3 (number)

Three is the largest number still written with as many lines as the number represents. (The Ancient Romans usually wrote 4 as IIII, but this was almost entirely replaced by the subtractive notation IV in the Middle Ages.) To this day 3 is written as three lines in Roman and Chinese numerals. This was the way the Brahmin Indians wrote it, and the Gupta made the three lines more curved. The Nagari started rotating the lines clockwise and ending each line with a slight downward stroke on the right. Eventually they made these strokes connect with the lines below, and evolved it to a character that looks very much like a modern 3 with an extra stroke at the bottom. It was the Western Ghubar Arabs who finally eliminated the extra stroke and created our modern 3. (The "extra" stroke, however, was very important to the Eastern Arabs, and they made it much larger, while rotating the strokes above to lie along a horizontal axis, and to this day Eastern Arabs write a 3 that looks like a mirrored 7 with ridges on its top line): ٣^[1]

While the shape of the 3 character has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender, as, for example, in . In some French text-figure typefaces, though, it has an ascender instead of a descender.

Flat top 3

A common variant of the digit 3 has a flat top, similar to the character Ʒ (ezh). This form is sometimes used to prevent people from fraudulently changing a 3 into an 8. It is usually found on UPC-A barcodes and standard 52-card decks.

In mathematics

Three is approximately $π$ (actually closer to 3.14159) when doing rapid guesses or estimates. The same is true if one wants a rough-and-ready estimate of e, which is actually approximately 2.71828.
Three is the first odd prime number,^[2] and the second smallest prime. It is both the first Fermat prime (2^2ⁿ + 1) and the first Mersenne prime (2ⁿ − 1), the only number that is both, as well as the first lucky prime. It is the first super-prime. However, it is the second Sophie Germain prime, the second Mersenne prime exponent, the second factorial prime (2! + 1), the second Lucas prime, and the second Stern prime.
Three is the first unique prime due to the properties of its reciprocal.
Three is the aliquot sum of 4.
Three is the third Heegner number.
According to Pythagoras and the Pythagorean school, the number 3, which they called triad, is the noblest of all digits, as it is the only number to equal the sum of all the terms below it, and the only number whose sum with those below equals the product of them and itself.^[3]
Three is the second triangular number and it is the only prime triangular number. Three is the only prime which is one less than a perfect square. Any other number which is n² − 1 for some integer n is not prime, since it is (n − 1)(n + 1). This is true for 3 as well (with n = 2), but in this case the smaller factor is 1. If n is greater than 2, both n − 1 and n + 1 are greater than 1 so their product is not prime.
Three non-collinear points determine a plane and a circle.
Three is the fourth Fibonacci number. In the Perrin sequence, however, 3 is both the zeroth and third Perrin numbers.
Three is the fourth open meandric number.
Vulgar fractions with 3 in the denominator have a single digit repeating sequences in their decimal expansions: 0.000..., 0.333..., 0.666... (See also 0.999..., which = 1.)
A natural number is divisible by three if the sum of its digits in base 10 is divisible by 3. For example, the number 21 is divisible by three (3 times 7) and the sum of its digits is 2 + 1 = 3. Because of this, the reverse of any number that is divisible by three (or indeed, any permutation of its digits) is also divisible by three. For instance, 1368 and its reverse 8631 are both divisible by three (and so are 1386, 3168, 3186, 3618, etc.). See also Divisibility rule. This works in base 10 and in any positional numeral system whose base divided by three leaves a remainder of one (bases 4, 7, 10, etc.).
3 is the smallest prime of a Mersenne prime power tower: 3, 7, 127, 7038170141183460469♠170141183460469231731687303715884105727; it is not known whether any more of the terms are prime.
3 is the smallest number of sides that a simple (non-self-intersecting) polygon can have.
Three of the five regular polyhedra have triangular faces — the tetrahedron, the octahedron, and the icosahedron. Also, three of the five regular polyhedra have vertices where three faces meet — the tetrahedron, the hexahedron (cube), and the dodecahedron. Furthermore, only three different types of polygons comprise the faces of the five regular polyhedra — the triangle, the quadrilateral, and the pentagon.
There are only three distinct 4×4 panmagic squares.
Only three tetrahedral numbers are also perfect squares.
The first number, according to the Pythagoreans, and the first male number.
The first number, according to Proclus, i.e. n² is greater than 2n.
The trisection of the angle was one of the three famous problems of antiquity.
Gauss proved that every integer is the sum of at most 3 triangular numbers.
Gauss proved that for any prime number p (with the sole exception of 3) the product of its primitive roots is ≡ 1 (mod p).
Any number not in the form of 4ⁿ(8m + 7) is the sum of 3 squares.
Each real number belongs to only 1 of the following 3 categories: positive, negative, and zero.

