# 3 (number)

This article discusses the number three. For the year AD 3, see 3. For other uses of 3, see 3 (disambiguation)
<tr><td>Hebrew<td>ג (Gimel)
 Template:Numbers (digits) Cardinal 3 three Ordinal 3rd third Numeral system ternary Factorization prime Divisors 1, 3 Roman numeral III Unicode representation of Roman numeral Ⅲ, ⅲ prefixes tri- (from Greek) tre-/ter- (from Latin) Binary 11 Octal 3 Duodecimal 3 Hexadecimal 3

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

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## Evolution of the glyph

Three is often the largest number written with as many lines as the number represents. The Romans tired of writing 4 as IIII, but 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).

In fonts with text figures, 3 usually has a descender, for example, Missing image
TextFigs036.png
Image:TextFigs036.png

, though in some French fonts it has an ascender instead of a descender.

## In mathematics

Three is the second smallest prime number (after two; the next prime number is five). Three is the first Fermat prime (220 + 1) as well as the first Mersenne prime (22 - 1). Three is the second Sophie Germain prime and the second Mersenne prime exponent. Three is also the first lucky prime, the second factorial prime (2! + 1), and the first unique prime due to the properties of its reciprocal.

Three is the second triangular number.

Three points form a plane (unless they are collinear).

Three is the fourth Fibonacci number and the third that is unique. It is also a Lucas number.

Three is the fourth open meandric number.

Vulgar fractions with 3 in the denominator have a single digit repeating sequences in their decimal expansions, (.000..., .333..., .666..., .999...)

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..).

A triangle is the most durable shape possible, the only "perfect" figure which if all endpoints have hinges will never change it's shape unless the sides themselves are bent.

## In human culture

Many human cultures have given the concept of three-ness symbolic meanings. The Holy Trinity in Christian doctrine (or trinity in general), is God both a single entity and three entities, the Father, the Son and the Spirit.

The process of synthesis in Hegelian dialectic creates three-ness from two-ness.

The three Doshas (weaknesses) and their antidotes are the basis of Ayurvedic medicine in India. The three Gunas underlie action, in the Vedic system of knowledge. There is also the concept of Trimurti in Hindu tradition.

Three (三, formal writing: 叁, pinyin san1) is considered a good number in Chinese culture because it sounds like the word "alive" (生 pinyin sheng1), compared to four.

## In other fields

Three' is:

• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy