216 (number)
Encyclopedia
216 is the natural number
following 215
and preceding 217
.
Since
, it is the smallest cube that's also the sum of three cubes (Plato
was among the first to notice this, and mentioned it in Book VIII of Republic
). It is also the sum of a twin prime
(107 + 109). But since there is no way to express it as the sum of the proper divisors of any other integer, it is an untouchable number
.
This multiplicative magic square
has magic constant 216.
In base 10, it is a Harshad number
.
There are 216 fixed hexomino
es, the polyomino
es made from 6 squares.
216 is a Friedman number
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 215
215 (number)
215 is the natural number following 214 and preceding 216.-In mathematics:*215 is a composite number and a semiprime.*215 = ^3 - 1...
and preceding 217
217 (number)
217 is the natural number following 216 and preceding 218.Here are the representations of 217 in other numeral systems: 217 base representation of 217 2 11011001 8 331 16 D9...
.
Since
, it is the smallest cube that's also the sum of three cubes (PlatoPlato
Plato , was a Classical Greek philosopher, mathematician, student of Socrates, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the Western world. Along with his mentor, Socrates, and his student, Aristotle, Plato helped to lay the...
was among the first to notice this, and mentioned it in Book VIII of Republic
Republic (Plato)
The Republic is a Socratic dialogue written by Plato around 380 BC concerning the definition of justice and the order and character of the just city-state and the just man...
). It is also 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...
(107 + 109). But since there is no way to express it as the sum of the proper divisors of any other integer, it is an untouchable number
Untouchable number
An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer ....
.
This multiplicative magic square
Magic square
In recreational mathematics, a magic square of order n is an arrangement of n2 numbers, usually distinct integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same constant. A normal magic square contains the integers from 1 to n2...
has magic constant 216.
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...
.
There are 216 fixed hexomino
Hexomino
A hexomino is a polyomino of order 6, that is, a polygon in the plane made of 6 equal-sized squares connected edge-to-edge. The name of this type of figure is formed with the prefix hex-. When rotations and reflections are not considered to be distinct shapes, there are 35 different free hexominoes...
es, the polyomino
Polyomino
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling with a connected interior....
es made from 6 squares.
216 is a Friedman number
Friedman number
A Friedman number is an integer which, in a given base, is the result of an expression using all its own digits in combination with any of the four basic arithmetic operators and sometimes exponentiation. For example, 347 is a Friedman number since 347 = 73 + 4...
In other fields
- The 216 colors formed by a 6×6×6 color cube are sometimes known as the web-safe color palette.
- ISO 216ISO 216ISO 216 specifies international standard paper sizes used in most countries in the world today. It defines the "A" and "B" series of paper sizes, including A4, the most commonly available size...
is the ISOInternational Organization for StandardizationThe International Organization for Standardization , widely known as ISO, is an international standard-setting body composed of representatives from various national standards organizations. Founded on February 23, 1947, the organization promulgates worldwide proprietary, industrial and commercial...
's standard for paper sizePaper sizeMany paper size standards conventions have existed at different times and in different countries. Today there is one widespread international ISO standard and a localised standard used in North America . The paper sizes affect writing paper, stationery, cards, and some printed documents...
s. - In the film PiPi (film)Pi, also titled ,WorldCat gives the title as [Pi] and provides a note which states, "Title is the mathematical symbol for Pi." . Amazon gives the title as Pi with no notation concerning the math symbol . is a 1998 American psychological thriller film written and directed by Darren Aronofsky...
, Max becomes obsessed with a 216-digit number in his quest to find the numeric equation behind existence, and is told by a group of Hasidic Jews that it represents the true name of God. - As six cubed (6*6*6), 216 is also symbolic of the Mark of the Beast in ChristianityChristianityChristianity is a monotheistic religion based on the life and teachings of Jesus as presented in canonical gospels and other New Testament writings...
. This has been expressed in the Left BehindLeft BehindLeft Behind is a series of 16 best-selling novels by Tim LaHaye and Jerry B. Jenkins, dealing with Christian dispensationalist End Times: pretribulation, premillennial, Christian eschatological viewpoint of the end of the world. The primary conflict of the series is the members of the Tribulation...
series. - According to the Ken BurnsKen BurnsKenneth Lauren "Ken" Burns is an American director and producer of documentary films, known for his style of using archival footage and photographs...
series Baseball, it is the number of stitches on a baseballBaseballBaseball is a bat-and-ball sport played between two teams of nine players each. The aim is to score runs by hitting a thrown ball with a bat and touching a series of four bases arranged at the corners of a ninety-foot diamond...
.