58 (fifty-eight) is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''Cardinal n ...
following
57 and preceding
59.
In mathematics
Fifty-eight is an 11-
gonal number, and a
Smith number
In number theory, a Smith number is a composite number for which, in a given number base, the sum of its digits is equal to the sum of the digits in its prime factorization in the given number base. In the case of numbers that are not square-free ...
.
Given 58, the
Mertens function
In number theory, the Mertens function is defined for all positive integers ''n'' as
: M(n) = \sum_^n \mu(k),
where \mu(k) is the Möbius function. The function is named in honour of Franz Mertens. This definition can be extended to positive r ...
returns
0.
58 is the smallest integer whose
square root
In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or ⋅ ) is . For example, 4 and −4 are square roots of 16, because .
E ...
has a
continued fraction
In mathematics, a continued fraction is an expression (mathematics), expression obtained through an iterative process of representing a number as the sum of its integer part and the multiplicative inverse, reciprocal of another number, then writ ...
with
period
Period may refer to:
Common uses
* Era, a length or span of time
* Full stop (or period), a punctuation mark
Arts, entertainment, and media
* Period (music), a concept in musical composition
* Periodic sentence (or rhetorical period), a concept ...
7.
58 is equal to the sum of the first seven consecutive prime numbers:
This is a difference of 1 from the 17th prime number and 7th
super-prime
Super-prime numbers, also known as higher-order primes or prime-indexed primes (PIPs), are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.
The subsequence begins
:3, 5, 11, 17, 31, ...
,
59.
There is no solution to the equation ''x'' –
φ(''x'') = 58, making 58 a
noncototient In mathematics, a noncototient is a positive integer ''n'' that cannot be expressed as the difference between a positive integer ''m'' and the number of coprime integers below it. That is, ''m'' − φ(''m'') = ''n'', where ...
. However, the sum of the totient function for the first thirteen integers is 58.
The
regular icosahedron
In geometry, a regular icosahedron ( or ) is a convex polyhedron with 20 faces, 30 edges and 12 vertices. It is one of the five Platonic solids, and the one with the most faces.
It has five equilateral triangular faces meeting at each vertex. It ...
produces 58 distinct
stellation
In geometry, stellation is the process of extending a polygon in two dimensions, polyhedron in three dimensions, or, in general, a polytope in ''n'' dimensions to form a new figure. Starting with an original figure, the process extends specific el ...
s. It's dual polyhedron, the
regular dodecahedron
A regular dodecahedron or pentagonal dodecahedron is a dodecahedron that is regular, which is composed of 12 regular pentagonal faces, three meeting at each vertex. It is one of the five Platonic solids. It has 12 faces, 20 vertices, 30 edges ...
, only produces three stellations, while the
regular octahedron
In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ea ...
produces a single one, the
stella octangula
The stellated octahedron is the only stellation of the octahedron. It is also called the stella octangula (Latin for "eight-pointed star"), a name given to it by Johannes Kepler in 1609, though it was known to earlier geometers. It was depict ...
. Neither the
tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the o ...
nor the
cube
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross.
The cube is the only r ...
produce of any of these
star polyhedra
In geometry, a star polyhedron is a polyhedron which has some repetitive quality of nonconvexity giving it a star-like visual quality.
There are two general kinds of star polyhedron:
*Polyhedra which self-intersect in a repetitive way.
*Concave p ...
, which makes the icosahedron the
Platonic solid
In geometry, a Platonic solid is a convex, regular polyhedron in three-dimensional Euclidean space. Being a regular polyhedron means that the faces are congruent (identical in shape and size) regular polygons (all angles congruent and all edges c ...
with the most stellations.
There are 58 distinct
uniform polytopes in the
fifth dimension that are generated from symmetries of three
Weyl group
In mathematics, in particular the theory of Lie algebras, the Weyl group (named after Hermann Weyl) of a root system Φ is a subgroup of the isometry group of that root system. Specifically, it is the subgroup which is generated by reflections th ...
s and
Coxeter group
In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors). Indeed, the finite Coxeter groups are precisely the finite Euclidean refl ...
s, the
A5 simplex group,
B5 cubic group, and the
D5 demihypercubic group.
