36 (number)
Encyclopedia
36 is the natural number
following 35
and preceding 37
.
, making it a square triangular number
. It is the smallest square triangular number other than 1, and it is also the only triangular number other than 1 whose square root
is also a triangular number.
It is also a 13-gonal number
.
It is the smallest number n with exactly 8 solutions to the equation φ(x) = n. Being the smallest number with exactly 9 divisor
s, 36 is a highly composite number
. Adding up some subsets of its divisors (e.g., 6, 12 and 18) gives 36, hence 36 is a semiperfect number
.
This number is the sum of a twin prime
(17 + 19), the sum of the cubes of the first three integer
s, and the product of the squares of the first three integers.
36 is the number of degrees in the interior angle of each tip of a regular pentagram
.
The thirty-six officers problem
is a mathematical puzzle
.
The number of possible outcomes (not summed) in the roll of two distinct dice
.
36 is the largest numeric base that some computer systems support because it exhausts the numerals, 0-9, and the letters, A-Z. See Base 36
.
The truncated cube
and the truncated octahedron
are Archimedean solid
s with 36 edges.
In base 10, it is a Harshad number
.
The number of domino tiling
s of a 4×4 checkerboard
is 36.
Since it is possible to find sequences of 36 consecutive integers such that each inner member shares a factor with either the first or the last member, 36 is an Erdős–Woods number
.
Because 362 + 1 = 1297, a prime, which is obviously more than 2 × 36, 36 is a Størmer number
.
The sum of the integers from 1 to 36 is 666
(see number of the beast
).
Natural number
In mathematics, the natural numbers are the ordinary whole numbers used for counting and ordering . These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively...
following 35
35 (number)
35 is the natural number following 34 and preceding 36.- In mathematics :35 is the sum of the first five triangular numbers, making it a tetrahedral number....
and preceding 37
37 (number)
37 is the natural number following 36 and preceding 38.-In mathematics:It is a prime number, the fifth lucky prime, the first irregular prime, the third unique prime and the third cuban prime of the form...
.
In mathematics
36 is both the square of 6 and a triangular numberTriangular number
A triangular number or triangle number numbers the objects that can form an equilateral triangle, as in the diagram on the right. The nth triangle number is the number of dots in a triangle with n dots on a side; it is the sum of the n natural numbers from 1 to n...
, making it a square triangular number
Square triangular number
In mathematics, a square triangular number is a number which is both a triangular number and a perfect square....
. It is the smallest square triangular number other than 1, and it is also the only triangular number other than 1 whose square root
Square root
In mathematics, a square root of a number x is a number r such that r2 = x, or, in other words, a number r whose square is x...
is also a triangular number.
It is also a 13-gonal number
Polygonal number
In mathematics, a polygonal number is a number represented as dots or pebbles arranged in the shape of a regular polygon. The dots were thought of as alphas . These are one type of 2-dimensional figurate numbers.- Definition and examples :...
.
It is the smallest number n with exactly 8 solutions to the equation φ(x) = n. Being the smallest number with exactly 9 divisor
Divisor
In mathematics, a divisor of an integer n, also called a factor of n, is an integer which divides n without leaving a remainder.-Explanation:...
s, 36 is a highly composite number
Highly composite number
A highly composite number is a positive integer with more divisors than any positive integer smaller than itself.The initial or smallest twenty-one highly composite numbers are listed in the table at right....
. Adding up some subsets of its divisors (e.g., 6, 12 and 18) gives 36, hence 36 is a semiperfect number
Semiperfect number
In number theory, a semiperfect number or pseudoperfect number is a natural number n that is equal to the sum of all or some of its proper divisors. A semiperfect number that is equal to the sum of all its proper divisors is a perfect number....
.
This number is the sum of a twin prime
Twin prime
A twin prime is a prime number that differs from another prime number by two. Except for the pair , this is the smallest possible difference between two primes. Some examples of twin prime pairs are , , , , and...
(17 + 19), the sum of the cubes of the first three integer
Integer
The integers are formed by the natural numbers together with the negatives of the non-zero natural numbers .They are known as Positive and Negative Integers respectively...
s, and the product of the squares of the first three integers.