In numeral systems

There is some evidence to suggest that early man may have used counting systems which consisted of "One, Two, Three" and thereafter "Many" to describe counting limits. Early peoples had a word to describe the quantities of one, two, and three but any quantity beyond was simply denoted as "Many". This is most likely based on the prevalence of this phenomena among people in such disparate regions as the deep Amazon and Borneo jungles, where western civilization's explorers have historical records of their first encounters with these indigenous people.^[4]

List of basic calculations

Multiplication	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	50	100	1000	10000
3 × x	3	6	9	12	15	18	21	24	27	30	33	36	39	42	45	48	51	54	57	60	63	66	69	72	75	150	300	3000	30000

Division	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20
3 ÷ x	3	1.5	1	0.75	0.6	0.5	0.428571	0.375	0.3	0.3		0.27	0.25	0.230769	0.2142857	0.2	0.1875	0.17647058823529411	0.16	0.157894736842105263	0.15
x ÷ 3	0.3	0.6	1	1.3	1.6	2	2.3	2.6	3	3.3		3.6	4	4.3	4.6	5	5.3	5.6	6	6.3	6.6

Exponentiation	1	2	3	4	5	6	7	8	9	10		11	12	13	14	15	16	17	18	19	20
3^x	3	9	27	81	243	729	2187	6561	19683	59049		177147	531441	1594323	4782969	14348907	43046721	129140163	387420489	1162261467	3486784401
x³	1	8	27	64	125	216	343	512	729	1000		1331	1728	2197	2744	3375	4096	4913	5832	6859	8000

In science

The Roman numeral III stands for giant star in the Yerkes spectral classification scheme.
Three is the atomic number of lithium.
Three is the ASCII code of "End of Text".
Three is the number of dimensions that humans can perceive. Humans perceive the universe to have three spatial dimensions, but some theories, such as string theory, suggest there are more.
The triangle, a polygon with three edges and three vertices, is the most stable physical shape. For this reason it is widely utilized in construction, engineering and design.^[5]
The ability of the human eye to distinguish colors is based upon the varying sensitivity of different cells in the retina to light of different wavelengths. Humans being trichromatic, the retina contains three types of color receptor cells, or cones.

In protoscience

In European alchemy, the three primes (Latin: tria prima) were salt (), sulfur () and mercury ().^[6]^[7]
The three doshas (weaknesses) and their antidotes are the basis of Ayurvedic medicine in India.

In astronomy

The Saros number of the solar eclipse series which began on April 24, 2814 BC and ended on June 1, 1534 BC. The duration of Saros series 3 was 1280.14 years, and it contained 72 solar eclipses.
The Saros number of the lunar eclipse series which began on December 30, 2567 BC and ended on March 21, 1214 BC. The duration of Saros series 3 was 1352.26 years, and it contained 76 lunar eclipses.

In philosophy

Main article: Trichotomy (philosophy)

Philosophers such as Aquinas, Kant, Hegel, and C. S. Peirce have made threefold divisions, or trichotomies, which have been important in their work.
Hegel's dialectic of Thesis + Antithesis = Synthesis creates three-ness from two-ness.

In religion

In Christianity

The threefold office of Christ is a Christian doctrine that Christ performs the functions of prophet, priest, and king.
The ministry of Jesus lasted three years.
During the Agony in the Garden Christ asked three times for the chalice to be taken from his lips.
Jesus rose from the dead on the third day after his death.
The devil tempted Jesus three times.
Saint Peter thrice denied Jesus and thrice affirmed his faith in Jesus
The Magi gave Jesus three gifts.
There are three Synoptic Gospels and three epistles of John.

