhouse * ''Sixteen'' (album), a 1983 album by Stacy Lattisaw *''Sixteen'' , a 2005 album by Shook Ones * ''16'', a 2020 album by Wejdene Songs * "16" (Sneaky Sound System song), 2009 * "Sixteen" (Thomas Rhett song), 2017 * "Sixteen" (Ellie Goulding song), 2019 *"16", by Craig David from ''Following My Intuition'', 2016 *"16", by Green Day from ''39/Smooth'', 1990 *"16", by High ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
15 Circles In A Square
Fifteen or 15 may refer to: *15 (number), the natural number following 14 and preceding 16 *one of the years 15 BC, AD 15, 1915, 2015 Music *Fifteen (band), a punk rock band Albums * ''15'' (Buckcherry album), 2005 * ''15'' (Ani Lorak album), 2007 * ''15'' (Phatfish album), 2008 * ''15'' (mixtape), a 2018 mixtape by Bhad Bhabie * ''Fifteen'' (Green River Ordinance album), 2016 * ''Fifteen'' (The Wailin' Jennys album), 2017 * ''Fifteen'', a 2012 album by Colin James Songs * "Fifteen" (song), a 2008 song by Taylor Swift *"Fifteen", a song by Harry Belafonte from the album '' Love Is a Gentle Thing'' *"15", a song by Rilo Kiley from the album ''Under the Blacklight'' *"15", a song by Marilyn Manson from the album ''The High End of Low'' *"The 15th", a 1979 song by Wire Other uses *Fifteen, Ohio, a community in the United States * ''15'' (film), a 2003 Singaporean film * ''Fifteen'' (TV series), international release name of ''Hillside'', a Canadian-American teen drama *Fif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
14 Circles In A Square
Fourteen or 14 may refer to: * 14 (number), the natural number following 13 and preceding 15 * one of the years 14 BC, AD 14, 1914, 2014 Music * 14th (band), a British electronic music duo * ''14'' (David Garrett album), 2013 *''14'', an unreleased album by Charli XCX * "14" (song), 2007, from ''Courage'' by Paula Cole Other uses * ''Fourteen'' (film), a 2019 American film directed by Dan Sallitt * ''Fourteen'' (play), a 1919 play by Alice Gerstenberg * ''Fourteen'' (manga), a 1990 manga series by Kazuo Umezu * ''14'' (novel), a 2013 science fiction novel by Peter Clines * ''The 14'', a 1973 British drama film directed by David Hemmings * Fourteen, West Virginia, United States, an unincorporated community * Lot Fourteen, redevelopment site in Adelaide, South Australia, previously occupied by the Royal Adelaide Hospital * "The Fourteen", a nickname for NASA Astronaut Group 3 * Fourteen Words, a phrase used by white supremacists and Nazis See also * 1/4 (other) * Fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
13 Circles In A Square
Thirteen or 13 may refer to: * 13 (number), the natural number following 12 and preceding 14 * One of the years 13 BC, AD 13, 1913, 2013 Music * 13AD (band), an Indian classic and hard rock band Albums * ''13'' (Black Sabbath album), 2013 * ''13'' (Blur album), 1999 * ''13'' (Borgeous album), 2016 * ''13'' (Brian Setzer album), 2006 * ''13'' (Die Ärzte album), 1998 * ''13'' (The Doors album), 1970 * ''13'' (Havoc album), 2013 * ''13'' (HLAH album), 1993 * ''13'' (Indochine album), 2017 * ''13'' (Marta Savić album), 2011 * ''13'' (Norman Westberg album), 2015 * ''13'' (Ozark Mountain Daredevils album), 1997 * ''13'' (Six Feet Under album), 2005 * ''13'' (Suicidal Tendencies album), 2013 * ''13'' (Solace album), 2003 * ''13'' (Second Coming album), 2003 * ''13'' (Ces Cru EP), 2012 * ''13'' (Denzel Curry EP), 2017 * ''Thirteen'' (CJ & The Satellites album), 2007 * ''Thirteen'' (Emmylou Harris album), 1986 * ''Thirteen'' (Harem Scarem album), 2014 * ''Thirtee ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
12 Circles In A Square
1 (one, unit, unity) is a number representing a single or the only entity. 1 is also a numerical digit and represents a single unit of counting or measurement. For example, a line segment of ''unit length'' is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. The fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number multiplied by 1 equals the same number. Most if not all properties of 1 can be deduced from this. In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number. 1 is by convention not considered a prime number; this was not universally accepted until the mid-20th century. Additionally, 1 is the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
11 Circles In A Square
Eleven or 11 may refer to: *11 (number), the natural number following 10 and preceding 12 * one of the years 11 BC, AD 11, 1911, 2011, or any year ending in 11 Literature * ''Eleven'' (novel), a 2006 novel by British author David Llewellyn *''Eleven'', a 1970 collection of short stories by Patricia Highsmith *''Eleven'', a 2004 children's novel in The Winnie Years by Lauren Myracle *''Eleven'', a 2008 children's novel by Patricia Reilly Giff *''Eleven'', a short story by Sandra Cisneros Music *Eleven (band), an American rock band * Eleven: A Music Company, an Australian record label *Up to eleven, an idiom from popular culture, coined in the movie ''This Is Spinal Tap'' Albums * ''11'' (The Smithereens album), 1989 * ''11'' (Ua album), 1996 * ''11'' (Bryan Adams album), 2008 * ''11'' (Sault album), 2022 * ''Eleven'' (Harry Connick, Jr. album), 1992 * ''Eleven'' (22-Pistepirkko album), 1998 * ''Eleven'' (Sugarcult album), 1999 * ''Eleven'' (B'z album), 2000 * ''Eleven'' (Reamonn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
