Contents 1 Name 2 In languages 2.1 Grammar 3 In mathematics 3.1 List of basic calculations 4 In numeral systems 5 In science 5.1 Astronomy 6 In religion 6.1 Christianity 6.2 Babylonian 7 In music 8 In sports 9 In the military 10 In computing 11 In Canada 12 In other fields 13 See also 14 References 15 External links


Name[edit] Eleven derives from the Old English ęndleofon 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 Lithuanian vienúolika, although -lika is used as the suffix for all numbers from 11 to 19 (analogous to "-teen").[3] The Old English form has closer cognates in Old Frisian, Saxon, and Norse, whose ancestor has been reconstructed as *ainlifun. This has formerly been considered 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 having already counted to ten.[3]


In languages[edit] Grammar[edit] While, as mentioned above, 11 has its own name in Germanic languages such as English, German, and Swedish. It is the first compound number in many other languages, e.g. Italian ùndici (but in Spanish and Portuguese, 16, and in French, 17 is the first compound number), Japanese 十一 jūichi.


In mathematics[edit] 11 is a prime number. It is the smallest two-digit prime number in the decimal base. The next prime is 13, with which it comprises a twin prime. If a number is divisible by 11, reversing its digits will result in another multiple of 11. As long as no two adjacent digits of a number added together exceed 9, then multiplying the number by 11, reversing the digits of the product, and dividing that new number by 11, will yield a number that is the reverse of the original number. (For example: 142,312 × 11 = 1,565,432 → 2,345,651 ÷ 11 = 213,241.) Multiples of 11 by one-digit numbers all have matching double digits: 00 (=0), 11, 22, 33, 44, etc. An 11-sided polygon is called a hendecagon or undecagon. In base 10, there is a simple test to determine if an integer is divisible by 11: take every digit of the number located in odd position and add them up, then take the remaining digits and add them up. If the difference between the two sums is a multiple of 11, including 0, then the number is divisible by 11.[6] For instance, if the number is 65,637 then (6 + 6 + 7) - (5 + 3) = 19 - 8 = 11, so 65,637 is divisible by 11. This technique also works with groups of digits rather than individual digits, so long as the number of digits in each group is odd, although not all groups have to have the same number of digits. For instance, if one uses three digits in each group, one gets from 65,637 the calculation (065) - 637 = -572, which is divisible by 11. Another test for divisibility is to separate a number into groups of two consecutive digits (adding a leading zero if there is an odd number of digits), and then add up the numbers so formed; if the result is divisible by 11, the number is divisible by 11. For instance, if the number is 65,637, 06 + 56 + 37 = 99, which is divisible by 11, so 65,637 is divisible by eleven. This also works by adding a trailing zero instead of a leading one: 65 + 63 + 70 = 198, which is divisible by 11. This also works with larger groups of digits, providing that each group has an even number of digits (not all groups have to have the same number of digits). An easy way of multiplying numbers by 11 in base 10 is: If the number has: 1 digit - Replicate the digit (so 2 x 11 becomes 22). 2 digits - Add the 2 digits together and place the result in the middle (so 47 x 11 becomes 4 (11) 7 or 4 (10+1) 7 or (4+1) 1 7 or 517). 3 digits - Keep the first digit in its place for the result's first digit, add the first and second digits together to form the result's second digit, add the second and third digits together to form the result's third digit, and keep the third digit as the result's fourth digit. For any resulting numbers greater than 9, carry the 1 to the left. Example 1: 123 x 11 becomes 1 (1+2) (2+3) 3 or 1353. Example 2: 481 x 11 becomes 4 (4+8) (8+1) 1 or 4 (10+2) 9 1 or (4+1) 2 9 1 or 5291. 4 or more digits - Follow the same pattern as for 3 digits. In base 13 and higher bases (such as hexadecimal), 11 is represented as B, where ten is A. In duodecimal, however, 11 is sometimes represented as E and ten as T or X. There are 11 orthogonal curvilinear coordinate systems (to within a conformal symmetry) in which the 3-variable Helmholtz equation can be solved using the separation of variables technique. See also 11-cell. 11 of the thirty-five hexominoes can be folded to form cubes. 11 of the sixty-six octiamonds can be folded to form octahedra. 11 is the fourth Sophie Germain prime,[7] the third safe prime,[8] the fourth Lucas prime,[9] the first repunit prime,[10] and the second good prime.[11] Although it is necessary for n to be prime for 2n − 1 to be a Mersenne prime, the converse is not true: 211 − 1 = 2047 which is 23 × 89. 11 raised to the nth power is the nth row of Pascal's Triangle. (This works for any base, but the number eleven must be changed to the number represented as 11 in that base; for example, in duodecimal this must be done using thirteen.) 11 is a Heegner number, meaning that the ring of integers of the field Q ( − 11 ) {\displaystyle \mathbb {Q} ({\sqrt {-11}})} has the property of unique factorization. One consequence of this is that there exists at most one point on the elliptic curve x3 = y2 + 11 that has positive-integer coordinates. In this case, this unique point is (15, 58). List of basic calculations[edit] Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 25 50 100 1000 11 × x 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176 187 198 209 220 275 550 1100 11000 Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 11 ÷ x 11 5.5 3.6 2.75 2.2 1.83 1.571428 1.375 1.2 1.1 1 0.916 0.846153 0.7857142 0.73 x ÷ 11 0.09 0.18 0.27 0.36 0.45 0.54 0.63 0.72 0.81 0.90 1 1.09 1.18 1.27 1.36 Exponentiation 1 2 3 4 5 6 7 8 9 10 11x 11 121 1331 14641 161051 1771561 19487171 214358881 2357947691 25937421601 x11 1 2048 177147 4194304 48828125 362797056 1977326743 8589934592 31381059609 100000000000 Radix 1 5 10 15 20 25 30 40 50 60 70 80 90 100 110 120 130 140 150 200 250 500 1000 10000 100000 1000000 x11 1 5 A11 1411 1911 2311 2811 3711 4611 5511 6411 7311 8211 9111 A011 AA11 10911 11811 12711 17211 20811 41511 82A11 757211 6914A11 62335111


In numeral systems[edit] ११ Devanagari ௧௧ Tamil ൧൧ Malayalam ౧౧ Telugu ১১ Bangla


In science[edit] 11 is the atomic number of the element sodium. In chemistry, Group 11 of the Periodic Table of the Elements (IUPAC numbering) consists of the three coinage metals copper, silver, and gold known from antiquity, and roentgenium, a recently synthesized superheavy element. The number of spacetime dimensions in M-theory. Astronomy[edit] Apollo 11 was the first manned spacecraft to land on the Moon. The approximate periodicity of a sunspot cycle is 11 years. Messier object M11, a magnitude 7.0 open cluster in the constellation Scutum, also known as the Wild Duck Cluster. The New General Catalogue object[12] NGC 11, a spiral galaxy in the constellation Andromeda The 11th moon of Jupiter is Himalia.


In religion[edit] Christianity[edit] After Judas Iscariot was disgraced, the remaining apostles of Jesus were sometimes described as "the Eleven" (Mark 16:11; Luke 24:9 and 24:33); this occurred even after Matthias was added to bring the number to twelve, as in Acts 2:14:[13] Peter stood up with the eleven (New International Version). The New Living Translation says Peter stepped forward with the eleven other apostles, making clear that the number of apostles was now twelve. Saint Ursula is said to have been martyred in the third or fourth century in Cologne with a number of companions, whose reported number "varies from five to eleven".[14] A legend that Ursula died with eleven thousand virgin companions[15] has been thought to appear from misreading XI. M. V. (Latin abbreviation for "Eleven martyr virgins") as "Eleven thousand virgins". Babylonian[edit] In the Enûma Eliš the goddess Tiamat creates eleven monsters to take revenge for the death of her husband, Apsû.


In music[edit] See also: Eleven (disambiguation) § Music The interval of an octave and a fourth is an 11th. A complete 11th chord has almost every note of a diatonic scale. The number of thumb keys on a bassoon, not counting the whisper key. (A few bassoons have a 12th thumb key.) In the mockumentary This Is Spinal Tap, Spinal Tap's amplifiers go up to eleven. In Igor Stravinsky's The Rite of Spring, there are 11 consecutive repetitions of the same chord. In Tool's song "Jimmy" and in Negativland's song "Time Zones", the number 11 is heard numerous times in the lyrics. "Eleven pipers piping" is the gift on the 11th day of Christmas in the carol "The Twelve Days of Christmas" In Green Grow the Rushes, O, Eleven is for "the eleven who went to heaven" "The Eleven" is a song by The Grateful Dead. In "Time Enough For Rocking When We're Old" by The Magnetic Fields, a lyric references "when our pheromones go up to eleven." Eleven Records is the record label of Jason Webley, and many of Webley's works feature the number 11.[16]


In sports[edit] There are 11 players on an association football (soccer) team on the field at a time An American football team also has 11 players on the field at one time during play. #11 is worn by quarterbacks, kickers, punter and wide receivers in American football's NFL. There are 11 players on a bandy team on the ice at a time In cricket, a team has 11 players on the field. The 11th player is usually the weakest batsman, at the tail-end. He is primarily in the team for his bowling abilities. There are 11 players in a field hockey team. The player wearing 11 will usually play on the left-hand side, as in soccer. In most rugby league competitions (but not the European Super League, which uses static squad numbering), one of the starting second-row forwards wears the number 11. In rugby union, the starting left wing wears the number 11 shirt.


In the military[edit] The number of guns in a gun salute to U.S. Army, Air Force and Marine Corps Brigadier Generals, and to Navy and Coast Guard Rear Admirals Lower Half. The Military Occupational Specialty (MOS) designator given to US Army Infantry Officer as well as to enlisted personnel (AKA 11 MOS Series, or 11B, 11C, 11D, 11H, 11M, etc.) The number of General Orders for Sentries in the Marine Corps and United States Navy. A page in the Service Record Book of an enlisted Marine for writing down disciplinary actions. World War I ended with an Armistice on November 11, 1918, which went into effect at 11:00 am—the 11th hour on the 11th day of the 11th month of the year. Armistice Day is still observed on November 11 of each year, although it is now called Veterans Day in the United States and Remembrance Day in the Commonwealth of Nations and parts of Europe.