There are a total of 58
paracompact Coxeter groups of
ranks four through ten. These solutions all contain infinite
facets
A facet is a flat surface of a geometric shape, e.g., of a cut gemstone.
Facet may also refer to:
Arts, entertainment, and media
* ''Facets'' (album), an album by Jim Croce
* ''Facets'', a 1980 album by jazz pianist Monty Alexander and his tri ...
and
vertex figure
In geometry, a vertex figure, broadly speaking, is the figure exposed when a corner of a polyhedron or polytope is sliced off.
Definitions
Take some corner or Vertex (geometry), vertex of a polyhedron. Mark a point somewhere along each connect ...
s, in contrast from
compact
Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to:
* Interstate compact
* Blood compact, an ancient ritual of the Philippines
* Compact government, a type of colonial rule utilized in British ...
hyperbolic groups that contain finite elements; there no other such groups with higher or lower ranks.
In science
*The
atomic number
The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...
of
cerium
Cerium is a chemical element with the symbol Ce and atomic number 58. Cerium is a soft, ductile, and silvery-white metal that tarnishes when exposed to air. Cerium is the second element in the lanthanide series, and while it often shows the +3 o ...
, a lanthanide.
Astronomy
*
Messier object
The Messier objects are a set of 110 astronomical objects catalogued by the French astronomer Charles Messier in his ''Catalogue des Nébuleuses et des Amas d'Étoiles'' (''Catalogue of Nebulae and Star Clusters'').
Because Messier was only int ...
M58, a
magnitude
Magnitude may refer to:
Mathematics
*Euclidean vector, a quantity defined by both its magnitude and its direction
*Magnitude (mathematics), the relative size of an object
*Norm (mathematics), a term for the size or length of a vector
*Order of ...
11.0
galaxy
A galaxy is a system of stars, stellar remnants, interstellar gas, dust, dark matter, bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System. ...
in the
constellation
A constellation is an area on the celestial sphere in which a group of visible stars forms Asterism (astronomy), a perceived pattern or outline, typically representing an animal, mythological subject, or inanimate object.
The origins of the e ...
Virgo
Virgo may refer to:
*Virgo (astrology), the sixth astrological sign of the zodiac
*Virgo (constellation), a constellation
*Virgo Cluster, a cluster of galaxies in the constellation Virgo
*Virgo Stellar Stream, remains of a dwarf galaxy
*Virgo Supe ...
.
*The
New General Catalogue
The ''New General Catalogue of Nebulae and Clusters of Stars'' (abbreviated NGC) is an astronomical catalogue of deep-sky objects compiled by John Louis Emil Dreyer in 1888. The NGC contains 7,840 objects, including galaxies, star clusters and ...
br>
objectNGC 58
NGC 47 (also known as NGC 58, MCG -1-1-55, IRAS00119-0726 and PGC 967) is a barred spiral galaxy in the constellation Cetus, discovered in 1886 by Ernst Wilhelm Leberecht Tempel. Its alternate name NGC 58 is due to the observation by Lewis Swift ...
, a
barred spiral galaxy
A barred spiral galaxy is a spiral galaxy with a central bar-shaped structure composed of stars. Bars are found in about two thirds of all spiral galaxies, and generally affect both the motions of stars and interstellar gas within spiral galaxi ...
in the constellation
Cetus
Cetus () is a constellation, sometimes called 'the whale' in English. The Cetus (mythology), Cetus was a sea monster in Greek mythology which both Perseus and Heracles needed to slay. Cetus is in the region of the sky that contains other water- ...
. It is also the object designated as
NGC 47
NGC 47 (also known as NGC 58, MCG -1-1-55, IRAS00119-0726 and PGC 967) is a barred spiral galaxy in the constellation Cetus, discovered in 1886 by Ernst Wilhelm Leberecht Tempel. Its alternate name NGC 58 is due to the observation by Lewis Swift ...
