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Problem in geometry
Moser's circle problem asks how many regions a circle can be divided into by choosing n {\displaystyle n} points along the circumference of the circle
Moser's_circle_problem
Humorous mathematical law
first ceases being true at 26861. A geometric example concerns Moser's circle problem (pictured), which appears to have the solution of 2n−1 for n points
Strong_law_of_small_numbers
Austrian-Canadian mathematician
known as Moser's worm problem and as of 2026 remains an open problem. Bell number Berlekamp switching game Salem–Spencer set Secretary problem Tournament
Leo_Moser
Two-dimensional packing problem
packing problem where the objective is to determine how many congruent squares can be packed into some larger shape, often a square or circle. Square
Square_packing
Concept in combinatorics
different independent real-valued equations. Dividing a circle into areas (Moser's circle problem) Lazy caterer's sequence Pizza theorem Yaglom, A. M.;
Cake_number
Equality of areas of a sliced disk
shares base, tomato and cheese. Cake number Dividing a circle into areas (Moser’s circle problem) The lazy caterer's sequence, a sequence of integers that
Pizza_theorem
Model in classical and quantum mechanics
line or a circle with quadratic or inverse quadratic interactions between them. CMS models are named after Francesco Calogero, Jürgen Moser and Bill Sutherland
Calogero–Moser–Sutherland model
Calogero–Moser–Sutherland_model
Mathematical problem
(2018), Coloring Problems for Arrangements of Circles (and Pseudocircles) Grime, James (February 27, 2019), "A Colorful Unsolved Problem", Numberphile,
Hadwiger–Nelson_problem
pair? The Gauss circle problem: how far can the number of integer points in a circle centered at the origin be from the area of the circle? Grimm's conjecture:
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Mathematical problem involving optimal stopping theory
known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem. Its solution is also
Secretary_problem
Geometric concept
Unsolved problem in mathematics What is the maximum possible kissing number for n-dimensional spheres in (n + 1)-dimensional Euclidean space? More unsolved
Kissing_number
Problem in discrete geometry
In discrete geometry, the Erdős distinct distances problem states that every set of points in the plane has a nearly linear number of distinct distances
Erdős distinct distances problem
Erdős_distinct_distances_problem
Unsolved geometry problem
least 0.832. Moser's worm problem, what is the minimum area of a shape that can cover every unit-length curve? Moving sofa problem, the problem of finding
Lebesgue's universal covering problem
Lebesgue's_universal_covering_problem
Geometry problem on grid points
line. The problem concerns lines of all slopes, not only those aligned with the grid. It was introduced by Henry Dudeney in 1900. Brass, Moser, and Pach
No-three-in-line_problem
Problem in physics and celestial mechanics
In physics, the n-body problem is the problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally
N-body_problem
Norman Oler on circle packing in an equilateral triangle with a number of circles one less than a triangular number. The minimum overlap problem to estimate
List of conjectures by Paul Erdős
List_of_conjectures_by_Paul_Erdős
Unsolved geometric problem
problems, including search strategies that are of practical importance. A bigger motivation for study has been the connection to Moser's worm problem
Bellman's lost-in-a-forest problem
Bellman's_lost-in-a-forest_problem
Task of computing complete subgraphs
In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete
Clique_problem
American mathematician (1943–2024)
defined means of deforming an arbitrary embedded circle in the Euclidean plane into a round circle. The modern understanding of the results of Gage–Hamilton
Richard_S._Hamilton
American author (born 1963)
Novel 'The Dutch House' And Her Problem with Villains". Time. Retrieved 2020-04-28. Maher, John (May 4, 2020). "Moser, Whitehead, McDaniel, Grandin, Boyer
Ann_Patchett
American mathematician and Nobel Laureate (1928–2015)
single nontrivial application. Due to Jürgen Moser's extension of Nash's ideas for application to other problems (notably in celestial mechanics), the resulting
John_Forbes_Nash_Jr.