In Judaism

Noah had three sons: Ham, Shem and Japheth
The Three Patriarchs: Abraham, Isaac and Jacob
The prophet Balaam beat his donkey three times.
The prophet Jonah spent three days and nights in the belly of a large fish
Three divisions of the Written Torah: Torah (Five Book of Moses), Nevi'im (Prophets), Ketuvim (Writings)^[8]
Three divisions of the Jewish people: Kohen, Levite, Yisrael
Three daily prayers: Shacharit, Mincha, Maariv
Three Shabbat meals
Shabbat ends when three stars are visible in the night sky^[9]
Three Pilgrimage Festivals: Passover, Shavuot, Sukkot
Three matzos on the Passover Seder table^[10]
The Three Weeks, a period of mourning bridging the fast days of Seventeenth of Tammuz and Tisha B'Av
Three cardinal sins for which a Jew must die rather than transgress: idolatry, murder, sexual immorality^[11]
Upsherin, a Jewish boy's first haircut at age 3^[12]
A Beth din is composed of three members
Potential converts are traditionally turned away three times to test their sincerity^[13]
In the Jewish mystical tradition of the Kabbalah, it is believed that the soul consists of three parts, with the highest being nefesh ("repose"), the middle being ruach ("wind" or "spirit") and the lowest being neshamah ("breath").^[14] Sometimes the two elements of Chayah ("life" or "animal") and Yechidah ("unit") are additionally mentioned.
In the Kabbalah, the Tree of Life (Hebrew: Etz ha-Chayim, עץ החיים) refers to a latter 3-pillar diagrammatic representation of its central mystical symbol, known as the 10 Sephirot.

In Buddhism

The Triple Bodhi (ways to understand the end of birth) are Budhu, Pasebudhu, and Mahaarahath.
The Three Jewels, the three things that Buddhists take refuge in.

In Taoism

The Three Treasures (Chinese: 三寶; pinyin: sānbǎo; Wade–Giles: san-pao), the basic virtues in Taoism.

In Hinduism

The "Om" symbol, in Devanagari is also written ओ३म् (ō̄m [õːːm]), where ३ is दीर्घ (dirgha, "three times as long")

The Trimurti: Brahma the Creator, Vishnu the Preserver, and Shiva the Destroyer.
The three Gunas underlie action, in the Vedic system of knowledge.
The Three Yogas in the context of monotheistic Hinduism are three religious paths for the human spirit to achieve union (yoga) with Ishvara, Supreme Being, i.e. God. They are Karma Yoga, Bhakti Yoga and Jnana Yoga.

In Zoroastrianism

The three virtues of Humata, Hukhta and Huvarshta (Good Thoughts, Good Words and Good Deeds) are a basic tenet in Zoroastrianism.

In Norse mythology

Three is a very significant number in Norse mythology, along with its powers 9 and 27.

Prior to Ragnarök, there will be three hard winters without an intervening summer, the Fimbulwinter.
Odin endured three hardships upon the World Tree in his quest for the runes: he hanged himself, wounded himself with a spear, and suffered from hunger and thirst.
Bor had three sons, Odin, Vili, and Vé.

In other religions

The Wiccan Rule of Three.
The Triple Goddess: Maiden, Mother, Crone; the three fates.
The sons of Cronus: Zeus, Poseidon, and Hades.

In esoteric tradition

The Theosophical Society has three conditions of membership.
Gurdjieff's Three Centers and the Law of Three.
Liber AL vel Legis, the central scripture of the religion of Thelema, consists of three chapters, corresponding to three divine narrators respectively: Nuit, Hadit and Ra-Hoor-Khuit.
The Triple Greatness of Hermes Trismegistus is an important theme in Hermeticism.

As a lucky or unlucky number

Three (三, formal writing: 叁, pinyin sān, Cantonese: saam¹) is considered a good number in Chinese culture because it sounds like the word "alive" (生 pinyin shēng, Cantonese: saang¹), compared to four (四, pinyin: sì, Cantonese: sei¹), which sounds like the word "death" (死 pinyin sǐ, Cantonese: sei²).

Counting to three is common in situations where a group of people wish to perform an action in synchrony: Now, on the count of three, everybody pull! Assuming the counter is proceeding at a uniform rate, the first two counts are necessary to establish the rate, and the count of "three" is predicted based on the timing of the "one" and "two" before it. Three is likely used instead of some other number because it requires the minimal amount counts while setting a rate.

In East and Southeast Asia, there is a widespread superstition that considers it inauspicious to take a photo with three people in it; it is professed that the person in the middle will die first.

