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Natural number
← 2
3
4 →
−1 0 1 2 3 4 5 6 7 8 9 → List of numbersIntegers← 0 10 20 30 40 50 60 70 80 90 →CardinalthreeOrdinal3rd(third)Numeral systemternaryFactorizationprimePrime2ndDivisors1, 3Greek numeralΓ´Roman numeralIII or iiiLatin prefixtre-/ter-Binary112Ternary103Senary36Octal38Duodecimal312Hexadecimal316Arabic, Kurdish, Persian, Sindhi, Urdu٣Bengali, Assamese৩Chinese三，弎，叄Devanāgarī३Santali᱓Ge'ez፫Greekγ (or Γ)HebrewגJapanese三/参Khmer៣ArmenianԳMalayalam൩Tamil௩Telugu౩Kannada೩Thai๓N'Ko߃Lao໓GeorgianႢ/ⴂ/გ (Gani)Babylonian numeral𒐗Maya numerals•••Morse code... _ _
3 (three) is a number, numeral and digit. It is the natural number following 2 and preceding 4, and is the smallest odd prime number and the only prime preceding a square number.[citation needed] It has religious and cultural significance in many societies.[1]
Evolution of the Arabic digit[edit]
The use of three lines to denote the number 3 occurred in many writing systems, including some (like Roman and Chinese numerals) that are still in use. That was also the original representation of 3 in the Brahmic (Indian) numerical notation, its earliest forms aligned vertically.[2] However, during the Gupta Empire the sign was modified by the addition of a curve on each line. The Nāgarī script rotated the lines clockwise, so they appeared horizontally, and ended each line with a short downward stroke on the right. In cursive script, the three strokes were eventually connected to form a glyph resembling a ⟨3⟩ with an additional stroke at the bottom: ३.
The Indian digits spread to the Caliphate in the 9th century. The bottom stroke was dropped around the 10th century in the western parts of the Caliphate, such as the Maghreb and Al-Andalus, when a distinct variant ("Western Arabic") of the digit symbols developed, including modern Western 3. In contrast, the Eastern Arabs retained and enlarged that stroke, rotating the digit once more to yield the modern ("Eastern") Arabic digit "٣".[3]
In most modern Western typefaces, the digit 3, like the other decimal digits, has the height of a capital letter, and sits on the baseline. In typefaces with text figures, on the other hand, the glyph usually has the height of a lowercase letter "x" and a descender: "
". In some French text-figure typefaces, though, it has an ascender instead of a descender.
A common graphic variant of the digit three has a flat top, similar to the letter Ʒ (ezh). This form, sometimes called a banker's 3, can stop a forger from turning the 3 into an 8. It is found on UPC-A barcodes and standard 52-card decks.[citation needed]
Mathematics[edit] Divisibility rule[edit]A natural number is divisible by 3 if the sum of its digits in base 10 is also divisible by 3. This known as the divisibility rule of 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. This divisibility rule works in any positional numeral system whose base divided by three lees a remainder of one (bases 4, 7, 10, etc.).[4]
Properties[edit]3 is the second smallest prime number and the first odd prime number. It is a twin prime with 5, and a cousin prime with 7.
A triangle is made of three sides. It is the smallest non-self-intersecting polygon and the only polygon not to he proper diagonals. When doing quick estimates, 3 is a rough approximation of π, 3.1415..., and a very rough approximation of e, 2.71828...
3 is the first Mersenne prime. It is also the first of five known Fermat primes. It is the second Fibonacci prime (and the second Lucas prime), the second Sophie Germain prime, and the second factorial prime.
3 is the second and only prime triangular number,[5] and Carl Friedrich Gauss proved that every integer is the sum of at most three triangular numbers.
Three is the only prime which is one less than a perfect square. Any other number which is n 2 {\displaystyle n^{2}} − 1 for some integer n {\displaystyle n} is not prime, since it is ( n {\displaystyle n} − 1)( n {\displaystyle n} + 1). This is true for 3 as well (with n {\displaystyle n} = 2), but in this case the smaller factor is 1. If n {\displaystyle n} is greater than 2, both n {\displaystyle n} − 1 and n {\displaystyle n} + 1 are greater than 1 so their product is not prime.
Numeral systems[edit]
− 1 for some integer
n
{\displaystyle n}
is not prime, since it is (
n
{\displaystyle n}
There is some evidence to suggest that early man may he 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 phenomenon among people in such disparate regions as the deep Amazon and Borneo jungles, where western civilization's explorers he historical records of their first encounters with these indigenous people.[6]
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 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 3x 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 Engineering[edit]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.[7]
Mystical[edit]Three is the symbolic representation for Mu, Augustus Le Plongeon's and James Churchward's lost continent.[8]
Religion and beliefs[edit]
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See also: Triple deity
Symbol of the Triple Goddess showing the waxing, full and waning Moon
Many world religions contain triple deities or concepts of trinity, including the Hindu Trimurti and Tridevi, the Trigl (lit. 'Three-headed one'), the chief god of the Sls, the three Jewels of Buddhism, the three Pure Ones of Taoism, the Christian Trinity, the Greek goddess hecate and the Triple Goddess of Wicca.
