49 (forty-nine) is the

natural number In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...

following 48 and preceding 50.

In mathematics

Forty-nine is the square of the prime number seven and hence the fourth non-unitary square

prime A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...

of the form ''p''². Both of its digits are square numbers, 4 being the square of 2 and 9 being the square of 3. It appears in the Padovan sequence, preceded by the terms 21, 28, 37 (it is the sum of the first two of these). Along with the number that immediately derives from it, 77, the only number under 100 not having its home prime known (). The smallest triple of three squares in arithmetic succession is (1,25,49), and the second smallest is (49,169,289). 49 is the smallest

discriminant In mathematics, the discriminant of a polynomial is a quantity that depends on the coefficients and allows deducing some properties of the zero of a function, roots without computing them. More precisely, it is a polynomial function of the coef ...

of a totally real cubic field. 49 and 94 are the only numbers below 100 whose all permutations are composites but they are not multiples of 3, repdigits or numbers which only have digits 0, 2, 4, 5, 6 and 8, even excluding the trivial one digit terms. 49 = 7^2 and 94 = 2 * 47 The number of prime knots with 9 crossings is 49.

Decimal representation

The sum of the digits of the square of 49 (2401) is the square root of 49. 49 is the first square where the digits are squares. In this case, 4 and 9 are squares.

Reciprocal

The fraction is a repeating decimal with a period of 42: : = (42 digits repeat) There are 42 positive integers less than 49 and coprime to 49. (42 is the period.) Multiplying 020408163265306122448979591836734693877551 by each of these integers results in a

cyclic permutation In mathematics, and in particular in group theory, a cyclic permutation is a permutation consisting of a single cycle. In some cases, cyclic permutations are referred to as cycles; if a cyclic permutation has ''k'' elements, it may be called a ''k ...

of the original number: *020408163265306122448979591836734693877551 × 2 = 040816326530612244897959183673469387755102 *020408163265306122448979591836734693877551 × 3 = 061224489795918367346938775510204081632653 *020408163265306122448979591836734693877551 × 4 = 081632653061224489795918367346938775510204 *... The repeating number can be obtained from 02 and repetition of doubles placed at two places to the right: 02 04 08 16 32 64 128 256 512 1024 2048 + ... ---------------------- 020408163265306122448979591836734693877551...0204081632... because satisfies: :

x = \frac + \frac = \frac(1 + x)\, .

In chemistry

* During the

Manhattan Project The Manhattan Project was a research and development program undertaken during World War II to produce the first nuclear weapons. It was led by the United States in collaboration with the United Kingdom and Canada. From 1942 to 1946, the ...

plutonium Plutonium is a chemical element; it has symbol Pu and atomic number 94. It is a silvery-gray actinide metal that tarnishes when exposed to air, and forms a dull coating when oxidized. The element normally exhibits six allotropes and four ...

was also often referred to simply as "49". Number 4 was for the last digit in 94 (atomic number of plutonium) and 9 for the last digit in Pu-239, the weapon-grade fissile isotope used in nuclear bombs.

In religion

* In

Judaism Judaism () is an Abrahamic religions, Abrahamic, Monotheism, monotheistic, ethnic religion that comprises the collective spiritual, cultural, and legal traditions of the Jews, Jewish people. Religious Jews regard Judaism as their means of o ...

: the number of days of the

Counting of the Omer Counting of the Omer (, Sefirat HaOmer, sometimes abbreviated as Sefira) is a ritual in Judaism. It consists of a verbal counting of each of the 49 days between the holidays of Passover and Shavuot. The period of 49 days is known as the "omer p ...

and the number of years in a

Jubilee (biblical) The Jubilee ( ''yōḇel;'' Yiddish: ''yoyvl'') is the year that follows the passage of seven "weeks of years" (seven cycles of sabbatical years, or 49 total years). This fiftieth year deals largely with land, property, and property rights. Acc ...

cycle. * In

Buddhism Buddhism, also known as Buddhadharma and Dharmavinaya, is an Indian religion and List of philosophies, philosophical tradition based on Pre-sectarian Buddhism, teachings attributed to the Buddha, a wandering teacher who lived in the 6th or ...

, 49 days is one of the lengths of the intermediate state ( bardo)

In other fields

Forty-nine is: * '' 49er'', one who participated in the 1849

California Gold Rush The California gold rush (1848–1855) began on January 24, 1848, when gold was found by James W. Marshall at Sutter's Mill in Coloma, California. The news of gold brought approximately 300,000 people to California from the rest of the U ...

. This meaning has endured and things continue to be referred to as "49er," such as a member of the

San Francisco 49ers The San Francisco 49ers (also written as the San Francisco Forty-Niners and nicknamed the Niners) are a professional American football team based in the San Francisco Bay Area. The 49ers compete in the National Football League (NFL) as a member ...

team of the

National Football League The National Football League (NFL) is a Professional gridiron football, professional American football league in the United States. Composed of 32 teams, it is divided equally between the American Football Conference (AFC) and the National ...

. * A 49 is a party after a

powwow A powwow (also pow wow or pow-wow) is a gathering with dances held by many Native Americans in the United States, Native American and First Nations in Canada, First Nations communities. Inaugurated in 1923, powwows today are an opportunity fo ...

or any gathering of American Indians, held by the participants. It is also type of song that is sung on such occasions. A 49 is typically held in an isolated place and features drumming and singing.

References

{{DEFAULTSORT:49 (Number) Integers