There is another superstition that it is unlucky to take a third light, that is, to be the third person to light a cigarette from the same match or lighter. This superstition is sometimes asserted to have originated among soldiers in the trenches of the First World War when a sniper might see the first light, take aim on the second and fire on the third.

The phrase "Third time's the charm" refers to the superstition that after two failures in any endeavor, a third attempt is more likely to succeed. This is also sometimes seen in reverse, as in "third man [to do something, presumably forbidden] gets caught".

Luck, especially bad luck, is often said to "come in threes".^[15]

In sports

In association football in almost all leagues, and in the group phases of most international competitions, three competition points are awarded for a win.
In Gaelic football, hurling and camogie, a "goal", with a scoring value of three, is awarded when the attacking team legally sends the ball into the opponent's goal.
In baseball, three is the number of strikes before the batter is out and the number of outs per side per inning; in scorekeeping, "3" denotes the first baseman.
In basketball:
- A shot made from behind the three-point arc is worth three points (except in the 3x3 variant, in which it is worth two points).
- A potential "three-point play" exists when a player is fouled while successfully completing a two-point field goal, thus being awarded one additional free throw attempt.
- On offense, the "three-second rule" states that an offensive player cannot remain in the opponent's free-throw lane for more than three seconds while his team is in possession of the ball and the clock is running.
- In the NBA only, the defensive three-second violation, also known as "illegal defense", states that a defensive player cannot remain in his own free-throw lane for more than three seconds unless he is actively guarding an offensive player.
- The "3 position" is the small forward.
In gridiron football, a field goal is a scoring play in which a kicker kicks the football from behind the line of scrimmage through the goalposts on the opponent's side of the field. This play, if successful, is worth three points.
A hat trick in sports is associated with succeeding at anything three times in three consecutive attempts, as well as when any player in ice hockey or soccer scores three goals in one game (whether or not in succession). In cricket, if a bowler takes three wickets in a row it is called a hat trick.
A "threepeat" is a term for winning three consecutive championships.
A triathlon consists of three events: swimming, bicycling, and running.
A pin (professional wrestling) in professional wrestling is when one's shoulders are held the opponent's shoulders against the mat for a count of three.
NASCAR driver Dale Earnhardt, Sr. drove under number 3 for most of his career for car owner Richard Childress.

References

↑ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 393, Fig. 24.63
↑ Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 39
↑ Priya Hemenway (2005), Divine Proportion: Phi In Art, Nature, and Science, Sterling Publishing Company Inc., pp. 53–54, ISBN 1-4027-3522-7
↑ Big Numbers. ISBN 1840464313.
↑ "Most stable shape- triange". Maths in the city. Retrieved February 23, 2015.
↑ Eric John Holmyard. Alchemy. 1995. p.153
↑ Walter J. Friedlander. The golden wand of medicine: a history of the caduceus symbol in medicine. 1992. p.76-77
↑ Marcus, Rabbi Yossi (2015). "Why are many things in Judaism done three times?". Ask Moses. Retrieved 16 March 2015.
↑ "Shabbat". Judaism 101. 2011. Retrieved 16 March 2015.
↑ Kitov, Eliyahu (2015). "The Three Matzot". Chabad.org. Retrieved 16 March 2015.
↑ Kaplan, Rabbi Aryeh (28 August 2004). "Judaism and Martyrdom". Aish.com. Retrieved 16 March 2015.
↑ "The Basics of the Upsherin: A Boy's First Haircut". Chabad.org. 2015. Retrieved 16 March 2015.
↑ "The Conversion Process". Center for Conversion to Judaism. Retrieved 16 March 2015.
↑ Kaplan, Aryeh. "The Soul". Aish. From The Handbook of Jewish Thought (Vol. 2, Maznaim Publishing. Reprinted with permission.) September 4, 2004. Retrieved February 24, 2015.
↑ See "bad" in the Oxford Dictionary of Phrase and Fable, 2006, via Encyclopedia.com.

Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 46–48

External links

Look up three in Wiktionary, the free dictionary.

Wikimedia Commons has media related to 3 (number).

Tricyclopedic Book of Threes by Michael Eck
Threes in Human Anatomy by Dr. John A. McNulty
Grime, James. "3 is everywhere". Numberphile. Brady Haran.
The Number 3
The Positive Integer 3
Prime curiosities: 3

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

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