36 is the number of degrees in the interior angle of each tip of a regular pentagram
Pentagram
A pentagram is the shape of a five-pointed star drawn with five straight strokes...
.
The thirty-six officers problem
Thirty-six officers problem
The thirty-six officers problem is a mathematical puzzle proposed by Leonhard Euler in 1782.The problem asks if it is possible to arrange 6 regiments consisting of 6 officers each of different ranks in a 6 × 6 square so that no rank or regiment will be repeated in any row or column. Such an...
is a mathematical puzzle
Mathematical puzzle
Mathematical puzzles make up an integral part of recreational mathematics. They have specific rules as do multiplayer games, but they do not usually involve competition between two or more players. Instead, to solve such a puzzle, the solver must find a solution that satisfies the given conditions....
.
The number of possible outcomes (not summed) in the roll of two distinct dice
Dice
A die is a small throwable object with multiple resting positions, used for generating random numbers...
.
36 is the largest numeric base that some computer systems support because it exhausts the numerals, 0-9, and the letters, A-Z. See Base 36
Base 36
Base 36 is a positional numeral system using 36 as the radix. The choice of 36 is convenient in that the digits can be represented using the Arabic numerals 0-9 and the Latin letters A-Z...
.
The truncated cube
Truncated cube
In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces , 36 edges, and 24 vertices....
and the truncated octahedron
Truncated octahedron
In geometry, the truncated octahedron is an Archimedean solid. It has 14 faces , 36 edges, and 24 vertices. Since each of its faces has point symmetry the truncated octahedron is a zonohedron....
are Archimedean solid
Archimedean solid
In geometry an Archimedean solid is a highly symmetric, semi-regular convex polyhedron composed of two or more types of regular polygons meeting in identical vertices...
s with 36 edges.
In base 10, it is a Harshad number
Harshad number
A Harshad number, or Niven number in a given number base, is an integer that is divisible by the sum of its digits when written in that base. Harshad numbers were defined by D. R. Kaprekar, a mathematician from India. The word "Harshad" comes from the Sanskrit + , meaning joy-giver. The Niven...
.
The number of domino tiling
Domino tiling
A domino tiling of a region in the Euclidean plane is a tessellation of the region by dominos, shapes formed by the union of two unit squares meeting edge-to-edge...
s of a 4×4 checkerboard
Checkerboard
A checkerboard or chequerboard is a board of chequered pattern on which English draughts is played. It is an 8×8 board and the 64 squares are of alternating dark and light color, often red and black....
is 36.
Since it is possible to find sequences of 36 consecutive integers such that each inner member shares a factor with either the first or the last member, 36 is an Erdős–Woods number
Erdos–Woods number
In number theory, an Erdős–Woods number is a positive integer that has the following property:Consider a sequence of consecutive positive integers [a, a+1, \dots, a+k]. The number k is an Erdős–Woods number if there exists such a sequence, beginning with some number a, in which each of the elements...
.
Because 362 + 1 = 1297, a prime, which is obviously more than 2 × 36, 36 is a Størmer number
Størmer number
In mathematics, a Størmer number or arc-cotangent irreducible number, named after Carl Størmer, is a positive integer n for which the greatest prime factor of n2 + 1 meets or exceeds 2n. The first few Størmer numbers are 1, 2, 4, 5, 6, 9, 10, 11, 12, 14, 15, 16, 19, 20, etc....
.
The sum of the integers from 1 to 36 is 666
666 (number)
666 is the natural number following 665 and preceding 667.- In mathematics :666 is the sum of the first 36 natural numbers 666 (six hundred and sixty-six) is the natural number following 665 and preceding 667.- In mathematics :666 is the sum of the first 36 natural numbers 666 (six hundred and...
(see number of the beast
Number of the Beast
The Number of the Beast is a term in the Book of Revelation, of the New Testament, that is associated with the first Beast of Revelation chapter 13, the Beast of the sea. In most manuscripts of the New Testament and in English translations of the Bible, the number of the Beast is...
).
Measurements
- The number of inches in a yard.
