50 (number)

Natural number

50 (fifty) is the natural number following 49 and preceding 51.

In mathematics

50 as the sum of two non-zero squares

Fifty is the smallest number that is the sum of two non-zero square numbers in two distinct ways: 50 = 1² + 7² = 5² + 5² (see image).^[1] It is also the sum of three squares, 50 = 3² + 4² + 5², and the sum of four squares, 50 = 6² + 3² + 2² + 1² (which are the squares of divisors of 6). It is furthermore the sum of the squares of the divisors of 7.^[2]

50 is a Stirling number of the first kind: ${\displaystyle \left[{5 \atop 2}\right]=50}$ and also a Narayana number: ${\displaystyle \operatorname {N} (6,3)=\operatorname {N} (6,4)=50}$

There is no solution to the equation φ(x) = 50, making 50 a nontotient.^[3] Nor is there a solution to the equation x − φ(x) = 50, making 50 a noncototient.^[4]

Fifty is the sum of the number of faces that make up the Platonic solids (4 + 6 + 8 + 12 + 20 = 50).

In science

• The atomic number of tin
• The fifth magic number in nuclear physics

In religion

• In Kabbalah, there are 50 Gates of Wisdom (or Understanding) and 50 Gates of Impurity^{[citation needed]}
• The traditional number of years in a jubilee period.^[5]
• The Christian Feast of Pentecost takes place on the 50th day of the Easter Season
• The Jewish Pentecost takes place 50 days after the Passover feast (the holiday of Shavuoth).
• In Hindu tantric tradition, the number 50 holds significance as the 50 Rudras in the Malinīvijayottara correlate with the 50 phonemes of Sanskrit, as well as with the 50 severed heads worn around goddess Kali's head. The mantra Aham ("I am"), as laid out in the Vijñāna Bhairava represents the first अ(a) and last ह(ha) phonemes of the Sanskrit alphabet and is believed to represent ultimate reality, in accordance with its non-dual philosophy.

In sports

• In cricket one day internationals, each side may bat for 50 overs.

In other fields

Fifty is:

• There are 50 states in the United States of America.
• The TV show Hawaii Five-O and its reimagined version, Hawaii Five-0, are so called because Hawaii is the last (50th) of the states to officially become a state.
• 5-O (Five-Oh) - Slang for police officers and/or a warning that police are approaching. Derived from the television show Hawaii Five-O^[6]
• A calibre of ammunition (0.50 inches: see .50 BMG)
• In millimetres, the focal length of the normal lens in 35 mm photography
• The percentage (50%) equivalent to one half, so that the phrase "fifty-fifty" commonly expresses something divided equally in two; in business this is often denoted as being the ultimate in equal partnership
• In years of marriage, the gold or "golden" wedding anniversary

Businesses

• Fifty (outlet store) - Formerly "Fifty Outlet". Outlet stores, mostly in Spain, owned by Tendam, selling its brands e.g. Cortefiel, Springfield, and others'

See also

• List of highways numbered 50

References

1. de Koninck, J.M. (2009). Those fascinating numbers. AMS Bookstore. p. 18. ISBN 0-8218-4807-0.
2. Sloane, N. J. A. (ed.). "Sequence A001157 (a(n) as sigma_2(n): sum of squares of divisors of n.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-07-21.
3. "Sloane's A005277 : Nonients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
4. "Sloane's A005278 : Noncotients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
5. Leviticus 25:10
6. Karen Rhodes (1 February 1997). Booking Hawaii Five-O: An Episode Guide and Critical History of the 1968–1980 Television Detective Series. McFarland. p. 265. ISBN 978-0-7864-8666-3.