11 (eleven) is the natural number following 10 and preceding 12. It is the first repdigit. In English, it is the smallest positive integer whose name has three syllables.
Name
"Eleven" derives from the Old Englishęndleofon, which is first attested in Bede's late 9th-century Ecclesiastical History of the English People.[2][3] It has cognates in every Germanic language (for example, German elf), whose Proto-Germanic ancestor has been reconstructed as *ainalifa-,[4] from the prefix *aina- (adjectival "one") and suffix *-lifa-, of uncertain meaning.[3] It is sometimes compared with the Lithuanianvienúolika, though -lika is used as the suffix for all numbers from 11 to 19 (analogously to "-teen").[3]
The Old English form has closer cognates in Old Frisian, Saxon, and Norse, whose ancestor has been reconstructed as *ainlifun. This was formerly thought to be derived from Proto-Germanic *tehun ("ten");[3][5] it is now sometimes connected with *leikʷ- or *leip- ("left; remaining"), with the implicit meaning that "one is left" after counting to ten.[3]
Languages
While 11 has its own name in Germanic languages such as English, German, or Swedish, and some Latin-based languages such as Spanish, Portuguese, and French, it is the first compound number in many other languages: Chinese 十一shí yī, Korean 열하나yeol hana or 십일ship il.
Arithmetic and algebraic properties arising from the number or its use
The first prime exponent that does not yield a Mersenne prime is 11, where , which is the first composite generalized Mersenne number. 11 is the first strong prime,[8] such that for a prime there is , and it is also the second good prime, whose square is greater than the product of any two prime numbers at the same number of positions before and after it in the sequence of prime numbers.[9]
11 is also the number of ways a Triangular Orthobiprism or Orthobifastigium or Digonal Orthobicupola can tile space. The ways are because of sum of solid angles being 360 degrees. They are:
Apollo 11 was the first crewed spacecraft to land on the Moon. In our solar system, the Sun has a sunspot cycle's periodicity that is approximately 11 years.
The interval of an octave plus a fourth is an 11th. A complete 11th chord has almost every note of a diatonic scale.
Regarding musical instruments, there are 11 thumb keys on a bassoon, not counting the whisper key. (A few bassoons have a 12th thumb key.)
Sports and games
In sports, there are 11 players on an association football (soccer) team, 11 players on an American football team during play, 11 players on a cricket team on the field, and 11 players in a field hockey team. In the game of blackjack, an ace can count as either one or 11, whichever is more advantageous for the player.
Being one hour before 12:00, the eleventh hour means the last possible moment to take care of something, and often implies a situation of urgent danger or emergency (see Doomsday clock).
Mysticism
The number 11 (alongside its multiples 22 and 33) are master numbers in numerology, especially in New Age.[16]
^Mueller, Francis J. (1965). "More on Pascal's Triangle and powers of 11". The Mathematics Teacher. 58 (5): 425–428. doi:10.5951/MT.58.5.0425. JSTOR27957164.