3 (number)

← 2 3 4 →
−1 0 1 2 3 4 5 6 7 8 9 → List of numbers — Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	three
Ordinal	3rd (third)
Numeral system	ternary
Factorization	prime
Divisors	1, 3
Roman numeral	III
Roman numeral (unicode)	Ⅲ, ⅲ
Greek prefix	tri-
Latin prefix	tre-/ter-
Binary	112
Ternary	103
Quaternary	34
Quinary	35
Senary	36
Octal	38
Duodecimal	312
Hexadecimal	316
Vigesimal	320
Base 36	336
Arabic & Kurdish	٣
Urdu
Bengali	৩
Chinese	三，弎，叁
Devanāgarī	३ (tin)
Ge'ez	፫
Greek	γ (or Γ)
Hebrew	ג
Japanese	三
Khmer	៣
Korean	셋,삼
Malayalam	൩
Tamil	௩
Telugu	౩
Thai	๓

3 (three; /ˈθriː/) is a number, numeral, and glyph. It is the natural number following 2 and preceding 4.

Evolution of the glyph

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 as ३. 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

3 is:

• a rough approximation of π (3.1415...) and a very rough approximation of e (2.71828..) when doing quick estimates.
• the first odd prime number,^[2] and the second smallest prime.
• the first Fermat prime (2²ⁿ + 1).
• the first Mersenne prime (2ⁿ − 1).
• the only number that is both a Fermat prime and a Mersenne prime.
• the first lucky prime.
• the first super-prime.
• the first unique prime due to the properties of its reciprocal.
• the second Sophie Germain prime.
• the second Mersenne prime exponent.
• the second factorial prime (2! + 1).
• the second Lucas prime.
• the second Stern prime.^[3]
• the second triangular number and it is the only prime triangular number.
• the third Heegner number.^[4]
• both the zeroth and third Perrin numbers in the Perrin sequence.^[5]
• the fourth Fibonacci number.
• the fourth open meandric number.
• the aliquot sum of 4.
• the smallest number of sides that a simple (non-self-intersecting) polygon can have.
• 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.
• the number of non-collinear points needed to determine a plane and a circle.

Also:

• 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.).
• 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.
• 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.^[6]
• Three was the first number, according to the Pythagoreans, and the first male number.
• Three was 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.^[7]

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
x^3	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.^[8]
• 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 ().^[9][10]
• 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 pseudoscience

• Three is the symbolic representation for Mu (lost continent), Augustus Le Plongeon's and James Churchward's lost continent.^[11]

In 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

Many world religions contain triple deities or concepts of trinity, including:

• the Hindu Trimurti
• the Hindu Tridevi
• the Three Jewels of Buddhism
• the Three Pure Ones of Taoism
• the Christian Holy Trinity
• the Triple Goddess of Wicca

The Shield of the Trinity is a diagram of the Christian doctrine of the Trinity

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 approximately three years (27-30 AD).
• 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 (Sunday April 9, 30 AD).
• The devil tempted Jesus three times.
• Saint Peter thrice denied Jesus and thrice affirmed his faith in Jesus
• The Magi - Zoroaster priests astronomers/astrologers from Persia - gave Jesus three gifts.
• There are three Synoptic Gospels and three epistles of John.
• Paul the Apostle went blind for three days after his conversion to Christianity.

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)^[12]
• 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^[13]
• Three Pilgrimage Festivals: Passover, Shavuot, Sukkot
• Three matzos on the Passover Seder table^[14]
• 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^[15]
• Upsherin, a Jewish boy's first haircut at age 3^[16]
• A Beth din is composed of three members
• Potential converts are traditionally turned away three times to test their sincerity^[17]
• In the Jewish mystical tradition of the Kabbalah, it is believed that the soul consists of three parts, with the highest being neshamah ("breath"), the middle being ruach ("wind" or "spirit") and the lowest being nefesh ("repose").^[18] 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 Shinto

• The Imperial Regalia of Japan of the sword, mirror, and jewel.

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".^[19]

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.
• In the NASCAR Sprint Cup Series, 3 is the number of a car owned by Richard Childress Racing. It was originally driven by team founder and owner Richard Childress, but became most famous as the car driven by seven-time Cup Series champion Dale Earnhardt, first in 1981 and then from 1984 until his death at the 2001 Daytona 500. Childress did not use the number again in the Cup Series until 2014; since then, his oldest grandson Austin Dillon has driven the #3 car.
• In Formula One, 3 is used by Australian driver, Daniel Ricciardo.
• In many sports a competitor or team is said to win a Triple Crown if they win three particularly prestigious competitions.
• In association football a team that wins three trophies in a season is said to have won a treble.
• In bowling, three strikes bowled consecutively is known as a "turkey".

See also

• Cube (algebra) – (3 superscript)
• Third
• Triad

References

1. 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
2. Bryan Bunch, The Kingdom of Infinite Number. New York: W. H. Freeman & Company (2000): 39
3. "Sloane's A042978 : Stern primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
4. "Sloane's A003173 : Heegner numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
5. "Sloane's A001608 : Perrin sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-01.
6. Priya Hemenway (2005), Divine Proportion: Phi In Art, Nature, and Science, Sterling Publishing Company Inc., pp. 53–54, ISBN 1-4027-3522-7
7. Big Numbers. ISBN 1840464313.
8. "Most stable shape- triange". Maths in the city. Retrieved February 23, 2015.
9. Eric John Holmyard. Alchemy. 1995. p.153
10. Walter J. Friedlander. The golden wand of medicine: a history of the caduceus symbol in medicine. 1992. p.76-77
11. Churchward, James (1931). "The Lost Continent of Mu - Symbols, Vignettes, Tableaux and Diagrams". Biblioteca Pleyades. Retrieved 2016-03-15.
12. Marcus, Rabbi Yossi (2015). "Why are many things in Judaism done three times?". Ask Moses. Retrieved 16 March 2015.
13. "Shabbat". Judaism 101. 2011. Retrieved 16 March 2015.
14. Kitov, Eliyahu (2015). "The Three Matzot". Chabad.org. Retrieved 16 March 2015.
15. Kaplan, Rabbi Aryeh (28 August 2004). "Judaism and Martyrdom". Aish.com. Retrieved 16 March 2015.
16. "The Basics of the Upsherin: A Boy's First Haircut". Chabad.org. 2015. Retrieved 16 March 2015.
17. "The Conversion Process". Center for Conversion to Judaism. Retrieved 16 March 2015.
18. 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.
19. 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

• 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