60 (number)

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59 60 61
Cardinal sixty
Ordinal 60th
(sixtieth)
Factorization 22· 3 · 5
Divisors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Roman numeral LX
Binary 1111002
Ternary 20203
Quaternary 3304
Quinary 2205
Senary 1406
Octal 748
Duodecimal 5012
Hexadecimal 3C16
Vigesimal 3020
Base 36 1O36

60 (sixty) (About this sound Listen ) is the natural number following 59 and preceding 61. Being three times twenty, 60 is called "three score" in some older literature.

In mathematics

Sixty is a composite number with divisors 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, making it also a highly composite number. Because 60 is the sum of its unitary divisors (excluding itself), it is a unitary perfect number, and it is also an excessive number with an abundance of 48. Being ten times a perfect number, 60 is a semiperfect number.

Sixty is the smallest number divisible by the numbers 1 to 6. (There is no smaller number divisible by the numbers 1 to 5). 60 is the smallest number with exactly 12 divisors. It is one of only 7 integers that have more divisors than any number twice itself (sequence A072938 in OEIS), and is one of only 6 that are also lowest common multiple of a consecutive set of integers from 1, and one of the 6 that are divisors of every highly composite number higher than itself.(sequence A106037 in OEIS)

Sixty is the sum of a pair of twin primes (29 + 31), as well as the sum of four consecutive primes (11 + 13 + 17 + 19). It is adjacent to two prime numbers (59,61). It is also the smallest number which is the sum of two odd primes in 6 ways.1

The smallest non-solvable group (A5) has order 60.

The icosidodecahedron has 60 edges, all equivalent.

There are four Archimedean solids with 60 vertices: the truncated icosahedron, the rhombicosidodecahedron, the snub dodecahedron, and the truncated dodecahedron. The skeletons of these polyhedra form 60-node vertex-transitive graphs. There are also two Archimedean solids with 60 edges: the snub cube and the icosidodecahedron. The skeleton of the icosidodecahedron forms a 60-edge symmetric graph.

There are 60 one-sided hexominoes, the polyominoes made from 6 squares.

In geometry, 60 is the number of seconds in a minute, and the number of minutes in a degree. In normal space, the 3 interior angles of an equilateral triangle each measure 60 degrees, adding up to 180 degrees.

Because 60 is divisible by the sum of its digits in base 10, it is a Harshad number.

A number system with base 60 is called sexagesimal (the original meaning of sexagesimal is sixtieth).

In science and technology

Buckminsterfullerene C60 has 60 carbon atoms in each molecule, arranged in a truncated icosahedron.

The first fullerene to be discovered was buckminsterfullerene C60 – an allotrope of carbon with 60 atoms in each molecule, arranged in a truncated icosahedron. This ball is known as a buckyball, and looks like a soccer ball.

The atomic number of Neodymium is 60, and Cobalt-60 (60Co) is a radioactive isotope of cobalt.

The electrical utility frequency in western Japan, South Korea, Taiwan, the Philippines, Saudi Arabia, the United States, and several other countries in the Americas is 60 Hz.

An exbibyte (sometimes called exabyte) is 260 bytes.

Cultural number systems

The Babylonians used base 60.

The Babylonian number system had a base of sixty, inherited from the Sumerian and Akkadian civilizations, and possibly motivated by the large number of divisors which 60 has. The sexagesimal measurement of time and of geometric angles is a legacy of the Babylonian system.

The number system in the Mali Empire was also based on sixty (this is reflected in the counting system of the Maasina Fulfulde, a variant of the Fula language spoken in contemporary Mali).2 The Ekagi of Western New Guinea have also used base 60,3 and the sexagenary cycle also plays a role in Chinese calendar and numerology.

In German: Schock and in Latin: sexagena refer to 60 = 5 dozen = 1/2 small gross. This quantity was used in international medieval treaties e.g. for ransom of captured Teutonic Knights.

In religion

In the Bible, the number 60 occurs several times, for example as the age of Isaac when Jacob and Esau were born,4 and the number of warriors escorting King Solomon.5

In the laws of kashrut of Judaism, 60 is also the proportion (60:1) of kosher to non-kosher ingredients which can render an admixture kosher post-facto.6

In the Koran, the number 60 is mentioned once: "..he should feed sixty indigent ones..",7 yet 60 is mentioned many times in the Hadith, most notably Muhammad being reported to say, "..Allah, the Exalted and Glorious, created Adam in His own image with His length of sixty cubits.."8

In other fields

There are 60 seconds in a minute, and 60 minutes in an hour

Sixty is:

In sports

References

  1. ^ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 109–110.
  2. ^ La Fontane, Jean sybil (2004). The Interpretation of Ritual: Essays in Honour of A.I. Richards. Routledge. p. 320. 
  3. ^ Bowers, Nancy (1977). "Kapauku numeration: Reckoning, racism, scholarship, and Melanesian counting systems". Journal of the Polynesian Society 86 (1): 105–116 
  4. ^ Biblegateway Genesis 25:26
  5. ^ Biblegateway Song of Solomon 3:7
  6. ^ Talmud, Tractate Chullin 98b ; Shulchan Aruch, Yoreh Deah 98.
  7. ^ Koran, Al-Mujadala,4
  8. ^ http://www.searchtruth.com/book_display.php?book=040&translator=2&start=0&number=6809#6809
  9. ^ Dennis Guedj, Numbers: The Universal Language, transl. Lory Frankel. New York: Harry N. Abrams, Inc. Publishers (1997): 71. "60: the ace of divisibility. The more divisible a number is ... the more useful it proves in certain situations. ... Is it because 60 is highly divisible that the hour has been divided into 60 minutes, and the minute into 60 seconds? Look at the list of its twelve divisors ... Compare this with the larger number 100, which has only nine divisors."

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