- In the UK, a standard beer barrelBarrel (unit)A barrel is one of several units of volume, with dry barrels, fluid barrels , oil barrel, etc...
is 36 UK gallons, about 163.7 litres.
In science
- The atomic numberAtomic numberIn chemistry and physics, the atomic number is the number of protons found in the nucleus of an atom and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol Z. The atomic number uniquely identifies a chemical element...
of kryptonKryptonKrypton is a chemical element with the symbol Kr and atomic number 36. It is a member of Group 18 and Period 4 elements. A colorless, odorless, tasteless noble gas, krypton occurs in trace amounts in the atmosphere, is isolated by fractionally distilling liquified air, and is often used with other...
- Many early computers featured a 36-bit word length36-bit word lengthMany early computers aimed at the scientific market had a 36-bit word length. This word length was just long enough to represent positive and negative integers to an accuracy of ten decimal digits . It also allowed the storage of six alphanumeric characters encoded in a six-bit character encoding...
- ASCIIASCIIThe American Standard Code for Information Interchange is a character-encoding scheme based on the ordering of the English alphabet. ASCII codes represent text in computers, communications equipment, and other devices that use text...
code for the symbol '$Dollar signThe dollar or peso sign is a symbol primarily used to indicate the various peso and dollar units of currency around the world.- Origin :...
'
- 36 is the number of characters required to store the display name of a UUID or GUID (e.g., 00000000-0000-0000-C000-000000000046).
Astronomy
- Messier objectMessier objectThe Messier objects are a set of astronomical objects first listed by French astronomer Charles Messier in 1771. The original motivation of the catalogue was that Messier was a comet hunter, and was frustrated by objects which resembled but were not comets...
M36Messier 36Open Cluster M36 is an open cluster in the Auriga constellation. It was discovered by Giovanni Batista Hodierna before 1654. M36 is at a distance of about 4,100 light years away from Earth and is about 14 light years across. There are at least sixty members in the cluster...
, a magnitude 6.5 open clusterOpen clusterAn open cluster is a group of up to a few thousand stars that were formed from the same giant molecular cloud and have roughly the same age. More than 1,100 open clusters have been discovered within the Milky Way Galaxy, and many more are thought to exist...
in the constellationConstellationIn modern astronomy, a constellation is an internationally defined area of the celestial sphere. These areas are grouped around asterisms, patterns formed by prominent stars within apparent proximity to one another on Earth's night sky....
AurigaAuriga (constellation)Auriga is a constellation in the northern sky. Its name is Latin for 'charioteer' and its stars form a shape that has been associated with the pointed helmet of a charioteer. It was one of the 48 constellations listed by the 2nd century astronomer Ptolemy, and remains among the 88 modern...
- The New General CatalogueNew General CatalogueThe New General Catalogue of Nebulae and Clusters of Stars is a well-known catalogue of deep sky objects in astronomy. It contains 7,840 objects, known as the NGC objects...
object NGC 36, a spiral galaxySpiral galaxyA spiral galaxy is a certain kind of galaxy originally described by Edwin Hubble in his 1936 work The Realm of the Nebulae and, as such, forms part of the Hubble sequence. Spiral galaxies consist of a flat, rotating disk containing stars, gas and dust, and a central concentration of stars known as...
in the constellation PiscesPisces (constellation)Pisces is a constellation of the zodiac. Its name is the Latin plural for fish, and its symbol is . It lies between Aquarius to the west and Aries to the east...
In religion
- Jewish tradition holds that the number 36 has had special significance since the beginning of time: According to the MidrashMidrashThe Hebrew term Midrash is a homiletic method of biblical exegesis. The term also refers to the whole compilation of homiletic teachings on the Bible....