Awareness of facts, or competency
value problem is sometimes used as an argument against reliabilism. Virtue epistemology, by contrast, offers a unique solution to the value problem. Virtue
Knowledge
1992 drama film directed by George Miller
parents to the United States, he begins to show signs of neurological problems, such as falling, loss of hearing, tantrums, etc. The boy is diagnosed
Lorenzo's_Oil
Geometric graph with unit edge lengths
between points and lines. In 1959, Erdős and Leo Moser asked about the special case of this problem for the vertices of a convex polygon. In this case
Unit_distance_graph
Polynomial equation whose integer solutions are sought
was an achievement of the twentieth century. However, Hilbert's tenth problem shows that there cannot exist a general algorithm that can decide whether
Diophantine_equation
Awareness of facts
well as describing and explaining them. It can guide the processes of problem-solving and decision-making. In many cases, its value is based on its usefulness
Declarative_knowledge
Medical condition of excess body fat
BMI of greater than 28 kg/m2. The preferred obesity metric in scholarly circles is the body fat percentage (BF%) – the ratio of the total weight of person's
Obesity
List of characters in the Dexter franchise
The Barrel Girl Gang, a raping/killing circle that folds out as the main target of Dexter for season 5. The circle is responsible for kidnapping, raping
List_of_Dexter_characters
Branch of geometry that studies combinatorial properties and constructive methods
sphere packing problems can be generalised to consider unequal spheres, n-dimensional Euclidean space (where the problem becomes circle packing in two
Discrete_geometry
American philosopher
internalism, requires the concept of a basic belief to solve the regress problem in epistemology: he wrote that this central concept is itself by no means
Laurence_BonJour
1977 collection of essays by Susan Sontag
is the problem of the norm and the repressive function of the idea of the norm in society. On Photography won the National Book Critics Circle Award for
On_Photography
Far-right political party in Germany
Retrieved 11 May 2015. "Germany's Far-Right Populists Have an Infighting Problem". The Atlantic. 22 September 2017. Archived from the original on 28 September
Alternative_for_Germany
Probability theorem on no events occurring
article Problems and results on 3-chromatic hypergraphs and some related questions. For other versions, see Alon & Spencer (2000). In 2020, Robin Moser and
Lovász_local_lemma
Political party in Germany (1918–1933)
elites." The writer Kurt Tucholsky wrote in 1924 that "Even in Jewish circles (of which a portion would still vote German-National today, were the party
German National People's Party
German_National_People's_Party
Abrahamic monotheistic religion
doctrines or practices, hidden from the public and accessible only to a narrow circle of "enlightened", "initiated", or highly educated people. Nondenominational
Christianity
Erotic practices involving domination and sadomasochism
of finding no partner. Moser states that BDSM practitioners having problems finding BDSM partners would probably have problems in finding a non-BDSM partner
BDSM
Russian politician and economist (born 1952)
dissertation was entitled "The socio-economic system of Russia and the problem of its modernisation". He is a professor at the National Research University
Grigory_Yavlinsky
Country in Eastern Europe and North Asia
members of The Mighty Handful, who were later succeeded by the Belyayev circle, and the Russian Musical Society led by composers Anton and Nikolay Rubinstein
Russia
Christian Trinity. Mathematics: π ≈ 3.141592653589793238, the ratio of a circle's circumference to its diameter. Religion: the Four Noble Truths in Buddhism
Orders_of_magnitude_(numbers)
Leader of Russia since 1999
information from Russian state media. In the early 2000s, Putin and his circle began promoting the idea in Russian media that they are the modern-day version
Vladimir_Putin
German politician, lawyer and journalist (born 1941)
CDU. In 2012 Gauland became involved in the Berliner Kreis [de] ("Berlin circle"), a loose association of federal and state politicians within the CDU,