In computing[edit] In Mozilla Firefox, Opera, Konqueror for KDE, Google Chrome and Internet Explorer for Windows, the function key F11 key toggles full screen viewing mode. In macOS, F11 hides all open windows. The windowing system for Unix computers is known as X11. Computers of the PDP-11 series from Digital Equipment Corporation were informally referred to as "elevens".


In Canada[edit] The stylized maple leaf on the Flag of Canada has 11 points. The loonie is a hendecagon, an 11-sided polygon. Clocks depicted on Canadian currency, like the Canadian fifty-dollar bill, show 11:00. Eleven denominations of Canadian currency are produced in large quantities. Due to Canada's federal nature, eleven legally distinct Crowns effectively exist in the country, with the Monarch represented separately in each province, and at the federal level.


In other fields[edit] Sector 11 [17] in the North American Industry Classification System is the code for Agriculture, Forestry, Fishing and Hunting industries. Being only 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). In Astrology, Aquarius is the 11th astrological sign of the Zodiac.[citation needed] In Basque, hamaika ("eleven") has the double meaning of "infinite", probably from amaigabe, "endless", as in Hamaika aldiz etortzeko esan dizut! ("I told you infinite/eleven times to come!"). English-speaking surveyors have developed several slang terms for 11 to distinguish it from its rhyme "seven": "punk," "top," & "railroad"[18] American Airlines flight 11, a Boston-Los Angeles flight which was reported to have crashed into the North Tower of the World Trade Center in New York City, New York on September 11, 2001. The number 11 bus is a low-cost way of sightseeing in London. In the game of blackjack, an Ace can be counted as either one or 11, whichever is more advantageous for the player. 11 is the number of the French department Aude. Three films -- Ben-Hur (1959), Titanic (1997), and The Lord of the Rings: The Return of the King (2003) -- have each won 11 Academy Awards, including Best Picture of their respective years. Ocean's Eleven is the name of two American films. In the anime series Code Geass, Japan is known as Area 11 of the Brittanian Empire. Eleven is the name of a character in the 2016 Netflix original series Stranger Things, Presented by Millie Bobby Brown. In bingo, the game, 11 is referred to as chicken legs.


See also[edit] 11:11 11:11 (numerology) Mathematics portal


References[edit] ^ Bede, Eccl. Hist., Bk. V, Ch. xviii. ^ Specifically, in the line jjvjv ðæt rice hæfde endleofan wintra.[1] ^ a b c d e Oxford English Dictionary, 1st ed. "eleven, adj. and n." Oxford University Press (Oxford), 1891. ^ Kroonen, Guus (2013). Etymological Dictionary of Proto-Germanic. Leiden: Brill. p. 11f. ISBN 978-90-04-18340-7.  ^ Dantzig, Tobias (1930), Number: The Language of Science . ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 47. ISBN 978-1-84800-000-1.  ^ "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.  ^ "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.  ^ "Sloane's A005479 : Prime Lucas numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.  ^ "Sloane's A004022 : Primes of the form (10^n - 1)/9". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.  ^ "Sloane's A028388 : Good primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.  ^ http://www.ngcicproject.org/ ^ http://bible.cc/acts/2-14.htm ^ Ursulines of the Roman Union, Province of Southern Africa, St. Ursula and Companions, accessed 10 July 2016 ^ Four scenes from the life of St Ursula, accessed 10 July 2016 ^ Corazon, Billy (July 1, 2009). "Imaginary Interview: Jason Webley". Three Imaginary Girls. Archived from the original on 2012-04-04. Retrieved 2012-09-06.  ^ https://www.census.gov\/cgi-bin/sssd/naics/naicsrch?code=11&search=2012%20NAICS%20Search ^ "Surveying Units and Terms". Directlinesoftware.com. 2012-07-30. Retrieved 2012-08-20. 


External links[edit] Look up eleven in Wiktionary, the free dictionary. Wikimedia Commons has media related to 11 (number). Grimes, James. "Eleven". Numberphile. Brady Haran.  v t e Integers 0s  0   1   2   3   4   5   6   7   8   9  10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100s 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200s 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300s 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400s 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500s 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600s 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700s 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800s 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900s 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 Retrieved from "https://en.wikipedia.org/w/index.php?title=11_(number)&oldid=820787701" Categories: IntegersHidden categories: Articles containing Old English-language textArticles with too many examplesArticles needing additional references from November 2008All articles needing additional referencesArticles with multiple maintenance issuesPages using infobox number with prime parameterArticles containing Lithuanian-language textArticles containing Hindi-language textArticles containing Tamil-language textArticles containing Malayalam-language textArticles containing Telugu-language textAll articles with unsourced statementsArticles with unsourced statements from September 2017


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