3
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. It has religious or cultural significance in many societies.
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.[1] 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".[2]
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 is sometimes used to prevent falsifying a 3 as an 8. It is found on UPC-A barcodes and standard 52-card decks.
3 is the second smallest prime number and the first odd prime number. It is the first unique prime, such that the period length value of 1 of the decimal expansion of its reciprocal, 0.333..., is unique. 3 is a twin prime with 5, and a cousin prime with 7, and the only known number such that ! − 1 and ! + 1 are prime, as well as the only prime number such that − 1 yields another prime number, 2. A triangle is made of three sides. It is the smallest non-self-intersecting polygon and the only polygon not to have proper diagonals. When doing quick estimates, 3 is a rough approximation of π, 3.1415..., and a very rough approximation of e, 2.71828...