, the light created by God on the first day of creation shone for exactly 36 hours; it was replaced by the light of the SunSunThe Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
that was created on the Fourth Day. The TorahTorahTorah- A scroll containing the first five books of the BibleThe Torah , is name given by Jews to the first five books of the bible—Genesis , Exodus , Leviticus , Numbers and Deuteronomy Torah- A scroll containing the first five books of the BibleThe Torah , is name given by Jews to the first five...
commands 36 times to love, respect and protect the stranger. Furthermore, in every generation there are 36 righteous peopleTzadikim NistarimThe Tzadikim Nistarim or Lamed Vav Tzadikim , often abbreviated to Lamed Vav, refers to 36 Righteous people, a notion rooted within the more mystical dimensions of Judaism. The singular form is Tzadik Nistar .-Origins:...
(the "Lamed Vav Tzadikim") in whose merit the world continues to exist. In the modern celebration of Hannukah, 36 candles are kindled in the menorah over the 8 days of that holiday (not including the shamash candle).
- In one Māori legend, concerning the creation of mankind by the god TāneTaneIn Māori mythology, Tāne is the god of forests and of birds, and the son of Ranginui and Papatuanuku, the sky father and the earth mother, who lie in a tight embrace...
, 36 gods took active part in assembling the various parts of the first human before Tāne breathed life into her.
- In ShaivismShaivismShaivism is one of the four major sects of Hinduism, the others being Vaishnavism, Shaktism and Smartism. Followers of Shaivism, called "Shaivas," and also "Saivas" or "Saivites," revere Shiva as the Supreme Being. Shaivas believe that Shiva is All and in all, the creator, preserver, destroyer,...
(s.a. Kaśmir Śaivism), The 36 tattvasThe 36 tattvasIn Kaśmir Śaivism, the 36 tattvas describe the Absolute, its internal aspects and the creation including living beings, down to the physical reality. The addition of 11 supplemental tattvas compared to the allows for a richer, fuller vision of the Absolute...
describe the Absolute, its internal aspects and the creation including living beings, down to the physical reality.
In the arts, culture, and philosophy
- The 36 Views of Mount Fuji36 Views of Mount Fuji (Hokusai)is an ukiyo-e series of large, color woodblock prints by the Japanese artist Katsushika Hokusai . The series depicts Mount Fuji in differing seasons and weather conditions from a variety of different places and distances. It actually consists of 46 prints created between 1826 and 1833...
, a famous series of prints by Japanese ukiyo-e artist Katsushika Hokusai - The The 36 view of the Eiffel Tower, a famous series of prints from Henri Riviere inspired by Japanese ukiyo-e artist Katsushika Hokusai
- The 36th Chamber of ShaolinThe 36th Chamber of ShaolinThe 36th Chamber of Shaolin , also known as The Master Killer and Shaolin Master Killer, is a 1978 Shaw Brothers kung fu film directed by Liu Chia-liang and starring Gordon Liu....
is a 1978 kung fu film - 36 Quai des Orfèvres36 Quai des Orfèvres (film)36 Quai des Orfèvres is a 2004 French film directed by Olivier Marchal and starring Daniel Auteuil and Gérard Depardieu. The film takes place in Paris, where two cops are competing for the vacant seat of Chief of Police while involved in a search for a gang of violent thieves...
, often referred to simply as 36, a French police film - The Thirty-Six Dramatic SituationsThe Thirty-Six Dramatic SituationsThe Thirty-Six Dramatic Situations is a descriptive list which was created by Georges Polti to categorize every dramatic situation that might occur in a story or performance. To do this Polti analyzed classical Greek texts, plus classical and contemporaneous French works. He also analyzed a handful...
are considered a useful conceptual aid in theater. - The Thirty-Six Stratagems are a collection of Chinese proverbs illustrating useful approaches to conflict situations.
- In French-speaking countries, 36 is often used as a placeholder number.
- 36 Crazyfists36 Crazyfists36 Crazyfists is a four-piece metal band originating from Anchorage, Alaska. They are now based in Portland, Oregon. The band's name comes from a Jackie Chan movie, Jackie Chan And The 36 Crazy Fists...
are a four-piece metal band from Alaska. - 36 is an ambient musician from the UK.
- 36 is a song on Steal This Album!Steal This Album!Steal This Album! is the third studio album by American heavy metal band System of a Down, released on November 26, 2002, on American Recordings...
by System of a DownSystem of a DownSystem of a Down, also known by the acronym SOAD and often shortened to System, is a rock band from Southern California. The band was formed in 1994. It consists of Serj Tankian , Daron Malakian , Shavo Odadjian and John Dolmayan...