Pythagoras and the Pythagorean school highlighted that the number 3, which they called triad, 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.[9]
The Shield of the Trinity is a diagram of the Christian doctrine of the Trinity.
As a lucky or unlucky number[edit]
Three (三, formal writing: 叁, pinyin sān, Cantonese: saam1) is considered a good number in Chinese culture because when pronounced, 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).
The phrase "Third time's the charm" refers to the superstition that after two failures in any endeor, a third attempt is more likely to succeed.[10] However, some superstitions say the opposite, stating that luck, especially bad luck, is often said to "come in threes".[11]
One such superstition, called "Three on a Match", says that it is unlucky to be the third person to light a cigarette from the same match or lighter. This superstition is sometimes asserted to he 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.[12][13]
See also[edit]
Mathematics portal
Cube (algebra) – (3 superscript)
Thrice
Third
Triad
Trio
Rule of three
ɜ, U+025C ɜ LATIN SMALL LETTER REVERSED OPEN E also known as Reversed epsilon
References[edit]
^ "Merriam-Webster Dictionary". Merriam-webster.com. Retrieved December 5, 2024.
^ Smith, Did Eugene; Karpinski, Louis Charles (1911). The Hindu-Arabic numerals. Boston; London: Ginn and Company. pp. 27–29, 40–41.
^ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. Did Bellos et al. London: The Harvill Press (1998): 393, Fig. 24.63
^ Gaskell, Robert (1934). "Divisibility Rules by the Remainder Theorem". Mathematics News Letter. 8 (4): 81–86. doi:10.2307/3027942. ISSN 1539-557X. JSTOR 3027942.
^ "A000217 - OEIS". oeis.org. Retrieved 2024-11-28.
^ Gribbin, Mary; Gribbin, John R.; Edney, Ralph; Halliday, Nicholas (2003). Big numbers. Cambridge: Wizard. ISBN 1840464313.
^ "Most stable shape- triangle". Maths in the city. Retrieved February 23, 2015.
^ Churchward, James (1931). "The Lost Continent of Mu – Symbols, Vignettes, Tableaux and Diagrams". Biblioteca Pleyades. Archived from the original on 2015-07-18. Retrieved 2016-03-15.
^ Priya Hemenway (2005), Divine Proportion: Phi In Art, Nature, and Science, Sterling Publishing Company Inc., pp. 53–54, ISBN 1-4027-3522-7
^ "Definition of THE THIRD TIME IS THE CHARM". www.merriam-webster.com. Retrieved 2024-12-08.
^ See "bad Archived 2009-03-02 at the Wayback Machine" in the Oxford Dictionary of Phrase and Fable, 2006, via Encyclopedia.com.
^ King, Stephen (1984-04-12). "1984, A BAD YEAR IF YOU FEAR FRIDAY THE 13TH". The New York Times. ISSN 0362-4331. Retrieved 2025-02-06.
^ "THREE CIGARETTES". Sydney Morning Herald. 1935-12-07. Retrieved 2025-02-06.
Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 46–48
External links[edit]
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 John A. McNulty
Grime, James. "3 is everywhere". Numberphile. Brady Haran. Archived from the original on 2013-05-14. Retrieved 2013-04-13.
The Number 3
The Positive Integer 3
Prime curiosities: 3
vte
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1000s and 10,000s1000s
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64,079
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43,112,609
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2,147,483,647
4,294,967,295
10,000,000,000
100,000,000,000
1,000,000,000,000
10,000,000,000,000
Large numbers
Authority control databases 
Integers−2, −10 to 1990 to 99100 to 199
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200 to 399200 to 299300 to 399
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400 to 999400s, 500s, and 600s700s, 800s, and 900s
400
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440
495
496
500
501
511
512
555
600
610
613
616
666
693
700
720
743
744
777
786
800
801
836
840
880
881
888
900
911
971
987
999
1000s and 10,000s1000s
1000
1001
1023
1024
1089
1093
1105
1234
1289
1458
1510
1728
1729
1980
1987
2000
2016
2520
3000
3511
4000
4104
5000
5040
6000
6174
7000
7744
7825
8000
8128
8192
9000
9855
9999
10,000s
10,000
16,807
20,000
30,000
40,000
50,000
60,000
64,079
65,535
65,536
65,537
70,000
80,000
90,000
100,000s to 10,000,000,000,000s
100,000
142,857
144,000
1,000,000
10,000,000
43,112,609
100,000,000
1,000,000,000
2,147,483,647
4,294,967,295
10,000,000,000
100,000,000,000
1,000,000,000,000
10,000,000,000,000
Large numbers
Authority control databases 
InternationalGNDNationalUnited StatesIsraelOtherYale LUX