.
In music
*
John Cage
John Milton Cage Jr. (September 5, 1912 – August 12, 1992) was an American composer and music theorist. A pioneer of indeterminacy in music, electroacoustic music, and non-standard use of musical instruments, Cage was one of the leading fi ...
composition ''Fifty-Eight''.
* ''Fifty-Eight Now Nine'', a collection of songs by Esther Lee.
*
58 was the name of a side project involving
Nikki Sixx
Nikki Sixx (born Frank Carlton Serafino Feranna Jr.; December 11, 1958) is an American musician, best known as the co-founder, bassist, and primary songwriter of the heavy metal band Mötley Crüe. Prior to forming Mötley Crüe, Sixx was a me ...
of
Mötley Crüe
Mötley Crüe is an American heavy metal band formed in Los Angeles in 1981. The group was founded by bassist Nikki Sixx, drummer Tommy Lee, lead guitarist Mick Mars and lead singer Vince Neil. Mötley Crüe has sold over 100 million albums ...
. They covered the song "
Alone Again (Naturally)
"Alone Again (Naturally)" is a song by Irish singer-songwriter Gilbert O'Sullivan. It was recorded in 1972 at the same time as his album '' Back to Front'' and was a worldwide hit.
The single spent six non-consecutive weeks at number one on ''Bi ...
".
* Band "Spur58".
* "58 Poems" by
Chicago
(''City in a Garden''); I Will
, image_map =
, map_caption = Interactive Map of Chicago
, coordinates =
, coordinates_footnotes =
, subdivision_type = Country
, subdivision_name ...
.
In sports
In the NBA, the most points ever scored in a fourth quarter was 58 by the
Buffalo Braves
The Buffalo Braves were an American professional basketball franchise based in Buffalo, New York. The Braves competed in the National Basketball Association (NBA) as a member club of the league's Eastern Conference Atlantic Division from 1970 ...
(at
Boston Celtics
The Boston Celtics ( ) are an American professional basketball team based in Boston. The Celtics compete in the National Basketball Association (NBA) as a member of the league's Eastern Conference Atlantic Division. Founded in 1946 as one of t ...
), October 20, 1972. The most points in a game by a rookie player:
Wilt Chamberlain
Wilton Norman Chamberlain (; August 21, 1936 – October 12, 1999) was an American professional basketball player who played as a Center (basketball), center. Standing at tall, he played in the National Basketball Association (NBA) for 14 yea ...
, 58: Philadelphia vs. Detroit, January 25, 1960, and Philadelphia vs. New York
Knicks
The New York Knickerbockers, shortened and more commonly referred to as the New York Knicks, are an American professional basketball team based in the New York City borough of Manhattan. The Knicks compete in the National Basketball Associat ...
, February 21, 1960.
In
MotoGP
Grand Prix motorcycle racing is the premier class of motorcycle road racing events held on road circuits sanctioned by the Fédération Internationale de Motocyclisme (FIM). Independent motorcycle racing events have been held since the start ...
, 58 was the number of
Marco Simoncelli
Marco Simoncelli (;
20 January 198723 October 2011), nicknamed Sic (), was an Italian professional motorcycle racer. He competed in the MotoGP World Championship for 10 years from 2002 to 2011. He started in the 125cc class before moving up to ...
who died in an accident at the Malaysian Round of the 2011 MotoGP season. MotoGP's governing body, the
FIM
FIM may refer to:
Organizations and companies
* Fédération Internationale de Motocyclisme, the International Motorcycling Federation
* Flint Institute of Music, in Michigan, United States
* Fox Interactive Media, now News Corp. Digital Media
* ...