Alexander_Gauland
Figure formed by two rays meeting at a common point
aspect Central angle Clock angle problem Decimal degrees Dihedral angle Exterior angle theorem Golden angle Great circle distance Horn angle Inscribed angle
Angle
German American aerospace engineer (1912–1977)
wheels-up landing and the fuselage having been on fire, it proved to official circles that an aircraft could be flown satisfactorily with a back-thrust system
Wernher_von_Braun
American writer, critic and public intellectual (1933–2004)
1976: Arts and Letters Award in Literature 1977: National Book Critics Circle Award for On Photography 1979: Became member of the American Arts 1990:
Susan_Sontag
Philosophical study of knowledge
Both can be understood as responses to the regress problem. In ancient philosophy, the underlying problem was discussed as Agrippa's trilemma. The trilemma
Epistemology
Trajectory of Earth around the Sun
and the weather is generally cooler. North of the Arctic Circle and south of the Antarctic Circle, an extreme case is reached in which there is no daylight
Earth's_orbit
Governor of Minnesota since 2019
his military career, he was posted in Arkansas, Texas, near the Arctic Circle in Norway; New Ulm, Minnesota, northwest of Mankato; Italy, and elsewhere
Tim_Walz
On graph drawing with integer edge lengths
Unsolved problem in mathematics Does every planar graph have an integral Fáry embedding? More unsolved problems in mathematics In mathematics, Harborth's
Harborth's_conjecture
Protests relating to the Gaza war
(October 12, 2023). "Israel, Palestine supporters face off in Monument Circle protests". WRTV. Archived from the original on May 8, 2024. Retrieved May
Gaza war protests in the United States
Gaza_war_protests_in_the_United_States
number Centillion, 10303 Skewes's number Googolplex, 10(10100) Mega/Circle(2) Moser's number Graham's number TREE(3) SSCG(3) Rayo's number Mathematics portal
List_of_numbers
Sony's video gaming brand
layout to the PS3 with its PlayStation logo button and its ('Triangle'), ('Circle/O'), ('Cross/X') and ('Square') buttons in their white-colored forms. The
PlayStation
Graph formed by touching unit circles
this problem. Constructing a penny graph from the locations of its n circles can be performed as an instance of the closest pair of points problem, taking
Penny_graph
Vertebrate brain region
in the mammalian hippocampus. The brain of the octopus is arranged in a circle of lobes around the esophagus. The vertical lobe has been shown to be involved
Hippocampus
Irregular beating of the atria of the heart
number of localized sources in the form of either a re-entrant leading circle or electrical spiral waves (rotors); these localized sources may be in the
Atrial_fibrillation
American scientist and science communicator (1934–1996)
planning on saving the lives of millions with antibiotics when he noticed a circle free of bacteria around a growth of mold; Watson and Crick weren't imagining
Carl_Sagan
National museum in London, England
Highlights of the African collection include objects found at megalithic circles in The Gambia, a dozen exquisite Afro-Portuguese ivories, a series of soapstone
British_Museum
American neo-fascist organization
pleads guilty to Jan. 6 seditious conspiracy: Jeremy Bertino was in inner circle of right-wing group led by Henry 'Enrique' Tarrio, accused with some Oath
Proud_Boys
Hôtel particulier in Paris, France
Qualities that ultimately enabled him to be accepted into the private circle of the Société de la Reine (the Queen's Society). In her memoirs
Hôtel_de_Besenval
) The identity element in the cycle graphs is represented by the black circle. The lowest order for which the cycle graph does not uniquely represent
List_of_small_groups
Measure of a civilization's evolution
Approach to the Basic Problem, in which he stated that: Detection and studies of extraterrestrial civilizations constitute a problem of immense significance
Kardashev_scale
Mountainous region in eastern North America
to an increase in clan feuding, which by the 1880s was reported to be a problem across most of Kentucky's Cumberland region as well as Carter County, Tennessee;
Appalachia
1890s–1920s US political reform movement