. - 36 is a movie releasing in 2010, directed by Martin Campbell.
- The 36 Lessons of Vivec is the title of a book series in the video game The Elder Scrolls III: MorrowindThe Elder Scrolls III: MorrowindThe Elder Scrolls III: Morrowind, often simply referred to as Morrowind, is a single-player computer role-playing game developed by Bethesda Game Studios, and published by Bethesda Softworks and Ubisoft. It is the third installment in The Elder Scrolls series of games, following The Elder Scrolls...
. - The game of roulette has '36' numbers on the playing grid and roulette wheel (together with a '0' or '00' depending on whether it is a European wheel '37' or American wheel '38')
In sports
- Australian Basketball team The Adelaide 36ersAdelaide 36ersThe Adelaide 36ers are Adelaide's men's professional basketball team, established as the Adelaide City Eagles when they joined the National Basketball League in 1982. The Adelaide 36ers tally of four championships is equal with the Melbourne Tigers and second behind the Perth Wildcats as the most...
- Retired number of former baseball players Robin RobertsRobin Roberts (baseball player)Robin Evan Roberts was a Major League Baseball starting pitcher who pitched primarily for the Philadelphia Phillies . He spent the latter part of his career with the Baltimore Orioles , Houston Astros , and Chicago Cubs...
of the PhilliesPhiladelphia PhilliesThe Philadelphia Phillies are a Major League Baseball team. They are the oldest continuous, one-name, one-city franchise in all of professional American sports, dating to 1883. The Phillies are a member of the Eastern Division of Major League Baseball's National League...
and Gaylord PerryGaylord PerryGaylord Jackson Perry is a former Major League Baseball right-handed pitcher. He pitched from 1962-1983 for eight different teams in his career. During a 22-year baseball career, Perry compiled 314 wins, 3,534 strikeouts, and a 3.11 earned run average...
of the GiantsSan Francisco GiantsThe San Francisco Giants are a Major League Baseball team based in San Francisco, California, playing in the National League West Division....
. - Retired number of former basketball player Lloyd NealLloyd NealLloyd Neal is an American former professional basketball player.A 6'7" center/forward from Tennessee State University, Neal spent his entire professional career with the National Basketball Association's Portland Trail Blazers...
of the Portland Trail BlazersPortland Trail BlazersThe Portland Trail Blazers, commonly known as the Blazers, are an American professional basketball team based in Portland, Oregon. They play in the Northwest Division of the Western Conference in the National Basketball Association . The Trail Blazers originally played their home games in the... - The number of vehicles that run in each race of NASCARNASCARThe National Association for Stock Car Auto Racing is a family-owned and -operated business venture that sanctions and governs multiple auto racing sports events. It was founded by Bill France Sr. in 1947–48. As of 2009, the CEO for the company is Brian France, grandson of the late Bill France Sr...
's Camping World Truck Series.
In other fields
Thirty-six may also refer to:- IBM System/36, a minicomputer
- The number of the French department IndreIndreIndre is a department in the center of France named after the river Indre. The inhabitants of the department are called Indriens.-History:Indre is one of the original 83 departments created during the French Revolution on March 4, 1790...
- Perfect score on the ACTACT (examination)The ACT is a standardized test for high school achievement and college admissions in the United States produced by ACT, Inc. It was first administered in November 1959 by Everett Franklin Lindquist as a competitor to the College Board's Scholastic Aptitude Test, now the SAT Reasoning Test...
. - (Oilfield terminologyOilfield terminologyOilfield terminology refers to the jargon used by those working in fields within and related to the petroleum industry. It includes words and phrases describing professions, equipment, and procedures specific to the industry...
): A pipe wrenchPipe wrenchThe pipe wrench is an adjustable wrench used for turning soft iron pipes and fittings with a rounded surface. The design of the adjustable jaw allows it to rock in the frame, such that any forward pressure on the handle tends to pull the jaws tighter together. Teeth angled in the direction of turn...
36 inches long