, are considering to retire number 58 from use in MotoGP as they did before with the numbers 74 and 48 of
Daijiro Kato
was a Japanese Grand Prix motorcycle road racer, the 2001 250cc world champion, and the 2000 and 2002 Suzuka 8 Hours winner. He died as a result of injuries sustained after a crash during the 2003 Japanese motorcycle Grand Prix at Suzuka Circu ...
and
Shoya Tomizawa
(10 December 1990 – 5 September 2010) was a Japanese motorcycle racer. After a successful career in the All Japan Road Race Championship, he switched to MotoGP and competed in the 250cc class during 2009. In the 2010 season he rode in the newly ...
, respectively. The retirement, from all motorcycle racing classes, eventually occurred in 2016, joining Kato's 74, the 34 of inaugural MotoGP champion
Kevin Schwantz
Kevin Schwantz (born June 19, 1964) is an American former professional motorcycle road racer. He was the world champion of the 1993 FIM Road Racing World Championship.
Early life
Schwantz, whose parents owned a motorcycle shop, learned to ride ...
and the 65 of
Loris Capirossi
Loris Capirossi (born 4 April 1973) is an Italian former Grand Prix motorcycle road racer, currently serving as Safety Advisor to Dorna Sports, the commercial rights holder of Grand Prix motorcycle racing.
He is a 9-time Premier Class race wi ...
.
On the
PGA Tour
The PGA Tour (stylized in all capital letters as PGA TOUR by its officials) is the organizer of professional golf tours in the United States and North America. It organizes most of the events on the flagship annual series of tournaments also k ...
, 58 is
the lowest score in an 18-hole round, achieved by
Jim Furyk
James Michael Furyk (born May 12, 1970) is an American professional golfer who plays on the PGA Tour and the PGA Tour Champions. In 2010, he was the FedEx Cup champion and PGA Tour Player of the Year. He has won one major championship, the 200 ...
in the final round of the 2016
Travelers Championship
Traveler(s), traveller(s), The Traveler(s), or The Traveller(s) may refer to:
People Generic terms
*One engaged in travel
*Explorer, one who searches for the purpose of discovery of information or resources
*Nomad, a member of a community withou ...
at TPC River Highlands.
In
Formula One
Formula One (also known as Formula 1 or F1) is the highest class of international racing for open-wheel single-seater formula racing cars sanctioned by the Fédération Internationale de l'Automobile (FIA). The World Drivers' Championship, ...
, 58 is the number of laps of the
Australian Grand Prix
The Australian Grand Prix is an annual motor racing event which is under contract to host Formula One until 2035. One of the oldest surviving motorsport competitions held in Australia, the Grand Prix has moved frequently with 23 different venu ...
since
1996
File:1996 Events Collage.png, From left, clockwise: A Centennial Olympic Park bombing, bomb explodes at Centennial Olympic Park in Atlanta, set off by a radical Anti-abortion violence, anti-abortionist; The center fuel tank explodes on TWA Flight 8 ...
, when the Grand Prix held at
Albert Park.
In
cricket
Cricket is a bat-and-ball game played between two teams of eleven players on a field at the centre of which is a pitch with a wicket at each end, each comprising two bails balanced on three stumps. The batting side scores runs by striki ...
, both batsmen must cross the between their
grounds to score one
run
Run(s) or RUN may refer to:
Places
* Run (island), one of the Banda Islands in Indonesia
* Run (stream), a stream in the Dutch province of North Brabant
People
* Run (rapper), Joseph Simmons, now known as "Reverend Run", from the hip-hop group ...
.
In mythology
Belief in the existence of 58 original sins by several civilizations native to
Central America
Central America ( es, América Central or ) is a subregion of the Americas. Its boundaries are defined as bordering the United States to the north, Colombia to the south, the Caribbean Sea to the east, and the Pacific Ocean to the west. ...
or
South America
South America is a continent entirely in the Western Hemisphere and mostly in the Southern Hemisphere, with a relatively small portion in the Northern Hemisphere at the northern tip of the continent. It can also be described as the southe ...
caused the number to symbolize misfortune. Aztec
oracles
An oracle is a person or agency considered to provide wise and insightful counsel or prophetic predictions, most notably including precognition of the future, inspired by deities. As such, it is a form of divination.