went to Harvard. Chicago was a hotbed for reform, led by the Hull House circle. Philosopher John Dewey and Ella Flagg Young at the University of Chicago's
Progressive_Era
Second-largest city in Greece
Peripheriaki Odos (Greek: Εξωτερική Περιφεριακή Οδός, outer ring road) to circle around the entirety of the Thessaloniki metropolitan area, crossing over
Thessaloniki
Techniques to study geometric data
form the basis for current research. The most fundamental of these is the problem of defining the spatial location of the entities being studied. Classification
Spatial_analysis
Educational technique
student interest and motivation and to build students ‘critical thinking, problem-solving and social skills". In a report from the Association for the Study
Active_learning
Kolmogorov–Arnold–Moser theorem in dynamical systems, solved Hilbert's 13th problem, raised the ADE classification and Arnold's rouble problems Alexander Beilinson
List of Russian mathematicians
List_of_Russian_mathematicians
Polish-British writer (1857–1924)
to predict major social trends, "seems to presuppose... a sort of select circle to which you address yourself, leaving the rest of the world outside the
Joseph_Conrad
Musical by Rodgers and Hammerstein
Rodgers remembered that he and Hart had a similar problem in Pal Joey. Rodgers and Hart had overcome the problem with a song that Joey sings to himself, "I'm
Carousel_(musical)
French rebel groups that fought Nazi Germany in World War II
Resistance movement began amongst the circle of the Russian immigration, and not from amongst ethnic French circles. – Boris Vildé, an arrival from Estonia
French_Resistance
Austrian bullpup assault rifle
models) and a three-position safety. The sight added a crosshair to the circle reticule. New Zealand issued both factory and locally modified carbines
Steyr_AUG
2010 studio album by Taylor Swift
Official Charts Company. Retrieved August 1, 2020. "South Korea Circle Album Chart". Circle Chart. Note: On the page, select "2010.10.24~2010.10.30" to obtain
Speak_Now
Philosophical view that knowledge may be justified by an infinite chain of reasons
independent justification (a foundation), The chain must come around in a circle in some finite number of steps (the belief may be justified by its coherence)
Infinitism
2014 video game
"hit-or-miss". Andrew Reiner from Game Informer described the game as a "full circle", in which Insomniac has incorporated all the elements from their previous
Sunset_Overdrive
Metaphilosophical study of epistemology
Chrisman 2012. Another problem for expressivism, more traditionally raised in metaethics, is the Frege–Geach problem. This is the problem that epistemic expressivism
Metaepistemology
Sights and sounds of Earth, encoded in a time capsule in interstellar space
Nick Sagan, aged 6, gives the final greeting in English (around 4:19) Problems playing these files? See media help. The second audio section ("Greetings
Contents of the Voyager Golden Record
Contents_of_the_Voyager_Golden_Record
German soldier and author (1895–1998)
1952, Besuch auf Godenholm (Visit to Godenholm) 1983, Aladins Problem (Aladdin's Problem) Klett-Cotta edited Jünger's correspondence with Rudolf Schlichter
Ernst_Jünger
Graph formed by subdivision of triangles
Apollonius of Perga, who studied the Problem of Apollonius of constructing a circle tangent to three other circles. One method of constructing Apollonian
Apollonian_network
Chancellor of Germany from 1871 to 1890
Prussian Ministry of Culture. That left the Catholics without a voice in high circles. Moreover, in 1872, the Jesuits were expelled from Germany. In 1873, more
Otto_von_Bismarck
Austrian neurologist and founder of psychoanalysis (1856–1939)
Adler, regarded as the most formidable intellect among the early Freud circle, was a socialist who, in 1898, had written a health manual for the tailoring
Sigmund_Freud
Subdivision of the plane by lines
Math. Soc., pp. 45–66, MR 1143288 Borwein, P.; Moser, W. O. J. (1990), "A survey of Sylvester's problem and its generalizations" (PDF), Aequationes Mathematicae
Arrangement_of_lines
irritating effects of X-rays. In a publication, he mentioned his increasing problems with his hands. Although Kassabian recognized X-rays as the cause, he avoided
