180 (number)
From Wikipedia, the free encyclopedia
180 (one hundred eighty in American English, one hundred and eighty in British English) is the natural number following 179 and preceding 181.
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Ordinal | One hundred [and] eighty |
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Cardinal | 180th | ||
Factorization | |||
Roman numeral | CLXXX | ||
Binary | 10110100 | ||
Duodecimal | 130 | ||
Hexadecimal | B4 | ||
Vigesimal | 90 |
[edit] In mathematics
One hundred [and] eighty is the sum of six consecutive primes (19 + 23 + 29 + 31 + 37 + 41), as well as the sum of eight consecutive primes (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37).
The sum of Euler's totient function φ(x) over the first twenty-four integers is 180. Since 180 is divisible by the total number of its divisors, it is a refactorable number.
Using degrees (°) to measure angles, 180° is called straight angle, and makes a semicircle. 180° is equivalent to π rads. In normal space, the interior angles of a triangle add up to 180°.
180 is a Harshad number in base 10.
[edit] In other fields
- 180° also means antipode. For example, a "180-degree change" indicates a radical change.
- Interstate 180, the designation of some spur routes of Interstate 80 in the United States.
- The maximum possible score in one turn at darts (three treble 20s).
- In astronomy, when two planets are 180 degrees apart, they are said to be in opposition. In astrology, this is an aspect that is considered to be negative in influence.
- The year AD 180 or 180 BC.
- 180 is a perfect score on the LSAT. Thus, it is often used by law students and attorneys in conversation to signify agreement or appreciation of a point.
- In the movie series Final Destination, Final Destination 2, and Final Destination 3, 180 is a number that often foreshadows death and suffering (FD1: Plane that blew up was Flight 180; FD2: Sign showing "Next 180 feet" during pile-up; FD3: Subway car was car 081, which is 180 backward)
[edit] Other numbers in the 180s
181 = prime number, Chen prime, palindromic prime, star number, centered square number, centered pentagonal number, sum of five consecutive primes (29 + 31 + 37 + 41 + 43)
182 = 2 7 13, sphenic number, pronic number, nontotient
183 = 3 61, Middle day of the year (not leap years).
184 = 2^3 23, sum of four consecutive primes (41 + 43 + 47 + 53)
185, see 185 (number)
186 = 2 3 31, sphenic number, nontotient
187 = 11 17, sum of three consecutive primes (59 + 61 + 67), sum of nine consecutive primes (7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37), self number
188 = 2^2 47, nontotient, untouchable number
189 = 3^3 7 = 63+(-3)3 = 43+53, centered cube number