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Cardinal | three | |||
Ordinal | 3rd (third) | |||
Numeral system | ternary | |||
Factorization | prime | |||
Prime | 2nd | |||
Divisors | 1, 3 | |||
Greek numeral | Γ´ | |||
Roman numeral | III | |||
Roman numeral (unicode) | Ⅲ, ⅲ | |||
Greek prefix | tri- | |||
Latin prefix | tre-/ter- | |||
Binary | 11_{2} | |||
Ternary | 10_{3} | |||
Quaternary | 3_{4} | |||
Quinary | 3_{5} | |||
Senary | 3_{6} | |||
Octal | 3_{8} | |||
Duodecimal | 3_{12} | |||
Hexadecimal | 3_{16} | |||
Vigesimal | 3_{20} | |||
Base 36 | 3_{36} | |||
Arabic & Kurdish & Persian | ٣ | |||
Urdu | ||||
Bengali | ৩ | |||
Chinese | 三，弎，叄 | |||
Devanāgarī | ३ | |||
Ge'ez | ፫ | |||
Greek | γ (or Γ) | |||
Hebrew | ג | |||
Japanese | 三/参 | |||
Khmer | ៣ | |||
Korean | 셋,삼 | |||
Malayalam | ൩ | |||
Tamil | ௩ | |||
Telugu | ౩ | |||
Thai | ๓ |
3 (three) is a number, numeral, and glyph. It is the natural number following 2 and preceding 4.
Three remains the largest number still written with the number of lines corresponding to the value (though the Ancient Romans usually wrote 4 as IIII, the subtractive notation IV became the preferred notation throughout and after the Middle Ages). To this day, 3 is written as three lines in Roman and Chinese numerals. This is also true regarding the Brahmin Indians' numerical notation. However, the path towards the modern glyph began with the Gupta, who modified the number through the addition of a curve on each line. Henceforth, the Nagari rotated the lines in a clockwise manner, and began ending each line with a slight downward stroke on the right. Eventually, these strokes were connected (as a result of ease, in a manner similar to cursive) with the lines below, and therefore rendered the number a glyph that possesses many similarities to the modern 3, albeit with an additional stroke at the bottom as ३. The Western Ghubar Arabs, however, possess the accomplishment of eliminating the additional stroke and hence creating the modern 3.
The "extra" stroke, however, held great importance to the Eastern Arabs, which resulted in its enlargement. In addition, they rotated the strokes above to lie along a horizontal axis - and to this day Eastern Arabs write a 3 that appears to be a mirrored number 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.
A common variant of the digit three has a flat top, similar to the character Ʒ (ezh). This form is sometimes used to prevent people from fraudulently changing a three into an eight. It is usually found on UPC-A barcodes and standard 52-card decks.
3 is:
Three is the only prime which is one less than a perfect square. Any other number which is n^{2} − 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.
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 Platonic solids have triangular faces – the tetrahedron, the octahedron, and the icosahedron. Also, three of the five Platonic solids 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 Platonic solids – the triangle, the square, and the pentagon.
There are only three distinct 4×4 panmagic 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.^{[2]}
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.
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 phenomenon 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.^{[3]}
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 |
Many world religions contain triple deities or concepts of trinity, including:
Three is a very significant number in Norse mythology, along with its powers 9 and 27.
Three (三, formal writing: 叁, pinyin sān, Cantonese: saam^{1}) is considered a good number in Chinese culture because it sounds like the word "alive" (生 pinyin shēng, Cantonese: saang^{1}), compared to four (四, pinyin: sì, Cantonese: sei^{1}), which sounds like the word "death" (死 pinyin sǐ, Cantonese: sei^{2}).
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.
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".^{[18]}
Look up three in Wiktionary, the free dictionary. |
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