History of radiation protection
History_of_radiation_protection
Speakers of Austronesian languages
Nagsabaran pottery in the Philippines, including stamped circles as well as the cross-in-circle motif. They carried pottery technology as far as Tonga in
Austronesian_peoples
American singer and actor (1915–1998)
child. Dolly became influential in Hoboken and in local Democratic Party circles. During the Great Depression, Dolly provided money to her son for outings
Frank_Sinatra
French mathematician and economist
established with Jean-Christophe Yoccoz a theory of automorphic measures of circle diffeomorphisms, a basis for differentiating the rotation number function
Raphael_Douady
Arithmetic operation
as real numbers modulo 2π. This amounts to an addition operation on the circle, which in turn generalizes to the operations of higher-dimensional Lie groups
Addition
Hungarian sociologist (1893–1947)
War he was involved in a number of influential intellectual circles: the Galileo Circle founded by Karl Polanyi in which Michael Polanyi also participated
Karl_Mannheim
Two phonograph records on board Voyager spacecraft
the recipients to verify that they are decoding the signals correctly. A circle was used in this picture to ensure that the recipients use the correct ratio
Voyager_Golden_Record
stars discovered by Jocelyn Bell Burnell in 1967. The galaxy rotation problem A major piece of evidence for the presence of dark matter in the Universe
List of inventions and discoveries by women
List_of_inventions_and_discoveries_by_women
German polymath (1880–1936)
and wrote for magazines to earn additional income. Due to a severe heart problem, Spengler was exempted from military service. During the war, his inheritance
Oswald_Spengler
American politician (1792–1868)
began. Johnson embarked on a trip by rail, dubbed the "Swing Around the Circle" that won him few supporters; his arguments with hecklers were deemed undignified
Thaddeus_Stevens
Natural number
writing "$30k" for $30,000 or using "Y2K" to denote the Year 2000 computer problem. A thousand units of currency, especially dollars or pounds, are colloquially
1000_(number)
Genus of North American cicadas
laying eggs in a tree branch (video) (June 1, 2021) Magicicada egg slits (circled in red) (June 6, 2004) The nymphs emerge in very large numbers at nearly
Periodical_cicadas
Country in Central Europe
faces numerous problems when it comes to health, one example being that 2 in 5 Austrians have a chronic condition. Cancer is a big problem in the country
Austria
German experimental band
percussion, vocals), plus Jochen Arbeit (guitar, vocals), and Rudolph Moser (custom-built instruments, percussion, vocals), who both joined the line-up
Einstürzende_Neubauten
British princess (1930–2002)
1978. Margaret's private life, including her reputed romances and social circle, was often the subject of speculation by the press. Her divorce and lifestyle
Princess Margaret, Countess of Snowdon
Princess_Margaret,_Countess_of_Snowdon
Deliberate use of light to achieve practical or aesthetic effects
both offices and homes. Although it is easy to design, it has dramatic problems with glare and excess energy consumption due to large number of fittings
Lighting
2020 American musical animated sitcom
reveals her plan to buy up Central Park ("Central to My Plot"). 2 2 "Skater's Circle" Corey Barnes Halsted Sullivan May 29, 2020 (2020-05-29) 1LBV02 Owen tries
Central_Park_(TV_series)
(primarily the United States) in a covert manner If this did not alleviate the problem, an underground test would be performed to demonstrate South Africa's nuclear
South Africa and weapons of mass destruction
South_Africa_and_weapons_of_mass_destruction
German jurist and political philosopher (1888–1985)
In the lectures, Schmitt directly tackles the issues surrounding "the problem of the Partisan" figure: the guerrilla or revolutionary who "fights irregularly"
Carl_Schmitt
Totality of existing entities
the claims in question are ultimately only about concrete entities. The problem of abstract objects is central to the philosophy of mathematics and the
Reality
travel, tourism, insurance
MOSERS CIRCLE-PROBLEM
MOSERS CIRCLE-PROBLEM
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