Description
The word '' ...
supposedly stumbled across the number an unnaturally high number of times before disaster fell. One famous recording of this, though largely discredited as mere folktale, concerned the oracle of
Moctezuma II
Moctezuma Xocoyotzin ( – 29 June 1520; oteːkˈsoːmaḁ ʃoːkoˈjoːt͡sĩn̥), nci-IPA, Motēuczōmah Xōcoyōtzin, moteːkʷˈsoːma ʃoːkoˈjoːtsin variant spellings include Motewksomah, Motecuhzomatzin, Montezuma, Moteuczoma, Motecu ...
, who allegedly counted 58 pieces of
gold
Gold is a chemical element with the symbol Au (from la, aurum) and atomic number 79. This makes it one of the higher atomic number elements that occur naturally. It is a bright, slightly orange-yellow, dense, soft, malleable, and ductile met ...
scattered before a sacrificial pit the day prior to the arrival of
Hernán Cortés
Hernán Cortés de Monroy y Pizarro Altamirano, 1st Marquess of the Valley of Oaxaca (; ; 1485 – December 2, 1547) was a Spanish ''conquistador'' who led an expedition that caused the fall of the Aztec Empire and brought large portions of w ...
.
In other fields
*The code for international direct dial phone calls to
Venezuela
Venezuela (; ), officially the Bolivarian Republic of Venezuela ( es, link=no, República Bolivariana de Venezuela), is a country on the northern coast of South America, consisting of a continental landmass and many islands and islets in th ...
*The number of usable cells on a ''
Hexxagon'' game board
*Book: ''58 Lonely Men: Southern Federal Judges and School
Desegregation
Desegregation is the process of ending the separation of two groups, usually referring to races. Desegregation is typically measured by the index of dissimilarity, allowing researchers to determine whether desegregation efforts are having impact o ...
'' about 58 judges in the South during the ''
Brown v. Board of Education
''Brown v. Board of Education of Topeka'', 347 U.S. 483 (1954), was a landmark decision by the U.S. Supreme Court, which ruled that U.S. state laws establishing racial segregation in public schools are unconstitutional, even if the segrega ...
'' decision
*The number of
counties
A county is a geographic region of a country used for administrative or other purposesChambers Dictionary, L. Brookes (ed.), 2005, Chambers Harrap Publishers Ltd, Edinburgh in certain modern nations. The term is derived from the Old French ...
in
California
California is a U.S. state, state in the Western United States, located along the West Coast of the United States, Pacific Coast. With nearly 39.2million residents across a total area of approximately , it is the List of states and territori ...
*The
minimum
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given ran ...
wind speed (mph) needed to issue a
Severe Thunderstorm Warning
A severe thunderstorm warning ( SAME code: SVR) is a severe weather warning product issued by regional offices of weather forecasting agencies throughout the world to alert the public that severe thunderstorms are imminent or occurring.
A sev ...
*The number of the French department
Nièvre
Nièvre () is a department in the Bourgogne-Franche-Comté region, central-east France. Named after the river Nièvre, it had a population of 204,452 in 2019.[SpongeBob SquarePants
''SpongeBob SquarePants'' (or simply ''SpongeBob'') is an American animated comedy television series created by marine science educator and animator Stephen Hillenburg for Nickelodeon. It chronicles the adventures of the title character a ...]
'', Patrick claims that "58 is like the luckiest number ever."
*''
58 Minutes'' is a book by Walter Wager, on which the film ''
Die Hard 2
''Die Hard 2'' (also known by its tagline ''Die Harder'')The film's onscreen title is ''Die Hard 2'', as also given at the initial home-video release'official website The film's original advertising used "Die Harder" as a tagline, and many rele ...
'' was based
*''
I-58'' was the name of one of the Type B3 submarines that fought in World War II
See also
*
List of highways numbered 58
References
{{Integers, zero
Integers