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 then 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.
The smallest non-solvable group (A5) has order 60.
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).
Read more about this topic: 60 (number)
Famous quotes containing the word mathematics:
“Mathematics alone make us feel the limits of our intelligence. For we can always suppose in the case of an experiment that it is inexplicable because we don’t happen to have all the data. In mathematics we have all the data ... and yet we don’t understand. We always come back to the contemplation of our human wretchedness. What force is in relation to our will, the impenetrable opacity of mathematics is in relation to our intelligence.”
—Simone Weil (1909–1943)
“The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.”
—Willard Van Orman Quine (b. 1908)